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Proof step 82 from proof rg2-lem2-term-unfair (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), N0 = N0'' + 1 until Boolvar, [:S | Boolvar ::- [PL N = n13 ∧ S = s13 ∧ N' = N'' + 1 until last ∧ 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' ∧ ¬ N' < N''), INDHYP-nat(n13 + 1) ∧ INDHYP-nat0(N0 + 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 ≤ n13 + 1, I(pm, s), G1(pm, s2, s3), R1(pm, s3, s13), R2(pm, s2, s3), I(pm, s13), I(pm, S) ⊦ [:S | Boolvar ::- [PL N' = N'' + 1 until last ∧ 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)] ] ∧ N0 = N0'' +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

Rule argument

Additional information

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