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Proof step 170 from proof rg2-lem2-term-unfair (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL N = n43 ∧ S = s43 ∧ N' = N'' + 1 until last ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL S = s42 ∧ N = n42 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ¬ □ R2(pm, S', S'')] ], □ (N = N' ∧ ¬ N' < N''), INDHYP-nat(n43 + 1) ∧ INDHYP-nat0(n2), R2(pm, s2, S), I(pm, s3), I(pm, s2), 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), N ≤ n43 + 1, I(pm, s), G2(pm, s2, s2), R2(pm, s2, s42), G1(pm, s2, s3), R1(pm, s3, s43), n42 ≤ n43 + 1, R2(pm, s2, s3), R1(pm, s2, s2), I(pm, s42), I(pm, s43), I(pm, S), boolvar1 → s2 = s3 ∧ boolvar0 ∧ n2 = n4, N < n43 + 1 ⊦ ◇ last

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%lels-03: ⊦ m < n → m ≤ n; from specification nat