diff --git a/src/plugins/wp/tests/wp_typed/oracle/user_init.0.res.oracle b/src/plugins/wp/tests/wp_typed/oracle/user_init.0.res.oracle index 6002f927642db4bde9f928a7f1e61766a55069dc..86999a74131fbcf821d72d8dc22c18a0b8225a7c 100644 --- a/src/plugins/wp/tests/wp_typed/oracle/user_init.0.res.oracle +++ b/src/plugins/wp/tests/wp_typed/oracle/user_init.0.res.oracle @@ -2,12 +2,18 @@ [kernel] Parsing tests/wp_typed/user_init.i (no preprocessing) [wp] Running WP plugin... [wp] Loading driver 'share/wp.driver' +[wp] [CFG] Goal init_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t1_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t2_v1_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t2_v2_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t2_v3_exits : Valid (Unreachable) [wp] Warning: Missing RTE guards +[wp] Computing [100 goals...] ------------------------------------------------------------ Function init ------------------------------------------------------------ -Goal Post-condition (file tests/wp_typed/user_init.i, line 3) in 'init': +Goal Post-condition (file tests/wp_typed/user_init.i, line 10) in 'init': Let a_1 = shift_sint32(a, 0). Assume { Type: is_sint32(i) /\ is_sint32(n). @@ -29,7 +35,7 @@ Prove: havoc(Mint_undef_0, Mint_0, a_1, i)[shift_sint32(a, i_1)] = v. ------------------------------------------------------------ -Goal Preservation of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 9): +Goal Preservation of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 17): Let a_1 = shift_sint32(a, 0). Let a_2 = havoc(Mint_undef_0, Mint_0, a_1, n). Assume { @@ -52,12 +58,12 @@ Prove: a_2[shift_sint32(a, i) <- v][shift_sint32(a, i_1)] = v. ------------------------------------------------------------ -Goal Establishment of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 9): +Goal Establishment of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 17): Prove: true. ------------------------------------------------------------ -Goal Preservation of Invariant 'Range' (file tests/wp_typed/user_init.i, line 8): +Goal Preservation of Invariant 'Range' (file tests/wp_typed/user_init.i, line 16): Let a_1 = shift_sint32(a, 0). Assume { Type: is_sint32(i) /\ is_sint32(n) /\ is_sint32(1 + i). @@ -77,18 +83,18 @@ Prove: (-1) <= i. ------------------------------------------------------------ -Goal Establishment of Invariant 'Range' (file tests/wp_typed/user_init.i, line 8): +Goal Establishment of Invariant 'Range' (file tests/wp_typed/user_init.i, line 16): Prove: true. ------------------------------------------------------------ -Goal Loop assigns (file tests/wp_typed/user_init.i, line 10) (1/2): +Goal Loop assigns 'Zone' (1/2): Prove: true. ------------------------------------------------------------ -Goal Loop assigns (file tests/wp_typed/user_init.i, line 10) (2/2): -Effect at line 12 +Goal Loop assigns 'Zone' (2/2): +Effect at line 20 Let a_1 = shift_sint32(a, 0). Let a_2 = shift_sint32(a, i). Assume { @@ -111,8 +117,1942 @@ Prove: included(a_2, 1, a_1, n). ------------------------------------------------------------ -Goal Assigns (file tests/wp_typed/user_init.i, line 4) in 'init': -Effect at line 12 +Goal Assigns (file tests/wp_typed/user_init.i, line 9) in 'init': +Effect at line 20 +Prove: true. + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 20): +Prove: true. + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 20): +Prove: true. + +------------------------------------------------------------ +------------------------------------------------------------ + Function init_t1 +------------------------------------------------------------ + +Goal Post-condition (file tests/wp_typed/user_init.i, line 24) in 'init_t1': +Assume { + Type: is_uint32(i_1). + (* Goal *) + When: (0 <= i) /\ (i <= 9). + (* Invariant 'Partial' *) + Have: forall i_2 : Z. ((0 <= i_2) -> ((i_2 < i_1) -> (t1_0[i_2] = v))). + (* Invariant 'Range' *) + Have: (0 <= i_1) /\ (i_1 <= 10). + (* Else *) + Have: 10 <= i_1. +} +Prove: t1_0[i] = v. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 32): +Assume { + Type: is_uint32(i). + (* Goal *) + When: (0 <= i_1) /\ (i_1 < to_uint32(1 + i)). + (* Invariant 'Partial' *) + Have: forall i_2 : Z. ((0 <= i_2) -> ((i_2 < i) -> (t1_0[i_2] = v))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. +} +Prove: t1_0[i <- v][i_1] = v. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 32): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range' (file tests/wp_typed/user_init.i, line 31): +Assume { + Type: is_uint32(i). + (* Invariant 'Partial' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < i) -> (t1_0[i_1] = v))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. +} +Prove: to_uint32(1 + i) <= 10. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range' (file tests/wp_typed/user_init.i, line 31): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'Zone': +Prove: true. + +------------------------------------------------------------ + +Goal Assigns (file tests/wp_typed/user_init.i, line 26) in 'init_t1' (1/2): +Effect at line 35 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns (file tests/wp_typed/user_init.i, line 26) in 'init_t1' (2/2): +Effect at line 35 +Prove: true. + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 35): +Assume { + Type: is_uint32(i). + (* Invariant 'Partial' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < i) -> (t1_0[i_1] = v))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. +} +Prove: i < to_uint32(1 + i). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 35): +Prove: true. + +------------------------------------------------------------ +------------------------------------------------------------ + Function init_t2_bis_v1 +------------------------------------------------------------ + +Goal Post-condition (file tests/wp_typed/user_init.i, line 127) in 'init_t2_bis_v1': +Let a = global(G_t2_48). +Assume { + Type: is_uint32(i_2) /\ is_sint32(v). + (* Goal *) + When: (0 <= i) /\ (0 <= i_1) /\ (i <= 9) /\ (i_1 <= 19). + (* Loop assigns 'lack,Zone' *) + Have: forall a_1 : addr. + ((forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (shift_sint32(shift_A20_sint32(a, i_4), i_3) != a_1)))))) -> + (Mint_1[a_1] = Mint_0[a_1])). + (* Invariant 'Partial' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i_2) -> + ((i_3 <= 19) -> + (Mint_0[shift_sint32(shift_A20_sint32(a, i_4), i_3)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i_2) /\ (i_2 <= 10). + (* Else *) + Have: 10 <= i_2. +} +Prove: Mint_0[shift_sint32(shift_A20_sint32(a, i), i_1)] = v. + +------------------------------------------------------------ + +Goal Exit-condition (file tests/wp_typed/user_init.i, line 129) in 'init_t2_bis_v1': +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 136): +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Let a_2 = shift_sint32(a_1, 0). +Let a_3 = havoc(Mint_undef_0, Mint_0, a_2, 20). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Goal *) + When: (0 <= i_1) /\ (0 <= i_2) /\ (i_1 < to_uint32(1 + i)) /\ (i_2 <= 19). + (* Loop assigns 'lack,Zone' *) + Have: forall a_4 : addr. + ((forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (shift_sint32(shift_A20_sint32(a, i_4), i_3) != a_4)))))) -> + (Mint_1[a_4] = Mint_0[a_4])). + (* Invariant 'Partial' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> + (Mint_0[shift_sint32(shift_A20_sint32(a, i_4), i_3)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Call 'init' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 <= 19) -> + (a_3[shift_sint32(a_1, i_3)] = v))). +} +Prove: a_3[shift_sint32(shift_A20_sint32(a, i_1), i_2)] = Mint_undef_0[a_2]. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 136): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range' (file tests/wp_typed/user_init.i, line 135): +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Loop assigns 'lack,Zone' *) + Have: forall a_2 : addr. + ((forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (shift_sint32(shift_A20_sint32(a, i_2), i_1) != a_2)))))) -> + (Mint_0[a_2] = Mint_1[a_2])). + (* Invariant 'Partial' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> + (Mint_1[shift_sint32(shift_A20_sint32(a, i_2), i_1)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Call 'init' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 19) -> + (havoc(Mint_undef_0, Mint_1, shift_sint32(a_1, 0), 20) + [shift_sint32(a_1, i_1)] = v))). +} +Prove: to_uint32(1 + i) <= 10. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range' (file tests/wp_typed/user_init.i, line 135): +Prove: true. + +------------------------------------------------------------ + +Goal Assertion 'Offset' (file tests/wp_typed/user_init.i, line 141): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone' (1/3): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone' (2/3): +Effect at line 139 +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Goal *) + When: (0 <= i_1) /\ (0 <= i_2) /\ (i_1 <= 9) /\ (i_2 <= 19). + (* Loop assigns 'lack,Zone' *) + Have: forall a_2 : addr. + ((forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (shift_sint32(shift_A20_sint32(a, i_4), i_3) != a_2)))))) -> + (Mint_0[a_2] = Mint_1[a_2])). + (* Invariant 'Partial' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> + (Mint_1[shift_sint32(shift_A20_sint32(a, i_4), i_3)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Call 'init' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 <= 19) -> + (havoc(Mint_undef_0, Mint_1, shift_sint32(a_1, 0), 20) + [shift_sint32(a_1, i_3)] = v))). +} +Prove: (forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> false))))) \/ + (forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (exists i_6,i_5 : Z. (0 <= i_5) /\ (i_3 <= i_5) /\ (0 <= i_6) /\ + (i_4 <= i_6) /\ (i_5 <= i_3) /\ (i_6 <= i_4) /\ (i_6 <= 9) /\ + (i_5 <= 19))))))). + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone' (3/3): +Call Effect at line 140 +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Goal *) + When: (0 <= i) /\ (0 <= i_1) /\ (i <= 9) /\ (i_1 <= 19). + (* Loop assigns 'lack,Zone' *) + Have: forall a_2 : addr. + ((forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> + (shift_sint32(shift_A20_sint32(a, i_3), i_2) != a_2)))))) -> + (Mint_0[a_2] = Mint_1[a_2])). + (* Invariant 'Partial' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 < i) -> + ((i_2 <= 19) -> + (Mint_1[shift_sint32(shift_A20_sint32(a, i_3), i_2)] = v))))). + (* Invariant 'Range' *) + Have: i <= 10. + (* Call 'init' *) + Have: forall i_2 : Z. ((0 <= i_2) -> ((i_2 <= 19) -> + (havoc(Mint_undef_0, Mint_1, shift_sint32(a_1, 0), 20) + [shift_sint32(a_1, i_2)] = v))). +} +Prove: exists i_3,i_2 : Z. (i_3 <= i) /\ (i_2 <= i_1) /\ (0 <= i_2) /\ + (i_1 <= i_2) /\ (0 <= i_3) /\ (i <= i_3) /\ (i_3 <= 9) /\ (i_2 <= 19). + +------------------------------------------------------------ + +Goal Assigns 'lack' in 'init_t2_bis_v1' (1/3): +Effect at line 139 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'lack' in 'init_t2_bis_v1' (2/3): +Effect at line 139 +Assume { + Have: 0 <= i_2. + Have: 0 <= i_3. + Have: i_2 <= 9. + Have: i_3 <= 19. + Have: 0 <= i. + Have: 0 <= i_1. + Have: i <= 9. + Have: i_1 <= 19. + (* Loop assigns 'lack,Zone' *) + Have: forall a : addr. + ((forall i_5,i_4 : Z. ((0 <= i_4) -> ((0 <= i_5) -> ((i_5 <= 9) -> + ((i_4 <= 19) -> + (shift_sint32(shift_A20_sint32(global(G_t2_48), i_5), i_4) != a)))))) -> + (Mint_0[a] = Mint_1[a])). +} +Prove: exists i_5,i_4 : Z. (i_5 <= i) /\ (i_4 <= i_1) /\ (0 <= i_4) /\ + (i_1 <= i_4) /\ (0 <= i_5) /\ (i <= i_5) /\ (i_5 <= 9) /\ (i_4 <= 19). + +------------------------------------------------------------ + +Goal Assigns 'lack' in 'init_t2_bis_v1' (3/3): +Call Effect at line 140 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'lack' in 'init_t2_bis_v1' (1/2): +Effect at line 139 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'lack' in 'init_t2_bis_v1' (2/2): +Effect at line 139 +Assume { + Have: 0 <= i_2. + Have: 0 <= i_3. + Have: i_2 <= 9. + Have: i_3 <= 19. + Have: 0 <= i. + Have: 0 <= i_1. + Have: i <= 9. + Have: i_1 <= 19. + (* Loop assigns 'lack,Zone' *) + Have: forall a : addr. + ((forall i_5,i_4 : Z. ((0 <= i_4) -> ((0 <= i_5) -> ((i_5 <= 9) -> + ((i_4 <= 19) -> + (shift_sint32(shift_A20_sint32(global(G_t2_48), i_5), i_4) != a)))))) -> + (Mint_0[a] = Mint_1[a])). +} +Prove: exists i_5,i_4 : Z. (i_5 <= i) /\ (i_4 <= i_1) /\ (0 <= i_4) /\ + (i_1 <= i_4) /\ (0 <= i_5) /\ (i <= i_5) /\ (i_5 <= 9) /\ (i_4 <= 19). + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 139): +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Loop assigns 'lack,Zone' *) + Have: forall a_2 : addr. + ((forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (shift_sint32(shift_A20_sint32(a, i_2), i_1) != a_2)))))) -> + (Mint_0[a_2] = Mint_1[a_2])). + (* Invariant 'Partial' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> + (Mint_1[shift_sint32(shift_A20_sint32(a, i_2), i_1)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Call 'init' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 19) -> + (havoc(Mint_undef_0, Mint_1, shift_sint32(a_1, 0), 20) + [shift_sint32(a_1, i_1)] = v))). +} +Prove: i < to_uint32(1 + i). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 139): +Prove: true. + +------------------------------------------------------------ + +Goal Instance of 'Pre-condition (file tests/wp_typed/user_init.i, line 7) in 'init'' in 'init_t2_bis_v1' at call 'init' (file tests/wp_typed/user_init.i, line 140) +: +Prove: true. + +------------------------------------------------------------ + +Goal Instance of 'Pre-condition (file tests/wp_typed/user_init.i, line 8) in 'init'' in 'init_t2_bis_v1' at call 'init' (file tests/wp_typed/user_init.i, line 140) +: +Prove: true. + +------------------------------------------------------------ +------------------------------------------------------------ + Function init_t2_bis_v2 +------------------------------------------------------------ + +Goal Post-condition (file tests/wp_typed/user_init.i, line 145) in 'init_t2_bis_v2': +Let a = global(G_t2_48). +Assume { + Type: is_uint32(i_2) /\ is_sint32(v). + (* Goal *) + When: (0 <= i) /\ (0 <= i_1) /\ (i <= 9) /\ (i_1 <= 19). + (* Loop assigns 'tactic,Zone' *) + Have: forall a_1 : addr. + ((forall i_4,i_3 : Z. ((0 <= i_4) -> ((i_4 <= 9) -> + (shift_sint32(shift_A20_sint32(a, i_4), i_3) != a_1)))) -> + (Mint_1[a_1] = Mint_0[a_1])). + (* Invariant 'Partial' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i_2) -> + ((i_3 <= 19) -> + (Mint_0[shift_sint32(shift_A20_sint32(a, i_4), i_3)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i_2) /\ (i_2 <= 10). + (* Else *) + Have: 10 <= i_2. +} +Prove: Mint_0[shift_sint32(shift_A20_sint32(a, i), i_1)] = v. + +------------------------------------------------------------ + +Goal Exit-condition (file tests/wp_typed/user_init.i, line 147) in 'init_t2_bis_v2': +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 154): +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Let a_2 = shift_sint32(a_1, 0). +Let a_3 = havoc(Mint_undef_0, Mint_0, a_2, 20). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Goal *) + When: (0 <= i_1) /\ (0 <= i_2) /\ (i_1 < to_uint32(1 + i)) /\ (i_2 <= 19). + (* Loop assigns 'tactic,Zone' *) + Have: forall a_4 : addr. + ((forall i_4,i_3 : Z. ((0 <= i_4) -> ((i_4 <= 9) -> + (shift_sint32(shift_A20_sint32(a, i_4), i_3) != a_4)))) -> + (Mint_1[a_4] = Mint_0[a_4])). + (* Invariant 'Partial' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> + (Mint_0[shift_sint32(shift_A20_sint32(a, i_4), i_3)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Call 'init' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 <= 19) -> + (a_3[shift_sint32(a_1, i_3)] = v))). +} +Prove: a_3[shift_sint32(shift_A20_sint32(a, i_1), i_2)] = Mint_undef_0[a_2]. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 154): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range' (file tests/wp_typed/user_init.i, line 153): +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Loop assigns 'tactic,Zone' *) + Have: forall a_2 : addr. + ((forall i_2,i_1 : Z. ((0 <= i_2) -> ((i_2 <= 9) -> + (shift_sint32(shift_A20_sint32(a, i_2), i_1) != a_2)))) -> + (Mint_0[a_2] = Mint_1[a_2])). + (* Invariant 'Partial' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> + (Mint_1[shift_sint32(shift_A20_sint32(a, i_2), i_1)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Call 'init' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 19) -> + (havoc(Mint_undef_0, Mint_1, shift_sint32(a_1, 0), 20) + [shift_sint32(a_1, i_1)] = v))). +} +Prove: to_uint32(1 + i) <= 10. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range' (file tests/wp_typed/user_init.i, line 153): +Prove: true. + +------------------------------------------------------------ + +Goal Assertion 'Offset_i' (file tests/wp_typed/user_init.i, line 159): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone' (1/3): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone' (2/3): +Effect at line 157 +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i_2). +Assume { + Have: 0 <= i. + Have: i <= 9. + Type: is_uint32(i_2) /\ is_sint32(v). + (* Goal *) + When: (0 <= i_3) /\ (0 <= i_4) /\ (i_3 <= 9) /\ (i_4 <= 19). + (* Loop assigns 'tactic,Zone' *) + Have: forall a_2 : addr. + ((forall i_6,i_5 : Z. ((0 <= i_6) -> ((i_6 <= 9) -> + (shift_sint32(shift_A20_sint32(a, i_6), i_5) != a_2)))) -> + (Mint_0[a_2] = Mint_1[a_2])). + (* Invariant 'Partial' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 < i_2) -> + ((i_5 <= 19) -> + (Mint_1[shift_sint32(shift_A20_sint32(a, i_6), i_5)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i_2) /\ (i_2 <= 10). + (* Then *) + Have: i_2 <= 9. + (* Call 'init' *) + Have: forall i_5 : Z. ((0 <= i_5) -> ((i_5 <= 19) -> + (havoc(Mint_undef_0, Mint_1, shift_sint32(a_1, 0), 20) + [shift_sint32(a_1, i_5)] = v))). +} +Prove: exists i_6,i_5 : Z. (i_6 <= i) /\ (i_5 <= i_1) /\ (i_1 <= i_5) /\ + (0 <= i_6) /\ (i <= i_6) /\ (i_6 <= 9). + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone' (3/3): +Call Effect at line 158 +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Goal *) + When: (0 <= i) /\ (0 <= i_1) /\ (i <= 9) /\ (i_1 <= 19). + (* Loop assigns 'tactic,Zone' *) + Have: forall a_2 : addr. + ((forall i_3,i_2 : Z. ((0 <= i_3) -> ((i_3 <= 9) -> + (shift_sint32(shift_A20_sint32(a, i_3), i_2) != a_2)))) -> + (Mint_0[a_2] = Mint_1[a_2])). + (* Invariant 'Partial' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 < i) -> + ((i_2 <= 19) -> + (Mint_1[shift_sint32(shift_A20_sint32(a, i_3), i_2)] = v))))). + (* Invariant 'Range' *) + Have: i <= 10. + (* Call 'init' *) + Have: forall i_2 : Z. ((0 <= i_2) -> ((i_2 <= 19) -> + (havoc(Mint_undef_0, Mint_1, shift_sint32(a_1, 0), 20) + [shift_sint32(a_1, i_2)] = v))). +} +Prove: exists i_3,i_2 : Z. (i_3 <= i) /\ (i_2 <= i_1) /\ (i_1 <= i_2) /\ + (0 <= i_3) /\ (i <= i_3) /\ (i_3 <= 9). + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_bis_v2' (1/3): +Effect at line 157 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_bis_v2' (2/3): +Effect at line 157 +Assume { + Have: 0 <= i_2. + Have: 0 <= i_3. + Have: i_2 <= 9. + Have: i_3 <= 19. + Have: 0 <= i. + Have: i <= 9. + (* Loop assigns 'tactic,Zone' *) + Have: forall a : addr. + ((forall i_5,i_4 : Z. ((0 <= i_5) -> ((i_5 <= 9) -> + (shift_sint32(shift_A20_sint32(global(G_t2_48), i_5), i_4) != a)))) -> + (Mint_0[a] = Mint_1[a])). +} +Prove: exists i_5,i_4 : Z. (i_5 <= i) /\ (i_4 <= i_1) /\ (i_1 <= i_4) /\ + (0 <= i_5) /\ (i <= i_5) /\ (i_5 <= 9). + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_bis_v2' (3/3): +Call Effect at line 158 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_bis_v2' (1/2): +Effect at line 157 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_bis_v2' (2/2): +Effect at line 157 +Assume { + Have: 0 <= i_2. + Have: 0 <= i_3. + Have: i_2 <= 9. + Have: i_3 <= 19. + Have: 0 <= i. + Have: i <= 9. + (* Loop assigns 'tactic,Zone' *) + Have: forall a : addr. + ((forall i_5,i_4 : Z. ((0 <= i_5) -> ((i_5 <= 9) -> + (shift_sint32(shift_A20_sint32(global(G_t2_48), i_5), i_4) != a)))) -> + (Mint_0[a] = Mint_1[a])). +} +Prove: exists i_5,i_4 : Z. (i_5 <= i) /\ (i_4 <= i_1) /\ (i_1 <= i_4) /\ + (0 <= i_5) /\ (i <= i_5) /\ (i_5 <= 9). + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 157): +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Loop assigns 'tactic,Zone' *) + Have: forall a_2 : addr. + ((forall i_2,i_1 : Z. ((0 <= i_2) -> ((i_2 <= 9) -> + (shift_sint32(shift_A20_sint32(a, i_2), i_1) != a_2)))) -> + (Mint_0[a_2] = Mint_1[a_2])). + (* Invariant 'Partial' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> + (Mint_1[shift_sint32(shift_A20_sint32(a, i_2), i_1)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Call 'init' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 19) -> + (havoc(Mint_undef_0, Mint_1, shift_sint32(a_1, 0), 20) + [shift_sint32(a_1, i_1)] = v))). +} +Prove: i < to_uint32(1 + i). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 157): +Prove: true. + +------------------------------------------------------------ + +Goal Instance of 'Pre-condition (file tests/wp_typed/user_init.i, line 7) in 'init'' in 'init_t2_bis_v2' at call 'init' (file tests/wp_typed/user_init.i, line 158) +: +Prove: true. + +------------------------------------------------------------ + +Goal Instance of 'Pre-condition (file tests/wp_typed/user_init.i, line 8) in 'init'' in 'init_t2_bis_v2' at call 'init' (file tests/wp_typed/user_init.i, line 158) +: +Prove: true. + +------------------------------------------------------------ +------------------------------------------------------------ + Function init_t2_v1 +------------------------------------------------------------ + +Goal Post-condition (file tests/wp_typed/user_init.i, line 39) in 'init_t2_v1': +Assume { + (* Goal *) + When: (0 <= i) /\ (0 <= i_1) /\ (i <= 9) /\ (i_1 <= 19). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> + (((i_2 < 0) \/ (i_3 < 0) \/ (10 <= i_3) \/ (20 <= i_2)) -> + (t2_1[i_3][i_2] = t2_0[i_3][i_2])))))). + (* Invariant 'Partial_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> (t2_0[i_3][i_2] = v))))). +} +Prove: t2_0[i][i_1] = v. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial_i' (file tests/wp_typed/user_init.i, line 48): +Let m = t2_0[i]. +Assume { + Type: is_uint32(i). + (* Goal *) + When: (0 <= i_1) /\ (0 <= i_2) /\ (i_1 < to_uint32(1 + i)) /\ (i_2 <= 19). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_1[i_4][i_3] = t2_2[i_4][i_3])))))). + (* Invariant 'Partial_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_2[i_4][i_3] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_0[i_4][i_3] = t2_2[i_4][i_3])))))). + (* Invariant 'Previous_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_0[i_4][i_3] = t2_2[i_4][i_3]))))). + (* Invariant 'Partial_j' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 <= 19) -> (m[i_3] = v))). +} +Prove: m[0] = t2_0[i_1][i_2]. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial_i' (file tests/wp_typed/user_init.i, line 48): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range_i' (file tests/wp_typed/user_init.i, line 47): +Assume { + Type: is_uint32(i). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 19) -> (t2_2[i][i_1] = v))). +} +Prove: to_uint32(1 + i) <= 10. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range_i' (file tests/wp_typed/user_init.i, line 47): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial_j' (file tests/wp_typed/user_init.i, line 54): +Let m = t2_0[i]. +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Goal *) + When: (0 <= i_1) /\ (i_1 < to_uint32(1 + j)). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> + (((i_2 < 0) \/ (i_3 < 0) \/ (10 <= i_3) \/ (20 <= i_2)) -> + (t2_1[i_3][i_2] = t2_2[i_3][i_2])))))). + (* Invariant 'Partial_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 < i) -> + ((i_2 <= 19) -> (t2_2[i_3][i_2] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> + (((i_2 < 0) \/ (i_3 < 0) \/ (10 <= i_3) \/ (20 <= i_2)) -> + (t2_0[i_3][i_2] = t2_2[i_3][i_2])))))). + (* Invariant 'Previous_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 < i) -> + ((i_2 <= 19) -> (t2_0[i_3][i_2] = t2_2[i_3][i_2]))))). + (* Invariant 'Partial_j' *) + Have: forall i_2 : Z. ((0 <= i_2) -> ((i_2 < j) -> (m[i_2] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: m[j <- v][i_1] = v. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial_j' (file tests/wp_typed/user_init.i, line 54): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Previous_i' (file tests/wp_typed/user_init.i, line 55): +Let m = t2_0[i]. +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Goal *) + When: (0 <= i_1) /\ (i_1 < i) /\ (0 <= i_2) /\ (i_2 <= 19). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_2[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Partial_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_1[i_4][i_3] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_0[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Previous_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_0[i_4][i_3] = t2_1[i_4][i_3]))))). + (* Invariant 'Partial_j' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 < j) -> (m[i_3] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: t2_0[i <- m[j <- v]][i_1][i_2] = t2_1[i_1][i_2]. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Previous_i' (file tests/wp_typed/user_init.i, line 55): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range_j' (file tests/wp_typed/user_init.i, line 53): +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < j) -> (t2_2[i][i_1] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: to_uint32(1 + j) <= 20. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range_j' (file tests/wp_typed/user_init.i, line 53): +Prove: true. + +------------------------------------------------------------ + +Goal Assertion 'Last_j' (file tests/wp_typed/user_init.i, line 61): +Prove: true. + +------------------------------------------------------------ + +Goal Assertion 'Last_i' (file tests/wp_typed/user_init.i, line 64): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone_i' (1/3): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone_i' (2/3): +Effect at line 51 +Assume { + Type: is_uint32(i). + (* Goal *) + When: (0 <= i_1) /\ (0 <= i_2) /\ (i_1 <= 9) /\ (i_2 <= 19). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_0[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Partial_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_1[i_4][i_3] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_2[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Previous_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_2[i_4][i_3] = t2_1[i_4][i_3]))))). + (* Invariant 'Partial_j' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 <= 19) -> (t2_2[i][i_3] = v))). +} +Prove: (forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> false))))) \/ + (forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (exists i_6,i_5 : Z. (0 <= i_5) /\ (i_3 <= i_5) /\ (0 <= i_6) /\ + (i_4 <= i_6) /\ (i_5 <= i_3) /\ (i_6 <= i_4) /\ (i_6 <= 9) /\ + (i_5 <= 19))))))). + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone_i' (3/3): +Effect at line 58 +Assume { + Type: is_uint32(i). + (* Goal *) + When: (0 <= i_1) /\ (0 <= i_2) /\ (i_1 <= 9) /\ (i_2 <= 19). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_0[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Partial_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_1[i_4][i_3] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_2[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Previous_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_2[i_4][i_3] = t2_1[i_4][i_3]))))). + (* Invariant 'Partial_j' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 <= 19) -> (t2_2[i][i_3] = v))). +} +Prove: (forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> false))))) \/ + (forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (exists i_6,i_5 : Z. (0 <= i_5) /\ (i_3 <= i_5) /\ (0 <= i_6) /\ + (i_4 <= i_6) /\ (i_5 <= i_3) /\ (i_6 <= i_4) /\ (i_6 <= 9) /\ + (i_5 <= 19))))))). + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone_j' (1/3): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone_j' (2/3): +Effect at line 58 +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Goal *) + When: (0 <= i_1) /\ (0 <= i_2) /\ (i_1 <= 9) /\ (i_2 <= 19). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_0[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Partial_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_1[i_4][i_3] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_2[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Previous_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_2[i_4][i_3] = t2_1[i_4][i_3]))))). + (* Invariant 'Partial_j' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 < j) -> (t2_2[i][i_3] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: (forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> false))))) \/ + (forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (exists i_6,i_5 : Z. (0 <= i_5) /\ (i_3 <= i_5) /\ (0 <= i_6) /\ + (i_4 <= i_6) /\ (i_5 <= i_3) /\ (i_6 <= i_4) /\ (i_6 <= 9) /\ + (i_5 <= 19))))))). + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone_j' (3/3): +Effect at line 59 +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Goal *) + When: (0 <= i) /\ (0 <= j) /\ (i <= 9) /\ (j <= 19). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: i <= 10. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < j) -> (t2_2[i][i_1] = v))). + (* Invariant 'Range_j' *) + Have: j <= 20. +} +Prove: exists i_2,i_1 : Z. (i_2 <= i) /\ (i_1 <= j) /\ (0 <= i_1) /\ + (j <= i_1) /\ (0 <= i_2) /\ (i <= i_2) /\ (i_2 <= 9) /\ (i_1 <= 19). + +------------------------------------------------------------ + +Goal Assigns 'lack' in 'init_t2_v1' (1/2): +Effect at line 51 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'lack' in 'init_t2_v1' (2/2): +Effect at line 51 +Assume { + Have: 0 <= i_2. + Have: 0 <= i_3. + Have: i_2 <= 9. + Have: i_3 <= 19. + Have: 0 <= i. + Have: 0 <= i_1. + Have: i <= 9. + Have: i_1 <= 19. + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_5,i_4 : Z. ((0 <= i_4) -> ((0 <= i_5) -> ((i_5 <= 9) -> + ((i_4 <= 19) -> + (((i_4 < 0) \/ (i_5 < 0) \/ (10 <= i_5) \/ (20 <= i_4)) -> + (t2_0[i_5][i_4] = t2_1[i_5][i_4])))))). +} +Prove: exists i_5,i_4 : Z. (i_5 <= i) /\ (i_4 <= i_1) /\ (0 <= i_4) /\ + (i_1 <= i_4) /\ (0 <= i_5) /\ (i <= i_5) /\ (i_5 <= 9) /\ (i_4 <= 19). + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 51): +Assume { + Type: is_uint32(i). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 19) -> (t2_2[i][i_1] = v))). +} +Prove: i < to_uint32(1 + i). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 51): +Prove: true. + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 58): +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < j) -> (t2_2[i][i_1] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: j < to_uint32(1 + j). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 58): +Prove: true. + +------------------------------------------------------------ +------------------------------------------------------------ + Function init_t2_v2 +------------------------------------------------------------ + +Goal Post-condition (file tests/wp_typed/user_init.i, line 68) in 'init_t2_v2': +Assume { + (* Goal *) + When: (0 <= i) /\ (0 <= i_1) /\ (i <= 9) /\ (i_1 <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> (((i_3 < 0) \/ (10 <= i_3)) -> + (t2_1[i_3][i_2] = t2_0[i_3][i_2])))))). + (* Invariant 'Partial_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> (t2_0[i_3][i_2] = v))))). +} +Prove: t2_0[i][i_1] = v. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial_i' (file tests/wp_typed/user_init.i, line 77): +Let m = t2_0[i]. +Assume { + Type: is_uint32(i). + (* Goal *) + When: (0 <= i_1) /\ (0 <= i_2) /\ (i_1 < to_uint32(1 + i)) /\ (i_2 <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> (((i_4 < 0) \/ (10 <= i_4)) -> + (t2_1[i_4][i_3] = t2_2[i_4][i_3])))))). + (* Invariant 'Partial_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_2[i_4][i_3] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> (((i_4 < 0) \/ (10 <= i_4)) -> + (t2_0[i_4][i_3] = t2_2[i_4][i_3])))))). + (* Invariant 'Previous_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_0[i_4][i_3] = t2_2[i_4][i_3]))))). + (* Invariant 'Partial_j' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 <= 19) -> (m[i_3] = v))). +} +Prove: m[0] = t2_0[i_1][i_2]. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial_i' (file tests/wp_typed/user_init.i, line 77): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range_i' (file tests/wp_typed/user_init.i, line 76): +Assume { + Type: is_uint32(i). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 19) -> (t2_2[i][i_1] = v))). +} +Prove: to_uint32(1 + i) <= 10. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range_i' (file tests/wp_typed/user_init.i, line 76): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial_j' (file tests/wp_typed/user_init.i, line 83): +Let m = t2_0[i]. +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Goal *) + When: (0 <= i_1) /\ (i_1 < to_uint32(1 + j)). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> (((i_3 < 0) \/ (10 <= i_3)) -> + (t2_1[i_3][i_2] = t2_2[i_3][i_2])))))). + (* Invariant 'Partial_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 < i) -> + ((i_2 <= 19) -> (t2_2[i_3][i_2] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> (((i_3 < 0) \/ (10 <= i_3)) -> + (t2_0[i_3][i_2] = t2_2[i_3][i_2])))))). + (* Invariant 'Previous_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 < i) -> + ((i_2 <= 19) -> (t2_0[i_3][i_2] = t2_2[i_3][i_2]))))). + (* Invariant 'Partial_j' *) + Have: forall i_2 : Z. ((0 <= i_2) -> ((i_2 < j) -> (m[i_2] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: m[j <- v][i_1] = v. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial_j' (file tests/wp_typed/user_init.i, line 83): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Previous_i' (file tests/wp_typed/user_init.i, line 84): +Let m = t2_0[i]. +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Goal *) + When: (0 <= i_1) /\ (i_1 < i) /\ (0 <= i_2) /\ (i_2 <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> (((i_4 < 0) \/ (10 <= i_4)) -> + (t2_2[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Partial_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_1[i_4][i_3] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> (((i_4 < 0) \/ (10 <= i_4)) -> + (t2_0[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Previous_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_0[i_4][i_3] = t2_1[i_4][i_3]))))). + (* Invariant 'Partial_j' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 < j) -> (m[i_3] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: t2_0[i <- m[j <- v]][i_1][i_2] = t2_1[i_1][i_2]. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Previous_i' (file tests/wp_typed/user_init.i, line 84): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range_j' (file tests/wp_typed/user_init.i, line 82): +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < j) -> (t2_2[i][i_1] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: to_uint32(1 + j) <= 20. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range_j' (file tests/wp_typed/user_init.i, line 82): +Prove: true. + +------------------------------------------------------------ + +Goal Assertion 'Last_j' (file tests/wp_typed/user_init.i, line 90): +Prove: true. + +------------------------------------------------------------ + +Goal Assertion 'Last_i' (file tests/wp_typed/user_init.i, line 93): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_i' (1/3): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_i' (2/3): +Effect at line 80 +Assume { + Have: 0 <= i. + Have: i <= 9. + Type: is_uint32(i_2). + (* Goal *) + When: (0 <= i_3) /\ (0 <= i_4) /\ (i_3 <= 9) /\ (i_4 <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 <= 9) -> + ((i_5 <= 19) -> (((i_6 < 0) \/ (10 <= i_6)) -> + (t2_0[i_6][i_5] = t2_1[i_6][i_5])))))). + (* Invariant 'Partial_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 < i_2) -> + ((i_5 <= 19) -> (t2_1[i_6][i_5] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i_2) /\ (i_2 <= 10). + (* Then *) + Have: i_2 <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 <= 9) -> + ((i_5 <= 19) -> (((i_6 < 0) \/ (10 <= i_6)) -> + (t2_2[i_6][i_5] = t2_1[i_6][i_5])))))). + (* Invariant 'Previous_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 < i_2) -> + ((i_5 <= 19) -> (t2_2[i_6][i_5] = t2_1[i_6][i_5]))))). + (* Invariant 'Partial_j' *) + Have: forall i_5 : Z. ((0 <= i_5) -> ((i_5 <= 19) -> + (t2_2[i_2][i_5] = v))). +} +Prove: exists i_6,i_5 : Z. (i_6 <= i) /\ (i_5 <= i_1) /\ (i_1 <= i_5) /\ + (0 <= i_6) /\ (i <= i_6) /\ (i_6 <= 9). + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_i' (3/3): +Effect at line 87 +Assume { + Have: 0 <= i. + Have: i <= 9. + Type: is_uint32(i_2). + (* Goal *) + When: (0 <= i_3) /\ (0 <= i_4) /\ (i_3 <= 9) /\ (i_4 <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 <= 9) -> + ((i_5 <= 19) -> (((i_6 < 0) \/ (10 <= i_6)) -> + (t2_0[i_6][i_5] = t2_1[i_6][i_5])))))). + (* Invariant 'Partial_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 < i_2) -> + ((i_5 <= 19) -> (t2_1[i_6][i_5] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i_2) /\ (i_2 <= 10). + (* Then *) + Have: i_2 <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 <= 9) -> + ((i_5 <= 19) -> (((i_6 < 0) \/ (10 <= i_6)) -> + (t2_2[i_6][i_5] = t2_1[i_6][i_5])))))). + (* Invariant 'Previous_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 < i_2) -> + ((i_5 <= 19) -> (t2_2[i_6][i_5] = t2_1[i_6][i_5]))))). + (* Invariant 'Partial_j' *) + Have: forall i_5 : Z. ((0 <= i_5) -> ((i_5 <= 19) -> + (t2_2[i_2][i_5] = v))). +} +Prove: exists i_6,i_5 : Z. (i_6 <= i) /\ (i_5 <= i_1) /\ (i_1 <= i_5) /\ + (0 <= i_6) /\ (i <= i_6) /\ (i_6 <= 9). + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_j' (1/3): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_j' (2/3): +Effect at line 87 +Assume { + Have: 0 <= i. + Have: i <= 9. + Type: is_uint32(i_2) /\ is_uint32(j). + (* Goal *) + When: (0 <= i_3) /\ (0 <= i_4) /\ (i_3 <= 9) /\ (i_4 <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 <= 9) -> + ((i_5 <= 19) -> (((i_6 < 0) \/ (10 <= i_6)) -> + (t2_0[i_6][i_5] = t2_1[i_6][i_5])))))). + (* Invariant 'Partial_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 < i_2) -> + ((i_5 <= 19) -> (t2_1[i_6][i_5] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i_2) /\ (i_2 <= 10). + (* Then *) + Have: i_2 <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 <= 9) -> + ((i_5 <= 19) -> (((i_6 < 0) \/ (10 <= i_6)) -> + (t2_2[i_6][i_5] = t2_1[i_6][i_5])))))). + (* Invariant 'Previous_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 < i_2) -> + ((i_5 <= 19) -> (t2_2[i_6][i_5] = t2_1[i_6][i_5]))))). + (* Invariant 'Partial_j' *) + Have: forall i_5 : Z. ((0 <= i_5) -> ((i_5 < j) -> (t2_2[i_2][i_5] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: exists i_6,i_5 : Z. (i_6 <= i) /\ (i_5 <= i_1) /\ (i_1 <= i_5) /\ + (0 <= i_6) /\ (i <= i_6) /\ (i_6 <= 9). + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_j' (3/3): +Effect at line 88 +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Goal *) + When: (0 <= i) /\ (0 <= j) /\ (i <= 9) /\ (j <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: i <= 10. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < j) -> (t2_2[i][i_1] = v))). + (* Invariant 'Range_j' *) + Have: j <= 20. +} +Prove: exists i_2,i_1 : Z. (i_2 <= i) /\ (i_1 <= j) /\ (j <= i_1) /\ + (0 <= i_2) /\ (i <= i_2) /\ (i_2 <= 9). + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_v2' (1/2): +Effect at line 80 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_v2' (2/2): +Effect at line 80 +Assume { + Have: 0 <= i_2. + Have: 0 <= i_3. + Have: i_2 <= 9. + Have: i_3 <= 19. + Have: 0 <= i. + Have: i <= 9. + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_5,i_4 : Z. ((0 <= i_4) -> ((0 <= i_5) -> ((i_5 <= 9) -> + ((i_4 <= 19) -> (((i_5 < 0) \/ (10 <= i_5)) -> + (t2_0[i_5][i_4] = t2_1[i_5][i_4])))))). +} +Prove: exists i_5,i_4 : Z. (i_5 <= i) /\ (i_4 <= i_1) /\ (i_1 <= i_4) /\ + (0 <= i_5) /\ (i <= i_5) /\ (i_5 <= 9). + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 80): +Assume { + Type: is_uint32(i). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 19) -> (t2_2[i][i_1] = v))). +} +Prove: i < to_uint32(1 + i). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 80): +Prove: true. + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 87): +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < j) -> (t2_2[i][i_1] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: j < to_uint32(1 + j). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 87): +Prove: true. + +------------------------------------------------------------ +------------------------------------------------------------ + Function init_t2_v3 +------------------------------------------------------------ + +Goal Post-condition (file tests/wp_typed/user_init.i, line 99) in 'init_t2_v3': +Assume { + Type: is_sint32(v). + (* Goal *) + When: (0 <= i) /\ (i <= 9). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_1[i_2][i_1] = t2_0[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 9) -> + P_MemSet20(t2_0[i_1], 20, v))). +} +Prove: P_MemSet20(t2_0[i], 20, v). + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial_i' (file tests/wp_typed/user_init.i, line 108): +Assume { + Type: IsArray1_sint32(v) /\ is_uint32(i) /\ is_sint32(v_1) /\ + IsArray1_sint32(t2_0[i]). + (* Goal *) + When: (0 <= i_1) /\ (i_1 < to_uint32(1 + i)). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> (((i_3 < 0) \/ (10 <= i_3)) -> + (t2_1[i_3][i_2] = t2_0[i_3][i_2])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2 : Z. ((0 <= i_2) -> ((i_2 < i) -> + P_MemSet20(t2_0[i_2], 20, v_1))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Invariant 'Partial_j' *) + Have: P_MemSet20(v, 20, v_1). +} +Prove: P_MemSet20(t2_0[i <- v][i_1], 20, v_1). + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial_i' (file tests/wp_typed/user_init.i, line 108): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range_i' (file tests/wp_typed/user_init.i, line 107): +Assume { + Type: IsArray1_sint32(v) /\ is_uint32(i) /\ is_sint32(v_1) /\ + IsArray1_sint32(t2_0[i]). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_1[i_2][i_1] = t2_0[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < i) -> + P_MemSet20(t2_0[i_1], 20, v_1))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Invariant 'Partial_j' *) + Have: P_MemSet20(v, 20, v_1). +} +Prove: to_uint32(1 + i) <= 10. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range_i' (file tests/wp_typed/user_init.i, line 107): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial_j' (file tests/wp_typed/user_init.i, line 114): +Let m = v[j <- v_1]. +Assume { + Type: IsArray1_sint32(v) /\ is_uint32(i) /\ is_uint32(j) /\ + is_sint32(v_1) /\ IsArray1_sint32(t2_0[i]) /\ IsArray1_sint32(m). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_1[i_2][i_1] = t2_0[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < i) -> + P_MemSet20(t2_0[i_1], 20, v_1))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Invariant 'Partial_j' *) + Have: P_MemSet20(v, j, v_1). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: P_MemSet20(m, to_uint32(1 + j), v_1). + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial_j' (file tests/wp_typed/user_init.i, line 114): +Let m = t2_0[i]. +Assume { + Type: is_uint32(i) /\ is_sint32(v) /\ IsArray1_sint32(m). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_1[i_2][i_1] = t2_0[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < i) -> + P_MemSet20(t2_0[i_1], 20, v))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. +} +Prove: P_MemSet20(m, 0, v). + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range_j' (file tests/wp_typed/user_init.i, line 113): +Assume { + Type: IsArray1_sint32(v) /\ is_uint32(i) /\ is_uint32(j) /\ + is_sint32(v_1) /\ IsArray1_sint32(t2_0[i]). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_1[i_2][i_1] = t2_0[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < i) -> + P_MemSet20(t2_0[i_1], 20, v_1))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Invariant 'Partial_j' *) + Have: P_MemSet20(v, j, v_1). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: to_uint32(1 + j) <= 20. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range_j' (file tests/wp_typed/user_init.i, line 113): +Prove: true. + +------------------------------------------------------------ + +Goal Assertion 'Last_j' (file tests/wp_typed/user_init.i, line 120): +Prove: true. + +------------------------------------------------------------ + +Goal Assertion 'Last_i' (file tests/wp_typed/user_init.i, line 123): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_i' (1/3): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_i' (2/3): +Effect at line 111 +Assume { + Have: 0 <= i. + Have: i <= 9. + Type: IsArray1_sint32(v) /\ is_uint32(i_2) /\ is_sint32(v_1) /\ + IsArray1_sint32(t2_0[i_2]). + (* Goal *) + When: (0 <= i_3) /\ (0 <= i_4) /\ (i_3 <= 9) /\ (i_4 <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 <= 9) -> + ((i_5 <= 19) -> (((i_6 < 0) \/ (10 <= i_6)) -> + (t2_1[i_6][i_5] = t2_0[i_6][i_5])))))). + (* Invariant 'Partial_i' *) + Have: forall i_5 : Z. ((0 <= i_5) -> ((i_5 < i_2) -> + P_MemSet20(t2_0[i_5], 20, v_1))). + (* Invariant 'Range_i' *) + Have: (0 <= i_2) /\ (i_2 <= 10). + (* Then *) + Have: i_2 <= 9. + (* Invariant 'Partial_j' *) + Have: P_MemSet20(v, 20, v_1). +} +Prove: exists i_6,i_5 : Z. (i_6 <= i) /\ (i_5 <= i_1) /\ (i_1 <= i_5) /\ + (0 <= i_6) /\ (i <= i_6) /\ (i_6 <= 9). + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_i' (3/3): +Effect at line 117 +Assume { + Type: IsArray1_sint32(v) /\ is_uint32(i) /\ is_sint32(v_1) /\ + IsArray1_sint32(t2_0[i]). + (* Goal *) + When: (0 <= i) /\ (0 <= i_1) /\ (i <= 9) /\ (i_1 <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> (((i_3 < 0) \/ (10 <= i_3)) -> + (t2_1[i_3][i_2] = t2_0[i_3][i_2])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2 : Z. ((0 <= i_2) -> ((i_2 < i) -> + P_MemSet20(t2_0[i_2], 20, v_1))). + (* Invariant 'Range_i' *) + Have: i <= 10. + (* Invariant 'Partial_j' *) + Have: P_MemSet20(v, 20, v_1). +} +Prove: exists i_3,i_2 : Z. (i_3 <= i) /\ (i_2 <= i_1) /\ (i_1 <= i_2) /\ + (0 <= i_3) /\ (i <= i_3) /\ (i_3 <= 9). + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_j' (1/2): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_j' (2/2): +Effect at line 117 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_v3' (1/2): +Effect at line 111 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_v3' (2/2): +Effect at line 111 +Assume { + Have: 0 <= i_2. + Have: 0 <= i_3. + Have: i_2 <= 9. + Have: i_3 <= 19. + Have: 0 <= i. + Have: i <= 9. + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_5,i_4 : Z. ((0 <= i_4) -> ((0 <= i_5) -> ((i_5 <= 9) -> + ((i_4 <= 19) -> (((i_5 < 0) \/ (10 <= i_5)) -> + (t2_0[i_5][i_4] = t2_1[i_5][i_4])))))). +} +Prove: exists i_5,i_4 : Z. (i_5 <= i) /\ (i_4 <= i_1) /\ (i_1 <= i_4) /\ + (0 <= i_5) /\ (i <= i_5) /\ (i_5 <= 9). + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 111): +Assume { + Type: IsArray1_sint32(v) /\ is_uint32(i) /\ is_sint32(v_1) /\ + IsArray1_sint32(t2_0[i]). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_1[i_2][i_1] = t2_0[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < i) -> + P_MemSet20(t2_0[i_1], 20, v_1))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Invariant 'Partial_j' *) + Have: P_MemSet20(v, 20, v_1). +} +Prove: i < to_uint32(1 + i). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 111): +Prove: true. + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 117): +Assume { + Type: IsArray1_sint32(v) /\ is_uint32(i) /\ is_uint32(j) /\ + is_sint32(v_1) /\ IsArray1_sint32(t2_0[i]). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_1[i_2][i_1] = t2_0[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < i) -> + P_MemSet20(t2_0[i_1], 20, v_1))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Invariant 'Partial_j' *) + Have: P_MemSet20(v, j, v_1). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: j < to_uint32(1 + j). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 117): Prove: true. ------------------------------------------------------------ diff --git a/src/plugins/wp/tests/wp_typed/oracle/user_init.1.res.oracle b/src/plugins/wp/tests/wp_typed/oracle/user_init.1.res.oracle index 69788521bcfcd18f513e5c93c896d2230864b615..847496eab27e2dc4b13dbd1c913be550dd2aeda9 100644 --- a/src/plugins/wp/tests/wp_typed/oracle/user_init.1.res.oracle +++ b/src/plugins/wp/tests/wp_typed/oracle/user_init.1.res.oracle @@ -2,12 +2,18 @@ [kernel] Parsing tests/wp_typed/user_init.i (no preprocessing) [wp] Running WP plugin... [wp] Loading driver 'share/wp.driver' +[wp] [CFG] Goal init_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t1_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t2_v1_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t2_v2_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t2_v3_exits : Valid (Unreachable) [wp] Warning: Missing RTE guards +[wp] Computing [100 goals...] ------------------------------------------------------------ Function init ------------------------------------------------------------ -Goal Post-condition (file tests/wp_typed/user_init.i, line 3) in 'init': +Goal Post-condition (file tests/wp_typed/user_init.i, line 10) in 'init': Let a_1 = shift_sint32(a, 0). Assume { Type: is_sint32(i) /\ is_sint32(n). @@ -29,7 +35,7 @@ Prove: havoc(Mint_undef_0, Mint_0, a_1, i)[shift_sint32(a, i_1)] = v. ------------------------------------------------------------ -Goal Preservation of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 9): +Goal Preservation of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 17): Let a_1 = shift_sint32(a, 0). Let a_2 = havoc(Mint_undef_0, Mint_0, a_1, n). Assume { @@ -52,12 +58,12 @@ Prove: a_2[shift_sint32(a, i) <- v][shift_sint32(a, i_1)] = v. ------------------------------------------------------------ -Goal Establishment of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 9): +Goal Establishment of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 17): Prove: true. ------------------------------------------------------------ -Goal Preservation of Invariant 'Range' (file tests/wp_typed/user_init.i, line 8): +Goal Preservation of Invariant 'Range' (file tests/wp_typed/user_init.i, line 16): Let a_1 = shift_sint32(a, 0). Assume { Type: is_sint32(i) /\ is_sint32(n) /\ is_sint32(1 + i). @@ -77,18 +83,18 @@ Prove: (-1) <= i. ------------------------------------------------------------ -Goal Establishment of Invariant 'Range' (file tests/wp_typed/user_init.i, line 8): +Goal Establishment of Invariant 'Range' (file tests/wp_typed/user_init.i, line 16): Prove: true. ------------------------------------------------------------ -Goal Loop assigns (file tests/wp_typed/user_init.i, line 10) (1/2): +Goal Loop assigns 'Zone' (1/2): Prove: true. ------------------------------------------------------------ -Goal Loop assigns (file tests/wp_typed/user_init.i, line 10) (2/2): -Effect at line 12 +Goal Loop assigns 'Zone' (2/2): +Effect at line 20 Let a_1 = shift_sint32(a, 0). Let a_2 = shift_sint32(a, i). Assume { @@ -111,8 +117,1942 @@ Prove: included(a_2, 1, a_1, n). ------------------------------------------------------------ -Goal Assigns (file tests/wp_typed/user_init.i, line 4) in 'init': -Effect at line 12 +Goal Assigns (file tests/wp_typed/user_init.i, line 9) in 'init': +Effect at line 20 +Prove: true. + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 20): +Prove: true. + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 20): +Prove: true. + +------------------------------------------------------------ +------------------------------------------------------------ + Function init_t1 +------------------------------------------------------------ + +Goal Post-condition (file tests/wp_typed/user_init.i, line 24) in 'init_t1': +Assume { + Type: is_uint32(i_1). + (* Goal *) + When: (0 <= i) /\ (i <= 9). + (* Invariant 'Partial' *) + Have: forall i_2 : Z. ((0 <= i_2) -> ((i_2 < i_1) -> (t1_0[i_2] = v))). + (* Invariant 'Range' *) + Have: (0 <= i_1) /\ (i_1 <= 10). + (* Else *) + Have: 10 <= i_1. +} +Prove: t1_0[i] = v. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 32): +Assume { + Type: is_uint32(i). + (* Goal *) + When: (0 <= i_1) /\ (i_1 < to_uint32(1 + i)). + (* Invariant 'Partial' *) + Have: forall i_2 : Z. ((0 <= i_2) -> ((i_2 < i) -> (t1_0[i_2] = v))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. +} +Prove: t1_0[i <- v][i_1] = v. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 32): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range' (file tests/wp_typed/user_init.i, line 31): +Assume { + Type: is_uint32(i). + (* Invariant 'Partial' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < i) -> (t1_0[i_1] = v))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. +} +Prove: to_uint32(1 + i) <= 10. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range' (file tests/wp_typed/user_init.i, line 31): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'Zone': +Prove: true. + +------------------------------------------------------------ + +Goal Assigns (file tests/wp_typed/user_init.i, line 26) in 'init_t1' (1/2): +Effect at line 35 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns (file tests/wp_typed/user_init.i, line 26) in 'init_t1' (2/2): +Effect at line 35 +Prove: true. + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 35): +Assume { + Type: is_uint32(i). + (* Invariant 'Partial' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < i) -> (t1_0[i_1] = v))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. +} +Prove: i < to_uint32(1 + i). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 35): +Prove: true. + +------------------------------------------------------------ +------------------------------------------------------------ + Function init_t2_bis_v1 +------------------------------------------------------------ + +Goal Post-condition (file tests/wp_typed/user_init.i, line 127) in 'init_t2_bis_v1': +Let a = global(G_t2_48). +Assume { + Type: is_uint32(i_2) /\ is_sint32(v). + (* Goal *) + When: (0 <= i) /\ (0 <= i_1) /\ (i <= 9) /\ (i_1 <= 19). + (* Loop assigns 'lack,Zone' *) + Have: forall a_1 : addr. + ((forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (shift_sint32(shift_A20_sint32(a, i_4), i_3) != a_1)))))) -> + (Mint_1[a_1] = Mint_0[a_1])). + (* Invariant 'Partial' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i_2) -> + ((i_3 <= 19) -> + (Mint_0[shift_sint32(shift_A20_sint32(a, i_4), i_3)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i_2) /\ (i_2 <= 10). + (* Else *) + Have: 10 <= i_2. +} +Prove: Mint_0[shift_sint32(shift_A20_sint32(a, i), i_1)] = v. + +------------------------------------------------------------ + +Goal Exit-condition (file tests/wp_typed/user_init.i, line 129) in 'init_t2_bis_v1': +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 136): +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Let a_2 = shift_sint32(a_1, 0). +Let a_3 = havoc(Mint_undef_0, Mint_0, a_2, 20). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Goal *) + When: (0 <= i_1) /\ (0 <= i_2) /\ (i_1 < to_uint32(1 + i)) /\ (i_2 <= 19). + (* Loop assigns 'lack,Zone' *) + Have: forall a_4 : addr. + ((forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (shift_sint32(shift_A20_sint32(a, i_4), i_3) != a_4)))))) -> + (Mint_1[a_4] = Mint_0[a_4])). + (* Invariant 'Partial' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> + (Mint_0[shift_sint32(shift_A20_sint32(a, i_4), i_3)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Call 'init' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 <= 19) -> + (a_3[shift_sint32(a_1, i_3)] = v))). +} +Prove: a_3[shift_sint32(shift_A20_sint32(a, i_1), i_2)] = Mint_undef_0[a_2]. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 136): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range' (file tests/wp_typed/user_init.i, line 135): +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Loop assigns 'lack,Zone' *) + Have: forall a_2 : addr. + ((forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (shift_sint32(shift_A20_sint32(a, i_2), i_1) != a_2)))))) -> + (Mint_0[a_2] = Mint_1[a_2])). + (* Invariant 'Partial' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> + (Mint_1[shift_sint32(shift_A20_sint32(a, i_2), i_1)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Call 'init' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 19) -> + (havoc(Mint_undef_0, Mint_1, shift_sint32(a_1, 0), 20) + [shift_sint32(a_1, i_1)] = v))). +} +Prove: to_uint32(1 + i) <= 10. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range' (file tests/wp_typed/user_init.i, line 135): +Prove: true. + +------------------------------------------------------------ + +Goal Assertion 'Offset' (file tests/wp_typed/user_init.i, line 141): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone' (1/3): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone' (2/3): +Effect at line 139 +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Goal *) + When: (0 <= i_1) /\ (0 <= i_2) /\ (i_1 <= 9) /\ (i_2 <= 19). + (* Loop assigns 'lack,Zone' *) + Have: forall a_2 : addr. + ((forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (shift_sint32(shift_A20_sint32(a, i_4), i_3) != a_2)))))) -> + (Mint_0[a_2] = Mint_1[a_2])). + (* Invariant 'Partial' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> + (Mint_1[shift_sint32(shift_A20_sint32(a, i_4), i_3)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Call 'init' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 <= 19) -> + (havoc(Mint_undef_0, Mint_1, shift_sint32(a_1, 0), 20) + [shift_sint32(a_1, i_3)] = v))). +} +Prove: (forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> false))))) \/ + (forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (exists i_6,i_5 : Z. (0 <= i_5) /\ (i_3 <= i_5) /\ (0 <= i_6) /\ + (i_4 <= i_6) /\ (i_5 <= i_3) /\ (i_6 <= i_4) /\ (i_6 <= 9) /\ + (i_5 <= 19))))))). + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone' (3/3): +Call Effect at line 140 +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Goal *) + When: (0 <= i) /\ (0 <= i_1) /\ (i <= 9) /\ (i_1 <= 19). + (* Loop assigns 'lack,Zone' *) + Have: forall a_2 : addr. + ((forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> + (shift_sint32(shift_A20_sint32(a, i_3), i_2) != a_2)))))) -> + (Mint_0[a_2] = Mint_1[a_2])). + (* Invariant 'Partial' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 < i) -> + ((i_2 <= 19) -> + (Mint_1[shift_sint32(shift_A20_sint32(a, i_3), i_2)] = v))))). + (* Invariant 'Range' *) + Have: i <= 10. + (* Call 'init' *) + Have: forall i_2 : Z. ((0 <= i_2) -> ((i_2 <= 19) -> + (havoc(Mint_undef_0, Mint_1, shift_sint32(a_1, 0), 20) + [shift_sint32(a_1, i_2)] = v))). +} +Prove: exists i_3,i_2 : Z. (i_3 <= i) /\ (i_2 <= i_1) /\ (0 <= i_2) /\ + (i_1 <= i_2) /\ (0 <= i_3) /\ (i <= i_3) /\ (i_3 <= 9) /\ (i_2 <= 19). + +------------------------------------------------------------ + +Goal Assigns 'lack' in 'init_t2_bis_v1' (1/3): +Effect at line 139 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'lack' in 'init_t2_bis_v1' (2/3): +Effect at line 139 +Assume { + Have: 0 <= i_2. + Have: 0 <= i_3. + Have: i_2 <= 9. + Have: i_3 <= 19. + Have: 0 <= i. + Have: 0 <= i_1. + Have: i <= 9. + Have: i_1 <= 19. + (* Loop assigns 'lack,Zone' *) + Have: forall a : addr. + ((forall i_5,i_4 : Z. ((0 <= i_4) -> ((0 <= i_5) -> ((i_5 <= 9) -> + ((i_4 <= 19) -> + (shift_sint32(shift_A20_sint32(global(G_t2_48), i_5), i_4) != a)))))) -> + (Mint_0[a] = Mint_1[a])). +} +Prove: exists i_5,i_4 : Z. (i_5 <= i) /\ (i_4 <= i_1) /\ (0 <= i_4) /\ + (i_1 <= i_4) /\ (0 <= i_5) /\ (i <= i_5) /\ (i_5 <= 9) /\ (i_4 <= 19). + +------------------------------------------------------------ + +Goal Assigns 'lack' in 'init_t2_bis_v1' (3/3): +Call Effect at line 140 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'lack' in 'init_t2_bis_v1' (1/2): +Effect at line 139 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'lack' in 'init_t2_bis_v1' (2/2): +Effect at line 139 +Assume { + Have: 0 <= i_2. + Have: 0 <= i_3. + Have: i_2 <= 9. + Have: i_3 <= 19. + Have: 0 <= i. + Have: 0 <= i_1. + Have: i <= 9. + Have: i_1 <= 19. + (* Loop assigns 'lack,Zone' *) + Have: forall a : addr. + ((forall i_5,i_4 : Z. ((0 <= i_4) -> ((0 <= i_5) -> ((i_5 <= 9) -> + ((i_4 <= 19) -> + (shift_sint32(shift_A20_sint32(global(G_t2_48), i_5), i_4) != a)))))) -> + (Mint_0[a] = Mint_1[a])). +} +Prove: exists i_5,i_4 : Z. (i_5 <= i) /\ (i_4 <= i_1) /\ (0 <= i_4) /\ + (i_1 <= i_4) /\ (0 <= i_5) /\ (i <= i_5) /\ (i_5 <= 9) /\ (i_4 <= 19). + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 139): +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Loop assigns 'lack,Zone' *) + Have: forall a_2 : addr. + ((forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (shift_sint32(shift_A20_sint32(a, i_2), i_1) != a_2)))))) -> + (Mint_0[a_2] = Mint_1[a_2])). + (* Invariant 'Partial' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> + (Mint_1[shift_sint32(shift_A20_sint32(a, i_2), i_1)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Call 'init' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 19) -> + (havoc(Mint_undef_0, Mint_1, shift_sint32(a_1, 0), 20) + [shift_sint32(a_1, i_1)] = v))). +} +Prove: i < to_uint32(1 + i). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 139): +Prove: true. + +------------------------------------------------------------ + +Goal Instance of 'Pre-condition (file tests/wp_typed/user_init.i, line 7) in 'init'' in 'init_t2_bis_v1' at call 'init' (file tests/wp_typed/user_init.i, line 140) +: +Prove: true. + +------------------------------------------------------------ + +Goal Instance of 'Pre-condition (file tests/wp_typed/user_init.i, line 8) in 'init'' in 'init_t2_bis_v1' at call 'init' (file tests/wp_typed/user_init.i, line 140) +: +Prove: true. + +------------------------------------------------------------ +------------------------------------------------------------ + Function init_t2_bis_v2 +------------------------------------------------------------ + +Goal Post-condition (file tests/wp_typed/user_init.i, line 145) in 'init_t2_bis_v2': +Let a = global(G_t2_48). +Assume { + Type: is_uint32(i_2) /\ is_sint32(v). + (* Goal *) + When: (0 <= i) /\ (0 <= i_1) /\ (i <= 9) /\ (i_1 <= 19). + (* Loop assigns 'tactic,Zone' *) + Have: forall a_1 : addr. + ((forall i_4,i_3 : Z. ((0 <= i_4) -> ((i_4 <= 9) -> + (shift_sint32(shift_A20_sint32(a, i_4), i_3) != a_1)))) -> + (Mint_1[a_1] = Mint_0[a_1])). + (* Invariant 'Partial' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i_2) -> + ((i_3 <= 19) -> + (Mint_0[shift_sint32(shift_A20_sint32(a, i_4), i_3)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i_2) /\ (i_2 <= 10). + (* Else *) + Have: 10 <= i_2. +} +Prove: Mint_0[shift_sint32(shift_A20_sint32(a, i), i_1)] = v. + +------------------------------------------------------------ + +Goal Exit-condition (file tests/wp_typed/user_init.i, line 147) in 'init_t2_bis_v2': +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 154): +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Let a_2 = shift_sint32(a_1, 0). +Let a_3 = havoc(Mint_undef_0, Mint_0, a_2, 20). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Goal *) + When: (0 <= i_1) /\ (0 <= i_2) /\ (i_1 < to_uint32(1 + i)) /\ (i_2 <= 19). + (* Loop assigns 'tactic,Zone' *) + Have: forall a_4 : addr. + ((forall i_4,i_3 : Z. ((0 <= i_4) -> ((i_4 <= 9) -> + (shift_sint32(shift_A20_sint32(a, i_4), i_3) != a_4)))) -> + (Mint_1[a_4] = Mint_0[a_4])). + (* Invariant 'Partial' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> + (Mint_0[shift_sint32(shift_A20_sint32(a, i_4), i_3)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Call 'init' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 <= 19) -> + (a_3[shift_sint32(a_1, i_3)] = v))). +} +Prove: a_3[shift_sint32(shift_A20_sint32(a, i_1), i_2)] = Mint_undef_0[a_2]. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial' (file tests/wp_typed/user_init.i, line 154): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range' (file tests/wp_typed/user_init.i, line 153): +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Loop assigns 'tactic,Zone' *) + Have: forall a_2 : addr. + ((forall i_2,i_1 : Z. ((0 <= i_2) -> ((i_2 <= 9) -> + (shift_sint32(shift_A20_sint32(a, i_2), i_1) != a_2)))) -> + (Mint_0[a_2] = Mint_1[a_2])). + (* Invariant 'Partial' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> + (Mint_1[shift_sint32(shift_A20_sint32(a, i_2), i_1)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Call 'init' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 19) -> + (havoc(Mint_undef_0, Mint_1, shift_sint32(a_1, 0), 20) + [shift_sint32(a_1, i_1)] = v))). +} +Prove: to_uint32(1 + i) <= 10. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range' (file tests/wp_typed/user_init.i, line 153): +Prove: true. + +------------------------------------------------------------ + +Goal Assertion 'Offset_i' (file tests/wp_typed/user_init.i, line 159): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone' (1/3): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone' (2/3): +Effect at line 157 +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i_2). +Assume { + Have: 0 <= i. + Have: i <= 9. + Type: is_uint32(i_2) /\ is_sint32(v). + (* Goal *) + When: (0 <= i_3) /\ (0 <= i_4) /\ (i_3 <= 9) /\ (i_4 <= 19). + (* Loop assigns 'tactic,Zone' *) + Have: forall a_2 : addr. + ((forall i_6,i_5 : Z. ((0 <= i_6) -> ((i_6 <= 9) -> + (shift_sint32(shift_A20_sint32(a, i_6), i_5) != a_2)))) -> + (Mint_0[a_2] = Mint_1[a_2])). + (* Invariant 'Partial' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 < i_2) -> + ((i_5 <= 19) -> + (Mint_1[shift_sint32(shift_A20_sint32(a, i_6), i_5)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i_2) /\ (i_2 <= 10). + (* Then *) + Have: i_2 <= 9. + (* Call 'init' *) + Have: forall i_5 : Z. ((0 <= i_5) -> ((i_5 <= 19) -> + (havoc(Mint_undef_0, Mint_1, shift_sint32(a_1, 0), 20) + [shift_sint32(a_1, i_5)] = v))). +} +Prove: exists i_6,i_5 : Z. (i_6 <= i) /\ (i_5 <= i_1) /\ (i_1 <= i_5) /\ + (0 <= i_6) /\ (i <= i_6) /\ (i_6 <= 9). + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone' (3/3): +Call Effect at line 158 +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Goal *) + When: (0 <= i) /\ (0 <= i_1) /\ (i <= 9) /\ (i_1 <= 19). + (* Loop assigns 'tactic,Zone' *) + Have: forall a_2 : addr. + ((forall i_3,i_2 : Z. ((0 <= i_3) -> ((i_3 <= 9) -> + (shift_sint32(shift_A20_sint32(a, i_3), i_2) != a_2)))) -> + (Mint_0[a_2] = Mint_1[a_2])). + (* Invariant 'Partial' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 < i) -> + ((i_2 <= 19) -> + (Mint_1[shift_sint32(shift_A20_sint32(a, i_3), i_2)] = v))))). + (* Invariant 'Range' *) + Have: i <= 10. + (* Call 'init' *) + Have: forall i_2 : Z. ((0 <= i_2) -> ((i_2 <= 19) -> + (havoc(Mint_undef_0, Mint_1, shift_sint32(a_1, 0), 20) + [shift_sint32(a_1, i_2)] = v))). +} +Prove: exists i_3,i_2 : Z. (i_3 <= i) /\ (i_2 <= i_1) /\ (i_1 <= i_2) /\ + (0 <= i_3) /\ (i <= i_3) /\ (i_3 <= 9). + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_bis_v2' (1/3): +Effect at line 157 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_bis_v2' (2/3): +Effect at line 157 +Assume { + Have: 0 <= i_2. + Have: 0 <= i_3. + Have: i_2 <= 9. + Have: i_3 <= 19. + Have: 0 <= i. + Have: i <= 9. + (* Loop assigns 'tactic,Zone' *) + Have: forall a : addr. + ((forall i_5,i_4 : Z. ((0 <= i_5) -> ((i_5 <= 9) -> + (shift_sint32(shift_A20_sint32(global(G_t2_48), i_5), i_4) != a)))) -> + (Mint_0[a] = Mint_1[a])). +} +Prove: exists i_5,i_4 : Z. (i_5 <= i) /\ (i_4 <= i_1) /\ (i_1 <= i_4) /\ + (0 <= i_5) /\ (i <= i_5) /\ (i_5 <= 9). + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_bis_v2' (3/3): +Call Effect at line 158 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_bis_v2' (1/2): +Effect at line 157 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_bis_v2' (2/2): +Effect at line 157 +Assume { + Have: 0 <= i_2. + Have: 0 <= i_3. + Have: i_2 <= 9. + Have: i_3 <= 19. + Have: 0 <= i. + Have: i <= 9. + (* Loop assigns 'tactic,Zone' *) + Have: forall a : addr. + ((forall i_5,i_4 : Z. ((0 <= i_5) -> ((i_5 <= 9) -> + (shift_sint32(shift_A20_sint32(global(G_t2_48), i_5), i_4) != a)))) -> + (Mint_0[a] = Mint_1[a])). +} +Prove: exists i_5,i_4 : Z. (i_5 <= i) /\ (i_4 <= i_1) /\ (i_1 <= i_4) /\ + (0 <= i_5) /\ (i <= i_5) /\ (i_5 <= 9). + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 157): +Let a = global(G_t2_48). +Let a_1 = shift_A20_sint32(a, i). +Assume { + Type: is_uint32(i) /\ is_sint32(v). + (* Loop assigns 'tactic,Zone' *) + Have: forall a_2 : addr. + ((forall i_2,i_1 : Z. ((0 <= i_2) -> ((i_2 <= 9) -> + (shift_sint32(shift_A20_sint32(a, i_2), i_1) != a_2)))) -> + (Mint_0[a_2] = Mint_1[a_2])). + (* Invariant 'Partial' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> + (Mint_1[shift_sint32(shift_A20_sint32(a, i_2), i_1)] = v))))). + (* Invariant 'Range' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Call 'init' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 19) -> + (havoc(Mint_undef_0, Mint_1, shift_sint32(a_1, 0), 20) + [shift_sint32(a_1, i_1)] = v))). +} +Prove: i < to_uint32(1 + i). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 157): +Prove: true. + +------------------------------------------------------------ + +Goal Instance of 'Pre-condition (file tests/wp_typed/user_init.i, line 7) in 'init'' in 'init_t2_bis_v2' at call 'init' (file tests/wp_typed/user_init.i, line 158) +: +Prove: true. + +------------------------------------------------------------ + +Goal Instance of 'Pre-condition (file tests/wp_typed/user_init.i, line 8) in 'init'' in 'init_t2_bis_v2' at call 'init' (file tests/wp_typed/user_init.i, line 158) +: +Prove: true. + +------------------------------------------------------------ +------------------------------------------------------------ + Function init_t2_v1 +------------------------------------------------------------ + +Goal Post-condition (file tests/wp_typed/user_init.i, line 39) in 'init_t2_v1': +Assume { + (* Goal *) + When: (0 <= i) /\ (0 <= i_1) /\ (i <= 9) /\ (i_1 <= 19). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> + (((i_2 < 0) \/ (i_3 < 0) \/ (10 <= i_3) \/ (20 <= i_2)) -> + (t2_1[i_3][i_2] = t2_0[i_3][i_2])))))). + (* Invariant 'Partial_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> (t2_0[i_3][i_2] = v))))). +} +Prove: t2_0[i][i_1] = v. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial_i' (file tests/wp_typed/user_init.i, line 48): +Let m = t2_0[i]. +Assume { + Type: is_uint32(i). + (* Goal *) + When: (0 <= i_1) /\ (0 <= i_2) /\ (i_1 < to_uint32(1 + i)) /\ (i_2 <= 19). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_1[i_4][i_3] = t2_2[i_4][i_3])))))). + (* Invariant 'Partial_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_2[i_4][i_3] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_0[i_4][i_3] = t2_2[i_4][i_3])))))). + (* Invariant 'Previous_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_0[i_4][i_3] = t2_2[i_4][i_3]))))). + (* Invariant 'Partial_j' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 <= 19) -> (m[i_3] = v))). +} +Prove: m[0] = t2_0[i_1][i_2]. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial_i' (file tests/wp_typed/user_init.i, line 48): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range_i' (file tests/wp_typed/user_init.i, line 47): +Assume { + Type: is_uint32(i). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 19) -> (t2_2[i][i_1] = v))). +} +Prove: to_uint32(1 + i) <= 10. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range_i' (file tests/wp_typed/user_init.i, line 47): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial_j' (file tests/wp_typed/user_init.i, line 54): +Let m = t2_0[i]. +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Goal *) + When: (0 <= i_1) /\ (i_1 < to_uint32(1 + j)). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> + (((i_2 < 0) \/ (i_3 < 0) \/ (10 <= i_3) \/ (20 <= i_2)) -> + (t2_1[i_3][i_2] = t2_2[i_3][i_2])))))). + (* Invariant 'Partial_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 < i) -> + ((i_2 <= 19) -> (t2_2[i_3][i_2] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> + (((i_2 < 0) \/ (i_3 < 0) \/ (10 <= i_3) \/ (20 <= i_2)) -> + (t2_0[i_3][i_2] = t2_2[i_3][i_2])))))). + (* Invariant 'Previous_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 < i) -> + ((i_2 <= 19) -> (t2_0[i_3][i_2] = t2_2[i_3][i_2]))))). + (* Invariant 'Partial_j' *) + Have: forall i_2 : Z. ((0 <= i_2) -> ((i_2 < j) -> (m[i_2] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: m[j <- v][i_1] = v. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial_j' (file tests/wp_typed/user_init.i, line 54): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Previous_i' (file tests/wp_typed/user_init.i, line 55): +Let m = t2_0[i]. +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Goal *) + When: (0 <= i_1) /\ (i_1 < i) /\ (0 <= i_2) /\ (i_2 <= 19). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_2[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Partial_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_1[i_4][i_3] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_0[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Previous_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_0[i_4][i_3] = t2_1[i_4][i_3]))))). + (* Invariant 'Partial_j' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 < j) -> (m[i_3] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: t2_0[i <- m[j <- v]][i_1][i_2] = t2_1[i_1][i_2]. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Previous_i' (file tests/wp_typed/user_init.i, line 55): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range_j' (file tests/wp_typed/user_init.i, line 53): +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < j) -> (t2_2[i][i_1] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: to_uint32(1 + j) <= 20. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range_j' (file tests/wp_typed/user_init.i, line 53): +Prove: true. + +------------------------------------------------------------ + +Goal Assertion 'Last_j' (file tests/wp_typed/user_init.i, line 61): +Prove: true. + +------------------------------------------------------------ + +Goal Assertion 'Last_i' (file tests/wp_typed/user_init.i, line 64): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone_i' (1/3): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone_i' (2/3): +Effect at line 51 +Assume { + Type: is_uint32(i). + (* Goal *) + When: (0 <= i_1) /\ (0 <= i_2) /\ (i_1 <= 9) /\ (i_2 <= 19). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_0[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Partial_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_1[i_4][i_3] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_2[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Previous_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_2[i_4][i_3] = t2_1[i_4][i_3]))))). + (* Invariant 'Partial_j' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 <= 19) -> (t2_2[i][i_3] = v))). +} +Prove: (forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> false))))) \/ + (forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (exists i_6,i_5 : Z. (0 <= i_5) /\ (i_3 <= i_5) /\ (0 <= i_6) /\ + (i_4 <= i_6) /\ (i_5 <= i_3) /\ (i_6 <= i_4) /\ (i_6 <= 9) /\ + (i_5 <= 19))))))). + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone_i' (3/3): +Effect at line 58 +Assume { + Type: is_uint32(i). + (* Goal *) + When: (0 <= i_1) /\ (0 <= i_2) /\ (i_1 <= 9) /\ (i_2 <= 19). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_0[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Partial_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_1[i_4][i_3] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_2[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Previous_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_2[i_4][i_3] = t2_1[i_4][i_3]))))). + (* Invariant 'Partial_j' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 <= 19) -> (t2_2[i][i_3] = v))). +} +Prove: (forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> false))))) \/ + (forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (exists i_6,i_5 : Z. (0 <= i_5) /\ (i_3 <= i_5) /\ (0 <= i_6) /\ + (i_4 <= i_6) /\ (i_5 <= i_3) /\ (i_6 <= i_4) /\ (i_6 <= 9) /\ + (i_5 <= 19))))))). + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone_j' (1/3): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone_j' (2/3): +Effect at line 58 +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Goal *) + When: (0 <= i_1) /\ (0 <= i_2) /\ (i_1 <= 9) /\ (i_2 <= 19). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_0[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Partial_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_1[i_4][i_3] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (((i_3 < 0) \/ (i_4 < 0) \/ (10 <= i_4) \/ (20 <= i_3)) -> + (t2_2[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Previous_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_2[i_4][i_3] = t2_1[i_4][i_3]))))). + (* Invariant 'Partial_j' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 < j) -> (t2_2[i][i_3] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: (forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> false))))) \/ + (forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> + (exists i_6,i_5 : Z. (0 <= i_5) /\ (i_3 <= i_5) /\ (0 <= i_6) /\ + (i_4 <= i_6) /\ (i_5 <= i_3) /\ (i_6 <= i_4) /\ (i_6 <= 9) /\ + (i_5 <= 19))))))). + +------------------------------------------------------------ + +Goal Loop assigns 'lack,Zone_j' (3/3): +Effect at line 59 +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Goal *) + When: (0 <= i) /\ (0 <= j) /\ (i <= 9) /\ (j <= 19). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: i <= 10. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < j) -> (t2_2[i][i_1] = v))). + (* Invariant 'Range_j' *) + Have: j <= 20. +} +Prove: exists i_2,i_1 : Z. (i_2 <= i) /\ (i_1 <= j) /\ (0 <= i_1) /\ + (j <= i_1) /\ (0 <= i_2) /\ (i <= i_2) /\ (i_2 <= 9) /\ (i_1 <= 19). + +------------------------------------------------------------ + +Goal Assigns 'lack' in 'init_t2_v1' (1/2): +Effect at line 51 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'lack' in 'init_t2_v1' (2/2): +Effect at line 51 +Assume { + Have: 0 <= i_2. + Have: 0 <= i_3. + Have: i_2 <= 9. + Have: i_3 <= 19. + Have: 0 <= i. + Have: 0 <= i_1. + Have: i <= 9. + Have: i_1 <= 19. + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_5,i_4 : Z. ((0 <= i_4) -> ((0 <= i_5) -> ((i_5 <= 9) -> + ((i_4 <= 19) -> + (((i_4 < 0) \/ (i_5 < 0) \/ (10 <= i_5) \/ (20 <= i_4)) -> + (t2_0[i_5][i_4] = t2_1[i_5][i_4])))))). +} +Prove: exists i_5,i_4 : Z. (i_5 <= i) /\ (i_4 <= i_1) /\ (0 <= i_4) /\ + (i_1 <= i_4) /\ (0 <= i_5) /\ (i <= i_5) /\ (i_5 <= 9) /\ (i_4 <= 19). + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 51): +Assume { + Type: is_uint32(i). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 19) -> (t2_2[i][i_1] = v))). +} +Prove: i < to_uint32(1 + i). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 51): +Prove: true. + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 58): +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Loop assigns 'lack,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'lack,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> + (((i_1 < 0) \/ (i_2 < 0) \/ (10 <= i_2) \/ (20 <= i_1)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < j) -> (t2_2[i][i_1] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: j < to_uint32(1 + j). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 58): +Prove: true. + +------------------------------------------------------------ +------------------------------------------------------------ + Function init_t2_v2 +------------------------------------------------------------ + +Goal Post-condition (file tests/wp_typed/user_init.i, line 68) in 'init_t2_v2': +Assume { + (* Goal *) + When: (0 <= i) /\ (0 <= i_1) /\ (i <= 9) /\ (i_1 <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> (((i_3 < 0) \/ (10 <= i_3)) -> + (t2_1[i_3][i_2] = t2_0[i_3][i_2])))))). + (* Invariant 'Partial_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> (t2_0[i_3][i_2] = v))))). +} +Prove: t2_0[i][i_1] = v. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial_i' (file tests/wp_typed/user_init.i, line 77): +Let m = t2_0[i]. +Assume { + Type: is_uint32(i). + (* Goal *) + When: (0 <= i_1) /\ (0 <= i_2) /\ (i_1 < to_uint32(1 + i)) /\ (i_2 <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> (((i_4 < 0) \/ (10 <= i_4)) -> + (t2_1[i_4][i_3] = t2_2[i_4][i_3])))))). + (* Invariant 'Partial_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_2[i_4][i_3] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> (((i_4 < 0) \/ (10 <= i_4)) -> + (t2_0[i_4][i_3] = t2_2[i_4][i_3])))))). + (* Invariant 'Previous_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_0[i_4][i_3] = t2_2[i_4][i_3]))))). + (* Invariant 'Partial_j' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 <= 19) -> (m[i_3] = v))). +} +Prove: m[0] = t2_0[i_1][i_2]. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial_i' (file tests/wp_typed/user_init.i, line 77): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range_i' (file tests/wp_typed/user_init.i, line 76): +Assume { + Type: is_uint32(i). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 19) -> (t2_2[i][i_1] = v))). +} +Prove: to_uint32(1 + i) <= 10. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range_i' (file tests/wp_typed/user_init.i, line 76): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial_j' (file tests/wp_typed/user_init.i, line 83): +Let m = t2_0[i]. +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Goal *) + When: (0 <= i_1) /\ (i_1 < to_uint32(1 + j)). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> (((i_3 < 0) \/ (10 <= i_3)) -> + (t2_1[i_3][i_2] = t2_2[i_3][i_2])))))). + (* Invariant 'Partial_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 < i) -> + ((i_2 <= 19) -> (t2_2[i_3][i_2] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> (((i_3 < 0) \/ (10 <= i_3)) -> + (t2_0[i_3][i_2] = t2_2[i_3][i_2])))))). + (* Invariant 'Previous_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 < i) -> + ((i_2 <= 19) -> (t2_0[i_3][i_2] = t2_2[i_3][i_2]))))). + (* Invariant 'Partial_j' *) + Have: forall i_2 : Z. ((0 <= i_2) -> ((i_2 < j) -> (m[i_2] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: m[j <- v][i_1] = v. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial_j' (file tests/wp_typed/user_init.i, line 83): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Previous_i' (file tests/wp_typed/user_init.i, line 84): +Let m = t2_0[i]. +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Goal *) + When: (0 <= i_1) /\ (i_1 < i) /\ (0 <= i_2) /\ (i_2 <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> (((i_4 < 0) \/ (10 <= i_4)) -> + (t2_2[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Partial_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_1[i_4][i_3] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 <= 9) -> + ((i_3 <= 19) -> (((i_4 < 0) \/ (10 <= i_4)) -> + (t2_0[i_4][i_3] = t2_1[i_4][i_3])))))). + (* Invariant 'Previous_i' *) + Have: forall i_4,i_3 : Z. ((0 <= i_3) -> ((0 <= i_4) -> ((i_4 < i) -> + ((i_3 <= 19) -> (t2_0[i_4][i_3] = t2_1[i_4][i_3]))))). + (* Invariant 'Partial_j' *) + Have: forall i_3 : Z. ((0 <= i_3) -> ((i_3 < j) -> (m[i_3] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: t2_0[i <- m[j <- v]][i_1][i_2] = t2_1[i_1][i_2]. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Previous_i' (file tests/wp_typed/user_init.i, line 84): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range_j' (file tests/wp_typed/user_init.i, line 82): +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < j) -> (t2_2[i][i_1] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: to_uint32(1 + j) <= 20. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range_j' (file tests/wp_typed/user_init.i, line 82): +Prove: true. + +------------------------------------------------------------ + +Goal Assertion 'Last_j' (file tests/wp_typed/user_init.i, line 90): +Prove: true. + +------------------------------------------------------------ + +Goal Assertion 'Last_i' (file tests/wp_typed/user_init.i, line 93): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_i' (1/3): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_i' (2/3): +Effect at line 80 +Assume { + Have: 0 <= i. + Have: i <= 9. + Type: is_uint32(i_2). + (* Goal *) + When: (0 <= i_3) /\ (0 <= i_4) /\ (i_3 <= 9) /\ (i_4 <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 <= 9) -> + ((i_5 <= 19) -> (((i_6 < 0) \/ (10 <= i_6)) -> + (t2_0[i_6][i_5] = t2_1[i_6][i_5])))))). + (* Invariant 'Partial_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 < i_2) -> + ((i_5 <= 19) -> (t2_1[i_6][i_5] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i_2) /\ (i_2 <= 10). + (* Then *) + Have: i_2 <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 <= 9) -> + ((i_5 <= 19) -> (((i_6 < 0) \/ (10 <= i_6)) -> + (t2_2[i_6][i_5] = t2_1[i_6][i_5])))))). + (* Invariant 'Previous_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 < i_2) -> + ((i_5 <= 19) -> (t2_2[i_6][i_5] = t2_1[i_6][i_5]))))). + (* Invariant 'Partial_j' *) + Have: forall i_5 : Z. ((0 <= i_5) -> ((i_5 <= 19) -> + (t2_2[i_2][i_5] = v))). +} +Prove: exists i_6,i_5 : Z. (i_6 <= i) /\ (i_5 <= i_1) /\ (i_1 <= i_5) /\ + (0 <= i_6) /\ (i <= i_6) /\ (i_6 <= 9). + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_i' (3/3): +Effect at line 87 +Assume { + Have: 0 <= i. + Have: i <= 9. + Type: is_uint32(i_2). + (* Goal *) + When: (0 <= i_3) /\ (0 <= i_4) /\ (i_3 <= 9) /\ (i_4 <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 <= 9) -> + ((i_5 <= 19) -> (((i_6 < 0) \/ (10 <= i_6)) -> + (t2_0[i_6][i_5] = t2_1[i_6][i_5])))))). + (* Invariant 'Partial_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 < i_2) -> + ((i_5 <= 19) -> (t2_1[i_6][i_5] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i_2) /\ (i_2 <= 10). + (* Then *) + Have: i_2 <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 <= 9) -> + ((i_5 <= 19) -> (((i_6 < 0) \/ (10 <= i_6)) -> + (t2_2[i_6][i_5] = t2_1[i_6][i_5])))))). + (* Invariant 'Previous_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 < i_2) -> + ((i_5 <= 19) -> (t2_2[i_6][i_5] = t2_1[i_6][i_5]))))). + (* Invariant 'Partial_j' *) + Have: forall i_5 : Z. ((0 <= i_5) -> ((i_5 <= 19) -> + (t2_2[i_2][i_5] = v))). +} +Prove: exists i_6,i_5 : Z. (i_6 <= i) /\ (i_5 <= i_1) /\ (i_1 <= i_5) /\ + (0 <= i_6) /\ (i <= i_6) /\ (i_6 <= 9). + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_j' (1/3): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_j' (2/3): +Effect at line 87 +Assume { + Have: 0 <= i. + Have: i <= 9. + Type: is_uint32(i_2) /\ is_uint32(j). + (* Goal *) + When: (0 <= i_3) /\ (0 <= i_4) /\ (i_3 <= 9) /\ (i_4 <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 <= 9) -> + ((i_5 <= 19) -> (((i_6 < 0) \/ (10 <= i_6)) -> + (t2_0[i_6][i_5] = t2_1[i_6][i_5])))))). + (* Invariant 'Partial_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 < i_2) -> + ((i_5 <= 19) -> (t2_1[i_6][i_5] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i_2) /\ (i_2 <= 10). + (* Then *) + Have: i_2 <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 <= 9) -> + ((i_5 <= 19) -> (((i_6 < 0) \/ (10 <= i_6)) -> + (t2_2[i_6][i_5] = t2_1[i_6][i_5])))))). + (* Invariant 'Previous_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 < i_2) -> + ((i_5 <= 19) -> (t2_2[i_6][i_5] = t2_1[i_6][i_5]))))). + (* Invariant 'Partial_j' *) + Have: forall i_5 : Z. ((0 <= i_5) -> ((i_5 < j) -> (t2_2[i_2][i_5] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: exists i_6,i_5 : Z. (i_6 <= i) /\ (i_5 <= i_1) /\ (i_1 <= i_5) /\ + (0 <= i_6) /\ (i <= i_6) /\ (i_6 <= 9). + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_j' (3/3): +Effect at line 88 +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Goal *) + When: (0 <= i) /\ (0 <= j) /\ (i <= 9) /\ (j <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: i <= 10. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < j) -> (t2_2[i][i_1] = v))). + (* Invariant 'Range_j' *) + Have: j <= 20. +} +Prove: exists i_2,i_1 : Z. (i_2 <= i) /\ (i_1 <= j) /\ (j <= i_1) /\ + (0 <= i_2) /\ (i <= i_2) /\ (i_2 <= 9). + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_v2' (1/2): +Effect at line 80 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_v2' (2/2): +Effect at line 80 +Assume { + Have: 0 <= i_2. + Have: 0 <= i_3. + Have: i_2 <= 9. + Have: i_3 <= 19. + Have: 0 <= i. + Have: i <= 9. + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_5,i_4 : Z. ((0 <= i_4) -> ((0 <= i_5) -> ((i_5 <= 9) -> + ((i_4 <= 19) -> (((i_5 < 0) \/ (10 <= i_5)) -> + (t2_0[i_5][i_4] = t2_1[i_5][i_4])))))). +} +Prove: exists i_5,i_4 : Z. (i_5 <= i) /\ (i_4 <= i_1) /\ (i_1 <= i_4) /\ + (0 <= i_5) /\ (i <= i_5) /\ (i_5 <= 9). + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 80): +Assume { + Type: is_uint32(i). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 19) -> (t2_2[i][i_1] = v))). +} +Prove: i < to_uint32(1 + i). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 80): +Prove: true. + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 87): +Assume { + Type: is_uint32(i) /\ is_uint32(j). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_0[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_1[i_2][i_1] = v))))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Loop assigns 'tactic,Zone_j' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_2[i_2][i_1] = t2_1[i_2][i_1])))))). + (* Invariant 'Previous_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 < i) -> + ((i_1 <= 19) -> (t2_2[i_2][i_1] = t2_1[i_2][i_1]))))). + (* Invariant 'Partial_j' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < j) -> (t2_2[i][i_1] = v))). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: j < to_uint32(1 + j). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 87): +Prove: true. + +------------------------------------------------------------ +------------------------------------------------------------ + Function init_t2_v3 +------------------------------------------------------------ + +Goal Post-condition (file tests/wp_typed/user_init.i, line 99) in 'init_t2_v3': +Assume { + Type: is_sint32(v). + (* Goal *) + When: (0 <= i) /\ (i <= 9). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_1[i_2][i_1] = t2_0[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 <= 9) -> + P_MemSet20(t2_0[i_1], 20, v))). +} +Prove: P_MemSet20(t2_0[i], 20, v). + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial_i' (file tests/wp_typed/user_init.i, line 108): +Assume { + Type: IsArray1_sint32(v) /\ is_uint32(i) /\ is_sint32(v_1) /\ + IsArray1_sint32(t2_0[i]). + (* Goal *) + When: (0 <= i_1) /\ (i_1 < to_uint32(1 + i)). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> (((i_3 < 0) \/ (10 <= i_3)) -> + (t2_1[i_3][i_2] = t2_0[i_3][i_2])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2 : Z. ((0 <= i_2) -> ((i_2 < i) -> + P_MemSet20(t2_0[i_2], 20, v_1))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Invariant 'Partial_j' *) + Have: P_MemSet20(v, 20, v_1). +} +Prove: P_MemSet20(t2_0[i <- v][i_1], 20, v_1). + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial_i' (file tests/wp_typed/user_init.i, line 108): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range_i' (file tests/wp_typed/user_init.i, line 107): +Assume { + Type: IsArray1_sint32(v) /\ is_uint32(i) /\ is_sint32(v_1) /\ + IsArray1_sint32(t2_0[i]). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_1[i_2][i_1] = t2_0[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < i) -> + P_MemSet20(t2_0[i_1], 20, v_1))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Invariant 'Partial_j' *) + Have: P_MemSet20(v, 20, v_1). +} +Prove: to_uint32(1 + i) <= 10. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range_i' (file tests/wp_typed/user_init.i, line 107): +Prove: true. + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Partial_j' (file tests/wp_typed/user_init.i, line 114): +Let m = v[j <- v_1]. +Assume { + Type: IsArray1_sint32(v) /\ is_uint32(i) /\ is_uint32(j) /\ + is_sint32(v_1) /\ IsArray1_sint32(t2_0[i]) /\ IsArray1_sint32(m). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_1[i_2][i_1] = t2_0[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < i) -> + P_MemSet20(t2_0[i_1], 20, v_1))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Invariant 'Partial_j' *) + Have: P_MemSet20(v, j, v_1). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: P_MemSet20(m, to_uint32(1 + j), v_1). + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Partial_j' (file tests/wp_typed/user_init.i, line 114): +Let m = t2_0[i]. +Assume { + Type: is_uint32(i) /\ is_sint32(v) /\ IsArray1_sint32(m). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_1[i_2][i_1] = t2_0[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < i) -> + P_MemSet20(t2_0[i_1], 20, v))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. +} +Prove: P_MemSet20(m, 0, v). + +------------------------------------------------------------ + +Goal Preservation of Invariant 'Range_j' (file tests/wp_typed/user_init.i, line 113): +Assume { + Type: IsArray1_sint32(v) /\ is_uint32(i) /\ is_uint32(j) /\ + is_sint32(v_1) /\ IsArray1_sint32(t2_0[i]). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_1[i_2][i_1] = t2_0[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < i) -> + P_MemSet20(t2_0[i_1], 20, v_1))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Invariant 'Partial_j' *) + Have: P_MemSet20(v, j, v_1). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: to_uint32(1 + j) <= 20. + +------------------------------------------------------------ + +Goal Establishment of Invariant 'Range_j' (file tests/wp_typed/user_init.i, line 113): +Prove: true. + +------------------------------------------------------------ + +Goal Assertion 'Last_j' (file tests/wp_typed/user_init.i, line 120): +Prove: true. + +------------------------------------------------------------ + +Goal Assertion 'Last_i' (file tests/wp_typed/user_init.i, line 123): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_i' (1/3): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_i' (2/3): +Effect at line 111 +Assume { + Have: 0 <= i. + Have: i <= 9. + Type: IsArray1_sint32(v) /\ is_uint32(i_2) /\ is_sint32(v_1) /\ + IsArray1_sint32(t2_0[i_2]). + (* Goal *) + When: (0 <= i_3) /\ (0 <= i_4) /\ (i_3 <= 9) /\ (i_4 <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_6,i_5 : Z. ((0 <= i_5) -> ((0 <= i_6) -> ((i_6 <= 9) -> + ((i_5 <= 19) -> (((i_6 < 0) \/ (10 <= i_6)) -> + (t2_1[i_6][i_5] = t2_0[i_6][i_5])))))). + (* Invariant 'Partial_i' *) + Have: forall i_5 : Z. ((0 <= i_5) -> ((i_5 < i_2) -> + P_MemSet20(t2_0[i_5], 20, v_1))). + (* Invariant 'Range_i' *) + Have: (0 <= i_2) /\ (i_2 <= 10). + (* Then *) + Have: i_2 <= 9. + (* Invariant 'Partial_j' *) + Have: P_MemSet20(v, 20, v_1). +} +Prove: exists i_6,i_5 : Z. (i_6 <= i) /\ (i_5 <= i_1) /\ (i_1 <= i_5) /\ + (0 <= i_6) /\ (i <= i_6) /\ (i_6 <= 9). + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_i' (3/3): +Effect at line 117 +Assume { + Type: IsArray1_sint32(v) /\ is_uint32(i) /\ is_sint32(v_1) /\ + IsArray1_sint32(t2_0[i]). + (* Goal *) + When: (0 <= i) /\ (0 <= i_1) /\ (i <= 9) /\ (i_1 <= 19). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_3,i_2 : Z. ((0 <= i_2) -> ((0 <= i_3) -> ((i_3 <= 9) -> + ((i_2 <= 19) -> (((i_3 < 0) \/ (10 <= i_3)) -> + (t2_1[i_3][i_2] = t2_0[i_3][i_2])))))). + (* Invariant 'Partial_i' *) + Have: forall i_2 : Z. ((0 <= i_2) -> ((i_2 < i) -> + P_MemSet20(t2_0[i_2], 20, v_1))). + (* Invariant 'Range_i' *) + Have: i <= 10. + (* Invariant 'Partial_j' *) + Have: P_MemSet20(v, 20, v_1). +} +Prove: exists i_3,i_2 : Z. (i_3 <= i) /\ (i_2 <= i_1) /\ (i_1 <= i_2) /\ + (0 <= i_3) /\ (i <= i_3) /\ (i_3 <= 9). + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_j' (1/2): +Prove: true. + +------------------------------------------------------------ + +Goal Loop assigns 'tactic,Zone_j' (2/2): +Effect at line 117 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_v3' (1/2): +Effect at line 111 +Prove: true. + +------------------------------------------------------------ + +Goal Assigns 'tactic' in 'init_t2_v3' (2/2): +Effect at line 111 +Assume { + Have: 0 <= i_2. + Have: 0 <= i_3. + Have: i_2 <= 9. + Have: i_3 <= 19. + Have: 0 <= i. + Have: i <= 9. + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_5,i_4 : Z. ((0 <= i_4) -> ((0 <= i_5) -> ((i_5 <= 9) -> + ((i_4 <= 19) -> (((i_5 < 0) \/ (10 <= i_5)) -> + (t2_0[i_5][i_4] = t2_1[i_5][i_4])))))). +} +Prove: exists i_5,i_4 : Z. (i_5 <= i) /\ (i_4 <= i_1) /\ (i_1 <= i_4) /\ + (0 <= i_5) /\ (i <= i_5) /\ (i_5 <= 9). + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 111): +Assume { + Type: IsArray1_sint32(v) /\ is_uint32(i) /\ is_sint32(v_1) /\ + IsArray1_sint32(t2_0[i]). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_1[i_2][i_1] = t2_0[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < i) -> + P_MemSet20(t2_0[i_1], 20, v_1))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Invariant 'Partial_j' *) + Have: P_MemSet20(v, 20, v_1). +} +Prove: i < to_uint32(1 + i). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 111): +Prove: true. + +------------------------------------------------------------ + +Goal Decreasing of Loop variant at loop (file tests/wp_typed/user_init.i, line 117): +Assume { + Type: IsArray1_sint32(v) /\ is_uint32(i) /\ is_uint32(j) /\ + is_sint32(v_1) /\ IsArray1_sint32(t2_0[i]). + (* Loop assigns 'tactic,Zone_i' *) + Have: forall i_2,i_1 : Z. ((0 <= i_1) -> ((0 <= i_2) -> ((i_2 <= 9) -> + ((i_1 <= 19) -> (((i_2 < 0) \/ (10 <= i_2)) -> + (t2_1[i_2][i_1] = t2_0[i_2][i_1])))))). + (* Invariant 'Partial_i' *) + Have: forall i_1 : Z. ((0 <= i_1) -> ((i_1 < i) -> + P_MemSet20(t2_0[i_1], 20, v_1))). + (* Invariant 'Range_i' *) + Have: (0 <= i) /\ (i <= 10). + (* Then *) + Have: i <= 9. + (* Invariant 'Partial_j' *) + Have: P_MemSet20(v, j, v_1). + (* Invariant 'Range_j' *) + Have: (0 <= j) /\ (j <= 20). + (* Then *) + Have: j <= 19. +} +Prove: j < to_uint32(1 + j). + +------------------------------------------------------------ + +Goal Positivity of Loop variant at loop (file tests/wp_typed/user_init.i, line 117): Prove: true. ------------------------------------------------------------ diff --git a/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.0.report.json b/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.0.report.json index ab542867843fc6404fdda10d57a55a10cec8af43..7bfbab0fa1746f911b7be02cbe1784d4683333f5 100644 --- a/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.0.report.json +++ b/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.0.report.json @@ -1,6 +1,8 @@ -{ "wp:global": { "alt-ergo": { "total": 4, "valid": 4, "rank": 19 }, - "qed": { "total": 4, "valid": 4 }, - "wp:main": { "total": 8, "valid": 8, "rank": 19 } }, +{ "wp:global": { "alt-ergo": { "total": 27, "valid": 16, "unknown": 11, + "rank": 19 }, + "qed": { "total": 27, "valid": 27 }, + "wp:main": { "total": 54, "valid": 43, "unknown": 11, + "rank": 19 } }, "wp:functions": { "init": { "init_loop_invariant_Partial": { "alt-ergo": { "total": 1, "valid": 1, @@ -47,4 +49,211 @@ "valid": 4 }, "wp:main": { "total": 8, "valid": 8, - "rank": 19 } } } } } + "rank": 19 } } }, + "init_t1": { "init_t1_loop_invariant_Partial": { "alt-ergo": + { "total": 1, + "valid": 1, + "rank": 4 }, + "qed": + { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 2, + "valid": 2, + "rank": 4 } }, + "init_t1_loop_invariant_Range": { "alt-ergo": + { "total": 1, + "valid": 1, + "rank": 2 }, + "qed": + { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 2, + "valid": 2, + "rank": 2 } }, + "init_t1_assigns": { "qed": { "total": 2, + "valid": 2 }, + "wp:main": { "total": 2, + "valid": 2 } }, + "init_t1_loop_assigns": { "qed": { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 1, + "valid": 1 } }, + "init_t1_ensures": { "alt-ergo": { "total": 1, + "valid": 1, + "rank": 3 }, + "wp:main": { "total": 1, + "valid": 1, + "rank": 3 } }, + "wp:section": { "alt-ergo": { "total": 3, + "valid": 3, + "rank": 4 }, + "qed": { "total": 5, + "valid": 5 }, + "wp:main": { "total": 8, + "valid": 8, + "rank": 4 } } }, + "init_t2": { "init_t2_assert_i": { "qed": { "total": 1, + "valid": 1 }, + "wp:main": { "total": 1, + "valid": 1 } }, + "init_t2_assert_j": { "qed": { "total": 1, + "valid": 1 }, + "wp:main": { "total": 1, + "valid": 1 } }, + "init_t2_loop_invariant_Previous_i": + { "alt-ergo": { "total": 1, "valid": 1, + "rank": 5 }, + "qed": { "total": 1, "valid": 1 }, + "wp:main": { "total": 2, "valid": 2, + "rank": 5 } }, + "init_t2_loop_invariant_Partial_j": + { "alt-ergo": { "total": 1, "valid": 1, + "rank": 8 }, + "qed": { "total": 1, "valid": 1 }, + "wp:main": { "total": 2, "valid": 2, + "rank": 8 } }, + "init_t2_loop_invariant_Range_j": { "alt-ergo": + { "total": 1, + "valid": 1, + "rank": 3 }, + "qed": + { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 2, + "valid": 2, + "rank": 3 } }, + "init_t2_loop_invariant_Partial_i": + { "alt-ergo": { "total": 1, "valid": 1, + "rank": 11 }, + "qed": { "total": 1, "valid": 1 }, + "wp:main": { "total": 2, "valid": 2, + "rank": 11 } }, + "init_t2_loop_invariant_Range_i": { "alt-ergo": + { "total": 1, + "valid": 1, + "rank": 2 }, + "qed": + { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 2, + "valid": 2, + "rank": 2 } }, + "init_t2_assigns": { "alt-ergo": { "total": 1, + "unknown": 1 }, + "qed": { "total": 1, + "valid": 1 }, + "wp:main": { "total": 2, + "valid": 1, + "unknown": 1 } }, + "init_t2_loop_assigns_2": { "alt-ergo": + { "total": 2, + "unknown": 2 }, + "qed": { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 3, + "valid": 1, + "unknown": 2 } }, + "init_t2_loop_assigns": { "alt-ergo": + { "total": 2, + "unknown": 2 }, + "qed": { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 3, + "valid": 1, + "unknown": 2 } }, + "init_t2_ensures": { "alt-ergo": { "total": 1, + "valid": 1, + "rank": 2 }, + "wp:main": { "total": 1, + "valid": 1, + "rank": 2 } }, + "wp:section": { "alt-ergo": { "total": 11, + "valid": 6, + "unknown": 5, + "rank": 11 }, + "qed": { "total": 10, + "valid": 10 }, + "wp:main": { "total": 21, + "valid": 16, + "unknown": 5, + "rank": 11 } } }, + "init_t2_bis": { "init_requires_2": { "qed": { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 1, + "valid": 1 } }, + "init_requires": { "qed": { "total": 1, + "valid": 1 }, + "wp:main": { "total": 1, + "valid": 1 } }, + "init_t2_bis_assert_i": { "qed": + { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 1, + "valid": 1 } }, + "init_t2_bis_loop_invariant_Partial_i": + { "alt-ergo": { "total": 1, + "valid": 1, + "rank": 10 }, + "qed": { "total": 1, "valid": 1 }, + "wp:main": { "total": 2, "valid": 2, + "rank": 10 } }, + "init_t2_bis_loop_invariant_Range_i": + { "alt-ergo": { "total": 1, + "valid": 1, + "rank": 3 }, + "qed": { "total": 1, "valid": 1 }, + "wp:main": { "total": 2, "valid": 2, + "rank": 3 } }, + "init_t2_bis_assigns": { "alt-ergo": + { "total": 3, + "unknown": 3 }, + "qed": + { "total": 2, + "valid": 2 }, + "wp:main": + { "total": 5, + "valid": 2, + "unknown": 3 } }, + "init_t2_bis_loop_assigns": { "alt-ergo": + { "total": 2, + "unknown": 2 }, + "qed": + { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 3, + "valid": 1, + "unknown": 2 } }, + "init_t2_bis_exits": { "alt-ergo": + { "total": 1, + "unknown": 1 }, + "wp:main": + { "total": 1, + "unknown": 1 } }, + "init_t2_bis_ensures": { "alt-ergo": + { "total": 1, + "valid": 1, + "rank": 3 }, + "wp:main": + { "total": 1, + "valid": 1, + "rank": 3 } }, + "wp:section": { "alt-ergo": { "total": 9, + "valid": 3, + "unknown": 6, + "rank": 10 }, + "qed": { "total": 8, + "valid": 8 }, + "wp:main": { "total": 17, + "valid": 11, + "unknown": 6, + "rank": 10 } } } } } diff --git a/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.0.res.oracle b/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.0.res.oracle new file mode 100644 index 0000000000000000000000000000000000000000..476ee7df2e400ce497d6f2692ba419dd46bab530 --- /dev/null +++ b/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.0.res.oracle @@ -0,0 +1,117 @@ +# frama-c -wp -wp-timeout 90 -wp-steps 1500 [...] +[kernel] Parsing tests/wp_typed/user_init.i (no preprocessing) +[wp] Running WP plugin... +[wp] Loading driver 'share/wp.driver' +[wp] [CFG] Goal init_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t1_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t2_v1_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t2_v2_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t2_v3_exits : Valid (Unreachable) +[wp] Warning: Missing RTE guards +[wp] 91 goals scheduled +[wp] [Alt-Ergo] Goal typed_init_ensures : Valid +[wp] [Alt-Ergo] Goal typed_init_loop_invariant_Partial_preserved : Valid +[wp] [Qed] Goal typed_init_loop_invariant_Partial_established : Valid +[wp] [Alt-Ergo] Goal typed_init_loop_invariant_Range_preserved : Valid +[wp] [Qed] Goal typed_init_loop_invariant_Range_established : Valid +[wp] [Qed] Goal typed_init_loop_assigns_part1 : Valid +[wp] [Alt-Ergo] Goal typed_init_loop_assigns_part2 : Valid +[wp] [Qed] Goal typed_init_assigns : Valid +[wp] [Qed] Goal typed_init_loop_variant_decrease : Valid +[wp] [Qed] Goal typed_init_loop_variant_positive : Valid +[wp] [Alt-Ergo] Goal typed_init_t1_ensures : Valid +[wp] [Alt-Ergo] Goal typed_init_t1_loop_invariant_Partial_preserved : Valid +[wp] [Qed] Goal typed_init_t1_loop_invariant_Partial_established : Valid +[wp] [Alt-Ergo] Goal typed_init_t1_loop_invariant_Range_preserved : Valid +[wp] [Qed] Goal typed_init_t1_loop_invariant_Range_established : Valid +[wp] [Qed] Goal typed_init_t1_loop_assigns : Valid +[wp] [Qed] Goal typed_init_t1_assigns_part1 : Valid +[wp] [Qed] Goal typed_init_t1_assigns_part2 : Valid +[wp] [Alt-Ergo] Goal typed_init_t1_loop_variant_decrease : Valid +[wp] [Qed] Goal typed_init_t1_loop_variant_positive : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_bis_v1_ensures : Valid +[wp] [Qed] Goal typed_init_t2_bis_v1_exits : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_bis_v1_loop_invariant_Partial_preserved : Valid +[wp] [Qed] Goal typed_init_t2_bis_v1_loop_invariant_Partial_established : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_bis_v1_loop_invariant_Range_preserved : Valid +[wp] [Qed] Goal typed_init_t2_bis_v1_loop_invariant_Range_established : Valid +[wp] [Qed] Goal typed_init_t2_bis_v1_assert_Offset : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_bis_v1_loop_variant_decrease : Valid +[wp] [Qed] Goal typed_init_t2_bis_v1_loop_variant_positive : Valid +[wp] [Qed] Goal typed_init_t2_bis_v1_call_init_requires : Valid +[wp] [Qed] Goal typed_init_t2_bis_v1_call_init_requires_2 : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_bis_v2_ensures : Valid +[wp] [Qed] Goal typed_init_t2_bis_v2_exits : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_bis_v2_loop_invariant_Partial_preserved : Valid +[wp] [Qed] Goal typed_init_t2_bis_v2_loop_invariant_Partial_established : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_bis_v2_loop_invariant_Range_preserved : Valid +[wp] [Qed] Goal typed_init_t2_bis_v2_loop_invariant_Range_established : Valid +[wp] [Qed] Goal typed_init_t2_bis_v2_assert_Offset_i : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_bis_v2_loop_variant_decrease : Valid +[wp] [Qed] Goal typed_init_t2_bis_v2_loop_variant_positive : Valid +[wp] [Qed] Goal typed_init_t2_bis_v2_call_init_requires : Valid +[wp] [Qed] Goal typed_init_t2_bis_v2_call_init_requires_2 : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v1_ensures : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v1_loop_invariant_Partial_i_preserved : Valid +[wp] [Qed] Goal typed_init_t2_v1_loop_invariant_Partial_i_established : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v1_loop_invariant_Range_i_preserved : Valid +[wp] [Qed] Goal typed_init_t2_v1_loop_invariant_Range_i_established : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v1_loop_invariant_Partial_j_preserved : Valid +[wp] [Qed] Goal typed_init_t2_v1_loop_invariant_Partial_j_established : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v1_loop_invariant_Previous_i_preserved : Valid +[wp] [Qed] Goal typed_init_t2_v1_loop_invariant_Previous_i_established : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v1_loop_invariant_Range_j_preserved : Valid +[wp] [Qed] Goal typed_init_t2_v1_loop_invariant_Range_j_established : Valid +[wp] [Qed] Goal typed_init_t2_v1_assert_Last_j : Valid +[wp] [Qed] Goal typed_init_t2_v1_assert_Last_i : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v1_loop_variant_decrease : Valid +[wp] [Qed] Goal typed_init_t2_v1_loop_variant_positive : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v1_loop_variant_2_decrease : Valid +[wp] [Qed] Goal typed_init_t2_v1_loop_variant_2_positive : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v2_ensures : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v2_loop_invariant_Partial_i_preserved : Valid +[wp] [Qed] Goal typed_init_t2_v2_loop_invariant_Partial_i_established : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v2_loop_invariant_Range_i_preserved : Valid +[wp] [Qed] Goal typed_init_t2_v2_loop_invariant_Range_i_established : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v2_loop_invariant_Partial_j_preserved : Valid +[wp] [Qed] Goal typed_init_t2_v2_loop_invariant_Partial_j_established : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v2_loop_invariant_Previous_i_preserved : Valid +[wp] [Qed] Goal typed_init_t2_v2_loop_invariant_Previous_i_established : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v2_loop_invariant_Range_j_preserved : Valid +[wp] [Qed] Goal typed_init_t2_v2_loop_invariant_Range_j_established : Valid +[wp] [Qed] Goal typed_init_t2_v2_assert_Last_j : Valid +[wp] [Qed] Goal typed_init_t2_v2_assert_Last_i : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v2_loop_variant_decrease : Valid +[wp] [Qed] Goal typed_init_t2_v2_loop_variant_positive : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v2_loop_variant_2_decrease : Valid +[wp] [Qed] Goal typed_init_t2_v2_loop_variant_2_positive : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v3_ensures : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v3_loop_invariant_Partial_i_preserved : Valid +[wp] [Qed] Goal typed_init_t2_v3_loop_invariant_Partial_i_established : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v3_loop_invariant_Range_i_preserved : Valid +[wp] [Qed] Goal typed_init_t2_v3_loop_invariant_Range_i_established : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v3_loop_invariant_Partial_j_preserved : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v3_loop_invariant_Partial_j_established : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v3_loop_invariant_Range_j_preserved : Valid +[wp] [Qed] Goal typed_init_t2_v3_loop_invariant_Range_j_established : Valid +[wp] [Qed] Goal typed_init_t2_v3_assert_Last_j : Valid +[wp] [Qed] Goal typed_init_t2_v3_assert_Last_i : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v3_loop_variant_decrease : Valid +[wp] [Qed] Goal typed_init_t2_v3_loop_variant_positive : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v3_loop_variant_2_decrease : Valid +[wp] [Qed] Goal typed_init_t2_v3_loop_variant_2_positive : Valid +[wp] Proved goals: 91 / 91 + Qed: 51 + Alt-Ergo: 40 +[wp] Report in: 'tests/wp_typed/oracle_qualif/user_init.0.report.json' +[wp] Report out: 'tests/wp_typed/result_qualif/user_init.0.report.json' +------------------------------------------------------------- +Functions WP Alt-Ergo Total Success +init 6 4 (80..104) 10 100% +init_t1 6 4 (12..24) 10 100% +init_t2_v1 9 8 (40..52) 17 100% +init_t2_v2 9 8 (32..44) 17 100% +init_t2_v3 7 8 (28..40) 15 100% +init_t2_bis_v1 7 4 (208..256) 11 100% +init_t2_bis_v2 7 4 (192..240) 11 100% +------------------------------------------------------------- diff --git a/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.1.res.oracle b/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.1.res.oracle new file mode 100644 index 0000000000000000000000000000000000000000..ef5a6f0f00aca8f8c21e854555b7f7a3dde96813 --- /dev/null +++ b/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.1.res.oracle @@ -0,0 +1,49 @@ +# frama-c -wp -wp-timeout 90 -wp-steps 1500 [...] +[kernel] Parsing tests/wp_typed/user_init.i (no preprocessing) +[wp] Running WP plugin... +[wp] Loading driver 'share/wp.driver' +[wp] [CFG] Goal init_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t1_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t2_v1_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t2_v2_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t2_v3_exits : Valid (Unreachable) +[wp] Warning: Missing RTE guards +[wp] 23 goals scheduled +[wp] [Qed] Goal typed_init_t2_bis_v2_loop_assigns_part1 : Valid +[wp] Warning: creating session directory `tests/wp_typed/result_qualif/user_init-session-1' +[wp] Warning: creating session directory `tests/wp_typed/result_qualif/user_init-session-1/wp' +[wp] [Tactical] Goal typed_init_t2_bis_v2_loop_assigns_part2 : Valid +[wp] [Tactical] Goal typed_init_t2_bis_v2_loop_assigns_part3 : Valid +[wp] [Tactical] Goal typed_init_t2_bis_v2_assigns_exit_part1 : Valid +[wp] [Tactical] Goal typed_init_t2_bis_v2_assigns_exit_part2 : Valid +[wp] [Qed] Goal typed_init_t2_bis_v2_assigns_exit_part3 : Valid +[wp] [Tactical] Goal typed_init_t2_bis_v2_assigns_normal_part1 : Valid +[wp] [Tactical] Goal typed_init_t2_bis_v2_assigns_normal_part2 : Valid +[wp] [Qed] Goal typed_init_t2_v2_loop_assigns_part1 : Valid +[wp] [Tactical] Goal typed_init_t2_v2_loop_assigns_part2 : Valid +[wp] [Tactical] Goal typed_init_t2_v2_loop_assigns_part3 : Valid +[wp] [Qed] Goal typed_init_t2_v2_loop_assigns_2_part1 : Valid +[wp] [Tactical] Goal typed_init_t2_v2_loop_assigns_2_part2 : Valid +[wp] [Tactical] Goal typed_init_t2_v2_loop_assigns_2_part3 : Valid +[wp] [Tactical] Goal typed_init_t2_v2_assigns_part1 : Valid +[wp] [Tactical] Goal typed_init_t2_v2_assigns_part2 : Valid +[wp] [Qed] Goal typed_init_t2_v3_loop_assigns_part1 : Valid +[wp] [Tactical] Goal typed_init_t2_v3_loop_assigns_part2 : Valid +[wp] [Tactical] Goal typed_init_t2_v3_loop_assigns_part3 : Valid +[wp] [Qed] Goal typed_init_t2_v3_loop_assigns_2_part1 : Valid +[wp] [Tactical] Goal typed_init_t2_v3_loop_assigns_2_part2 : Valid +[wp] [Tactical] Goal typed_init_t2_v3_assigns_part1 : Valid +[wp] [Tactical] Goal typed_init_t2_v3_assigns_part2 : Valid +[wp] Proved goals: 23 / 23 + Qed: 11 + Alt-Ergo: 0 (unsuccess: 12) + Script: 12 +[wp] Updated session with 12 new valid scripts. +[wp] Report in: 'tests/wp_typed/oracle_qualif/user_init.1.report.json' +[wp] Report out: 'tests/wp_typed/result_qualif/user_init.1.report.json' +------------------------------------------------------------- +Functions WP Alt-Ergo Total Success +init_t2_v2 3 - (16..28) 8 100% +init_t2_v3 4 - (20..32) 7 100% +init_t2_bis_v2 4 - (28..40) 8 100% +------------------------------------------------------------- diff --git a/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.2.res.oracle b/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.2.res.oracle new file mode 100644 index 0000000000000000000000000000000000000000..17ce10c2bdd03887ea8140231d688fabb6510811 --- /dev/null +++ b/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.2.res.oracle @@ -0,0 +1,37 @@ +# frama-c -wp -wp-timeout 90 -wp-steps 300 [...] +[kernel] Parsing tests/wp_typed/user_init.i (no preprocessing) +[wp] Running WP plugin... +[wp] Loading driver 'share/wp.driver' +[wp] [CFG] Goal init_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t1_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t2_v1_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t2_v2_exits : Valid (Unreachable) +[wp] [CFG] Goal init_t2_v3_exits : Valid (Unreachable) +[wp] Warning: Missing RTE guards +[wp] 16 goals scheduled +[wp] [Qed] Goal typed_init_t2_bis_v1_loop_assigns_part1 : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_bis_v1_loop_assigns_part2 : Unsuccess +[wp] [Alt-Ergo] Goal typed_init_t2_bis_v1_loop_assigns_part3 : Unsuccess +[wp] [Qed] Goal typed_init_t2_bis_v1_assigns_exit_part1 : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_bis_v1_assigns_exit_part2 : Unsuccess +[wp] [Qed] Goal typed_init_t2_bis_v1_assigns_exit_part3 : Valid +[wp] [Qed] Goal typed_init_t2_bis_v1_assigns_normal_part1 : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_bis_v1_assigns_normal_part2 : Unsuccess +[wp] [Qed] Goal typed_init_t2_v1_loop_assigns_part1 : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v1_loop_assigns_part2 : Unsuccess +[wp] [Alt-Ergo] Goal typed_init_t2_v1_loop_assigns_part3 : Unsuccess +[wp] [Qed] Goal typed_init_t2_v1_loop_assigns_2_part1 : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v1_loop_assigns_2_part2 : Unsuccess +[wp] [Alt-Ergo] Goal typed_init_t2_v1_loop_assigns_2_part3 : Unsuccess +[wp] [Qed] Goal typed_init_t2_v1_assigns_part1 : Valid +[wp] [Alt-Ergo] Goal typed_init_t2_v1_assigns_part2 : Unsuccess +[wp] Proved goals: 7 / 16 + Qed: 7 + Alt-Ergo: 0 (unsuccess: 9) +[wp] Report in: 'tests/wp_typed/oracle_qualif/user_init.2.report.json' +[wp] Report out: 'tests/wp_typed/result_qualif/user_init.2.report.json' +------------------------------------------------------------- +Functions WP Alt-Ergo Total Success +init_t2_v1 3 - 8 37.5% +init_t2_bis_v1 4 - 8 50.0% +------------------------------------------------------------- diff --git a/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.i.0.report.json b/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.i.0.report.json index 1651d4db1362d3b7af4041cfded35531c28aef00..0b74bede002bfacbd63c33f39bd945aeb2728a45 100644 --- a/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.i.0.report.json +++ b/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.i.0.report.json @@ -1,6 +1,8 @@ -{ "wp:global": { "alt-ergo": { "total": 4, "valid": 4, "rank": 19 }, - "qed": { "total": 4, "valid": 4 }, - "wp:main": { "total": 8, "valid": 8, "rank": 19 } }, +{ "wp:global": { "alt-ergo": { "total": 27, "valid": 16, "unknown": 11, + "rank": 19 }, + "qed": { "total": 27, "valid": 27 }, + "wp:main": { "total": 54, "valid": 43, "unknown": 11, + "rank": 19 } }, "wp:functions": { "init": { "init_loop_invariant_Partial": { "alt-ergo": { "total": 1, "valid": 1, @@ -47,4 +49,211 @@ "valid": 4 }, "wp:main": { "total": 8, "valid": 8, - "rank": 19 } } } } } + "rank": 19 } } }, + "init_t1": { "init_t1_loop_invariant_Partial": { "alt-ergo": + { "total": 1, + "valid": 1, + "rank": 4 }, + "qed": + { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 2, + "valid": 2, + "rank": 4 } }, + "init_t1_loop_invariant_Range": { "alt-ergo": + { "total": 1, + "valid": 1, + "rank": 2 }, + "qed": + { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 2, + "valid": 2, + "rank": 2 } }, + "init_t1_assigns": { "qed": { "total": 2, + "valid": 2 }, + "wp:main": { "total": 2, + "valid": 2 } }, + "init_t1_loop_assigns": { "qed": { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 1, + "valid": 1 } }, + "init_t1_ensures": { "alt-ergo": { "total": 1, + "valid": 1, + "rank": 3 }, + "wp:main": { "total": 1, + "valid": 1, + "rank": 3 } }, + "wp:section": { "alt-ergo": { "total": 3, + "valid": 3, + "rank": 4 }, + "qed": { "total": 5, + "valid": 5 }, + "wp:main": { "total": 8, + "valid": 8, + "rank": 4 } } }, + "init_t2": { "init_t2_assert_i": { "qed": { "total": 1, + "valid": 1 }, + "wp:main": { "total": 1, + "valid": 1 } }, + "init_t2_assert_j": { "qed": { "total": 1, + "valid": 1 }, + "wp:main": { "total": 1, + "valid": 1 } }, + "init_t2_loop_invariant_Previous_i": + { "alt-ergo": { "total": 1, "valid": 1, + "rank": 5 }, + "qed": { "total": 1, "valid": 1 }, + "wp:main": { "total": 2, "valid": 2, + "rank": 5 } }, + "init_t2_loop_invariant_Partial_j": + { "alt-ergo": { "total": 1, "valid": 1, + "rank": 8 }, + "qed": { "total": 1, "valid": 1 }, + "wp:main": { "total": 2, "valid": 2, + "rank": 8 } }, + "init_t2_loop_invariant_Range_j": { "alt-ergo": + { "total": 1, + "valid": 1, + "rank": 3 }, + "qed": + { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 2, + "valid": 2, + "rank": 3 } }, + "init_t2_loop_invariant_Partial_i": + { "alt-ergo": { "total": 1, "valid": 1, + "rank": 11 }, + "qed": { "total": 1, "valid": 1 }, + "wp:main": { "total": 2, "valid": 2, + "rank": 11 } }, + "init_t2_loop_invariant_Range_i": { "alt-ergo": + { "total": 1, + "valid": 1, + "rank": 2 }, + "qed": + { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 2, + "valid": 2, + "rank": 2 } }, + "init_t2_assigns": { "alt-ergo": { "total": 1, + "unknown": 1 }, + "qed": { "total": 1, + "valid": 1 }, + "wp:main": { "total": 2, + "valid": 1, + "unknown": 1 } }, + "init_t2_loop_assigns_2": { "alt-ergo": + { "total": 2, + "unknown": 2 }, + "qed": { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 3, + "valid": 1, + "unknown": 2 } }, + "init_t2_loop_assigns": { "alt-ergo": + { "total": 2, + "unknown": 2 }, + "qed": { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 3, + "valid": 1, + "unknown": 2 } }, + "init_t2_ensures": { "alt-ergo": { "total": 1, + "valid": 1, + "rank": 2 }, + "wp:main": { "total": 1, + "valid": 1, + "rank": 2 } }, + "wp:section": { "alt-ergo": { "total": 11, + "valid": 6, + "unknown": 5, + "rank": 11 }, + "qed": { "total": 10, + "valid": 10 }, + "wp:main": { "total": 21, + "valid": 16, + "unknown": 5, + "rank": 11 } } }, + "init_t2_bis": { "init_requires_2": { "qed": { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 1, + "valid": 1 } }, + "init_requires": { "qed": { "total": 1, + "valid": 1 }, + "wp:main": { "total": 1, + "valid": 1 } }, + "init_t2_bis_assert_i": { "qed": + { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 1, + "valid": 1 } }, + "init_t2_bis_loop_invariant_Partial_i": + { "alt-ergo": { "total": 1, + "valid": 1, + "rank": 10 }, + "qed": { "total": 1, "valid": 1 }, + "wp:main": { "total": 2, "valid": 2, + "rank": 10 } }, + "init_t2_bis_loop_invariant_Range_i": + { "alt-ergo": { "total": 1, + "valid": 1, + "rank": 3 }, + "qed": { "total": 1, "valid": 1 }, + "wp:main": { "total": 2, "valid": 2, + "rank": 3 } }, + "init_t2_bis_assigns": { "alt-ergo": + { "total": 3, + "unknown": 3 }, + "qed": + { "total": 2, + "valid": 2 }, + "wp:main": + { "total": 5, + "valid": 2, + "unknown": 3 } }, + "init_t2_bis_loop_assigns": { "alt-ergo": + { "total": 2, + "unknown": 2 }, + "qed": + { "total": 1, + "valid": 1 }, + "wp:main": + { "total": 3, + "valid": 1, + "unknown": 2 } }, + "init_t2_bis_exits": { "alt-ergo": + { "total": 1, + "unknown": 1 }, + "wp:main": + { "total": 1, + "unknown": 1 } }, + "init_t2_bis_ensures": { "alt-ergo": + { "total": 1, + "valid": 1, + "rank": 3 }, + "wp:main": + { "total": 1, + "valid": 1, + "rank": 3 } }, + "wp:section": { "alt-ergo": { "total": 9, + "valid": 3, + "unknown": 6, + "rank": 10 }, + "qed": { "total": 8, + "valid": 8 }, + "wp:main": { "total": 17, + "valid": 11, + "unknown": 6, + "rank": 10 } } } } } diff --git a/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.res.oracle b/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.res.oracle deleted file mode 100644 index 6f23e12122e5977d74d6f3134b3006ec57b5ee79..0000000000000000000000000000000000000000 --- a/src/plugins/wp/tests/wp_typed/oracle_qualif/user_init.res.oracle +++ /dev/null @@ -1,23 +0,0 @@ -# frama-c -wp -wp-timeout 90 -wp-steps 1500 [...] -[kernel] Parsing tests/wp_typed/user_init.i (no preprocessing) -[wp] Running WP plugin... -[wp] Loading driver 'share/wp.driver' -[wp] Warning: Missing RTE guards -[wp] 8 goals scheduled -[wp] [Alt-Ergo] Goal typed_init_ensures : Valid -[wp] [Alt-Ergo] Goal typed_init_loop_invariant_Partial_preserved : Valid -[wp] [Qed] Goal typed_init_loop_invariant_Partial_established : Valid -[wp] [Alt-Ergo] Goal typed_init_loop_invariant_Range_preserved : Valid -[wp] [Qed] Goal typed_init_loop_invariant_Range_established : Valid -[wp] [Qed] Goal typed_init_loop_assigns_part1 : Valid -[wp] [Alt-Ergo] Goal typed_init_loop_assigns_part2 : Valid -[wp] [Qed] Goal typed_init_assigns : Valid -[wp] Proved goals: 8 / 8 - Qed: 4 - Alt-Ergo: 4 -[wp] Report in: 'tests/wp_typed/oracle_qualif/user_init.0.report.json' -[wp] Report out: 'tests/wp_typed/result_qualif/user_init.0.report.json' -------------------------------------------------------------- -Functions WP Alt-Ergo Total Success -init 4 4 (80..104) 8 100% -------------------------------------------------------------- diff --git a/src/plugins/wp/tests/wp_typed/user_init.i b/src/plugins/wp/tests/wp_typed/user_init.i index a7ab761501f124800831f0f654a28a71849a0c4f..a34d4664bb4cdb7cdbe9e5738e75b0b78a2a5de0 100644 --- a/src/plugins/wp/tests/wp_typed/user_init.i +++ b/src/plugins/wp/tests/wp_typed/user_init.i @@ -1,13 +1,162 @@ +/* run.config_qualif + EXECNOW: rm -rf @PTEST_DIR@/result@PTEST_CONFIG@/@PTEST_NAME@-session-1/ + OPT: -wp-prop=-lack,-tactic + OPT: -wp-prop=tactic -wp-auto=wp:split -session @PTEST_DIR@/result@PTEST_CONFIG@/@PTEST_NAME@-session-@PTEST_NUMBER@ + OPT: -wp-prop=lack -wp-steps 300 + */ /*@ requires \valid(a+(0..n-1)) ; @ requires n >= 0 ; - @ ensures \forall int k ; 0 <= k < n ==> a[k] == v ; @ assigns a[0..n-1] ; + @ ensures \forall int k ; 0 <= k < n ==> a[k] == v ; + @ exits \false; */ void init( int * a , int n , int v ) { - /*@ loop invariant Range: 0 <= i <= n ; + /*@ loop assigns Zone: i,a[0..n-1] ; + @ loop invariant Range: 0 <= i <= n ; @ loop invariant Partial: \forall int k ; 0 <= k < i ==> a[k] == v ; - @ loop assigns i,a[0..n-1] ; + @ loop variant Decr_i: n - i ; */ for (int i = 0 ; i < n ; i++) a[i] = v ; } +//------------------------- +int t1[10]; +/*@ ensures \forall integer k; 0 <= k < 10 ==> t1[k] == v ; + @ exits \false; + @ assigns t1[0..9] ; +*/ +void init_t1(int v) { + unsigned i; + /*@ loop assigns Zone: i,t1[0..9] ; + @ loop invariant Range: 0 <= i <= 10 ; + @ loop invariant Partial: \forall integer k ; 0 <= k < i ==> t1[k] ≡ v ; + @ loop variant Decr: 10 - i ; + */ + for (i = 0 ; i < 10 ; i++) t1[i] = v ; +} +//------------------------- +int t2[10][20]; +/*@ ensures \forall integer k, l; 0 <= k < 10 && 0 <= l < 20 ==> t2[k][l] == v; + @ exits \false; + @ assigns lack: t2[0..9][0..19]; + */ +void init_t2_v1(int v) { + + unsigned i,j; + /*@ loop assigns lack: Zone_i: i, j, t2[0..9][0..19]; + @ loop invariant Range_i: 0 <= i <= 10 ; + @ loop invariant Partial_i: \forall integer k,l; 0 <= k < i && 0 <= l < 20 ==> t2[k][l] == v; + @ loop variant Decr_i: 10 - i ; + */ + for(i = 0; i <= 9; i++) { + /*@ loop assigns lack: Zone_j: j, t2[0..9][0..19]; + @ loop invariant Range_j: 0 <= j <= 20 ; + @ loop invariant Partial_j: \forall integer l; 0 <= l < j ==> t2[i][l] == v; + @ loop invariant Previous_i: \forall integer k,l; 0 <= k < i && 0 <= l < 20 ==> t2[k][l] == \at(t2[k][l], LoopEntry); + @ loop variant Decr_j: 20 - j ; + */ + for(j = 0; j <= 19; j++) { + t2[i][j] = v; + } + //@ assert Last_j: j==20; + ; + } + //@ assert Last_i: i==10; + ; +} +//------------------------- +/*@ ensures \forall integer k, l; 0 <= k < 10 && 0 <= l < 20 ==> t2[k][l] == v; + @ exits \false; + @ assigns tactic: t2[..][..]; + */ +void init_t2_v2(int v) { + + unsigned i,j; + /*@ loop assigns tactic: Zone_i: i, j, t2[..][..]; + @ loop invariant Range_i: 0 <= i <= 10 ; + @ loop invariant Partial_i: \forall integer k,l; 0 <= k < i && 0 <= l < 20 ==> t2[k][l] == v; + @ loop variant Decr_i: 10 - i ; + */ + for(i = 0; i <= 9; i++) { + /*@ loop assigns tactic: Zone_j: j, t2[..][..]; + @ loop invariant Range_j: 0 <= j <= 20 ; + @ loop invariant Partial_j: \forall integer l; 0 <= l < j ==> t2[i][l] == v; + @ loop invariant Previous_i: \forall integer k,l; 0 <= k < i && 0 <= l < 20 ==> t2[k][l] == \at(t2[k][l], LoopEntry); + @ loop variant Decr_j: 20 - j ; + */ + for(j = 0; j <= 19; j++) { + t2[i][j] = v; + } + //@ assert Last_j: j==20; + ; + } + //@ assert Last_i: i==10; + ; +} +//------------------------- +//@ predicate MemSet20(int t2[20], integer n, integer v) = n <= 20 && \forall integer k ; 0 <= k < n ==> t2[k] == v; + +/*@ ensures \forall integer k; 0 <= k < 10 ==> MemSet20(t2[k], 20, v); + @ exits \false; + @ assigns tactic: t2[..][..]; + */ +void init_t2_v3(int v) { + + unsigned i,j; + /*@ loop assigns tactic: Zone_i: i, j, t2[..][..]; + @ loop invariant Range_i: 0 <= i <= 10 ; + @ loop invariant Partial_i: \forall integer k; 0 <= k < i ==> MemSet20(t2[k], 20, v); + @ loop variant V_i: 10 - i ; + */ + for(i = 0; i <= 9; i++) { + /*@ loop assigns tactic: Zone_j: j, t2[i][..]; + @ loop invariant Range_j: 0 <= j <= 20 ; + @ loop invariant Partial_j: MemSet20(t2[i], j, v); + @ loop variant Decr_j: 20 - j ; + */ + for(j = 0; j <= 19; j++) { + t2[i][j] = v; + } + //@ assert Last_j: j==20; + ; + } + //@ assert Last_i: i==10; + ; +} +//------------------------- +/*@ ensures \forall integer k, l; 0 <= k < 10 && 0 <= l < 20 ==> t2[k][l] == v; + @ assigns lack: t2[0..9][0..19]; + @ exits \false; + */ +void init_t2_bis_v1(int v) { + + unsigned i; + /*@ loop assigns lack: Zone: i, t2[0..9][0..19]; + @ loop invariant Range: 0 <= i <= 10 ; + @ loop invariant Partial: \forall integer k,l; 0 <= k < i && 0 <= l < 20 ==> t2[k][l] == v; + @ loop variant Decr: 10 - i ; + */ + for(i = 0; i <= 9; i++) { + init(&t2[i][0], 20, v); + //@ assert Offset: &t2[i][0] == &t2[0][0] + 20*i; + } +} +//------------------------- +/*@ ensures \forall integer k, l; 0 <= k < 10 && 0 <= l < 20 ==> t2[k][l] == v; + @ assigns tactic: t2[..][..]; + @ exits \false; + */ +void init_t2_bis_v2(int v) { + + unsigned i; + /*@ loop assigns tactic: Zone: i, t2[..][..]; + @ loop invariant Range: 0 <= i <= 10 ; + @ loop invariant Partial: \forall integer k,l; 0 <= k < i && 0 <= l < 20 ==> t2[k][l] == v; + @ loop variant Decr: 10 - i ; + */ + for(i = 0; i <= 9; i++) { + init(&t2[i][0], 20, v); + //@ assert Offset_i: &t2[i][0] == &t2[0][0] + 20*i; + ; + } +}