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Proof step 30 from proof rg2-lem1-term-unfair (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL N = n5 ∧ S = s13 ∧ N' = N'' + 1 until ¬ R1(pm, S', S'')] ∥nf false ::- [PL □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ (□ R2(pm, S', S'') → ◇ last)] ], □ (N = N' ∧ ¬ N' < N''), boolvar ∨ n2 = N + 1 ∧ N = N'' + 1 until Boolvar, INDHYP-nat(n2) ∧ INDHYP-nat0(n2), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), I(pm, s2), R1(pm, s3, S), R2(pm, s3, S), N ≤ n2, I(pm, s), boolvar1 → s2 = s3 ∧ (boolvar ↔ boolvar0), n2 = n5 + 1, G1(pm, s2, s3), ¬ R1(pm, s3, s13), ¬ boolvar1 ⊦ ◇ last

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL N = n5 ∧ S = s13 ∧ N' = N'' + 1 until ¬ R1(pm, S', S'')] ∥nf false ::- [PL □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ (□ R2(pm, S', S'') → ◇ last)] ], □ (N = N' ∧ ¬ N' < N''), boolvar ∨ n5 = N ∧ N = N'' + 1 until Boolvar, INDHYP-nat(n5 + 1) ∧ INDHYP-nat0(n5 + 1), R2(pm, s2, S), I(pm, s3), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), I(pm, s2), R1(pm, s3, S), R2(pm, s3, S), N ≤ n5 + 1, I(pm, s), G1(pm, s2, s3), R2(pm, s2, s3), I(pm, S), ¬ R1(pm, s3, s13) ⊦ ◇ last

Rule argument

Additional information

Used simplifier rules: g1-r2: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ G1(pm, s, s0) ∧ I(pm, s) → R2(pm, s, s0);%r2-trans: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R2(pm, s, s0) ∧ R2(pm, s0, s1) ∧ I(pm, s) → R2(pm, s, s1);%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);%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2