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Proof step 52 from proof rg2-lem2-term-unfair (previous step)

□ (N = N' ∧ ¬ N' < N''), [:S | Boolvar0 ∨ Boolvar ::- [PL N = n13 ∧ N' = N'' + 1 until last ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL N = n0 ∧ S = s1 ∧ □ ¬ N' < N'' ∧ ¬ □ R2(pm, S', S'')] ], □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), boolvar ∨ n3 = N0 + 1 ∧ N0 = N0'' + 1 until Boolvar0, (INDHYP-nat(n13 + 1) ∧ INDHYP-nat0(n2)) ∧ INDHYP-nat1(n3), Pre2(pm, s), Pre1(pm, s), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), I(pm, s2), R1(pm, s3, S), R2(pm, s3, S), N ≤ n13 + 1, I(pm, s), boolvar3 → s2 = s3 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2) ∧ n3 = n5, ¬ boolvar, ¬ boolvar0, G2(pm, s2, s3), ¬ n13 + 1 < n0, ¬ R2(pm, s3, s1), ¬ boolvar3 ⊦ ◇ last

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
□ (N = N' ∧ ¬ N' < N''), [:S | Boolvar0 ∨ Boolvar ::- [PL N = n13 ∧ N' = N'' + 1 until last ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL N = n0 ∧ S = s1 ∧ □ ¬ N' < N'' ∧ ¬ □ R2(pm, S', S'')] ], □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), N0 = N0'' + 1 until Boolvar0, (INDHYP-nat(n13 + 1) ∧ INDHYP-nat0(n2)) ∧ INDHYP-nat1(N0 + 1), R1(pm, s2, S), I(pm, s3), Pre2(pm, s), Pre1(pm, s), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), I(pm, s2), R1(pm, s3, S), R2(pm, s3, S), N ≤ n13 + 1, I(pm, s), G2(pm, s2, s3), n0 ≤ n13 + 1, R1(pm, s2, s3), I(pm, S), ¬ R2(pm, s3, s1) ⊦ ◇ last

Rule argument

Additional information

Used simplifier rules: g2-r1: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ G2(pm, s, s0) ∧ I(pm, s) → R1(pm, s, s0);%r1-trans: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R1(pm, s, s0) ∧ R1(pm, s0, s1) ∧ I(pm, s) → R1(pm, s, s1);%i-r1-i: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R1(pm, s, s0) ∧ I(pm, s) → I(pm, s0);%i-r2-i: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R2(pm, s, s0) ∧ I(pm, s) → I(pm, s0);%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat