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Proof step 144 from proof rg2-lem1-term-unfair (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), N = N'' + 1 until Boolvar, [:S | Boolvar ::- [PL N = n25 ∧ S = s33 ∧ N' = N'' + 1 until ¬ R1(pm, S', S'') ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL S = s34 ∧ N = n26 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ◇ last] ], □ (N = N' ∧ ¬ N' < N''), INDHYP-nat(N + 1) ∧ INDHYP-nat0(N + 1), n25 = N, R1(pm, s2, S), I(pm, s2), I(pm, s3), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), R1(pm, s3, S), R2(pm, s3, S), I(pm, s), G1(pm, s2, s2), R1(pm, s2, s33), G2(pm, s2, s3), R2(pm, s3, s34), n26 ≤ N + 1, R2(pm, s2, s2), R1(pm, s2, s3), I(pm, s33), I(pm, S), I(pm, s34), boolvar1 → s2 = s3 ∧ (boolvar ↔ boolvar0) ⊦ [:S | Boolvar ::- [PL N' = N'' + 1 until ¬ R1(pm, S', S'') ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(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'' +1 until Boolvar ∧ □ (N = N' ∧ ¬ N' < N'') ∧ □ (R1(pm, S', S'') ∧ R2(pm, S', S'')) ∧ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ Pre1(pm, s) ∧ Pre2(pm, s) ∧ I(pm, S) ∧ I(pm, s), ◇ last

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 145:
□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), N = N'' + 1 until Boolvar, [:S | Boolvar ::- [PL N = n25 ∧ S = s33 ∧ N' = N'' + 1 until ¬ R1(pm, S', S'') ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL S = s34 ∧ N = n26 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ◇ last] ], □ (N = N' ∧ ¬ N' < N''), INDHYP-nat(N + 1) ∧ INDHYP-nat0(N + 1), n25 = N, R1(pm, s2, S), I(pm, s2), I(pm, s3), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), R1(pm, s3, S), R2(pm, s3, S), I(pm, s), G1(pm, s2, s2), R1(pm, s2, s33), G2(pm, s2, s3), R2(pm, s3, s34), n26 ≤ N + 1, R2(pm, s2, s2), R1(pm, s2, s3), I(pm, s33), I(pm, S), I(pm, s34), boolvar1 → s2 = s3 ∧ (boolvar ↔ boolvar0) ⊦ ◇ last, [:S | Boolvar ::- [PL N' = N'' + 1 until ¬ R1(pm, S', S'') ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(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)] ]

Rule argument

Additional information

Used simplifier rules: succ: ⊦ m +1 = m + 1; from specification nat-basic2