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Proof step 198 from proof rg2-lem2-term-unfair (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL N = n48 ∧ S = s48 ∧ N' = N'' + 1 until last ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL S = s47 ∧ N = n47 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ◇ last] ], □ (N = N' ∧ ¬ N' < N''), INDHYP-nat(n48 + 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 ≤ n48 + 1, I(pm, s), G2(pm, s2, s2), R2(pm, s2, s47), G1(pm, s2, s3), R1(pm, s3, s48), n47 ≤ n48 + 1, R2(pm, s2, s3), R1(pm, s2, s2), I(pm, s47), I(pm, s48), I(pm, S), boolvar1 → s2 = s3 ∧ boolvar0 ∧ n2 = n4, ¬ N < n48 + 1 ⊦ ◇ last

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 199:
□ (N = N' ∧ ¬ N' < N''), [:S | Boolvar ::- [PL N = n48 ∧ S = s48 ∧ N' = N'' + 1 until last ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL S = s47 ∧ N = n47 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ◇ last] ], □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), INDHYP-nat(n48 + 1) ∧ INDHYP-nat0(n2), N = n48 + 1, R2(pm, s3, S), R1(pm, s3, S), Pre2(pm, s), Pre1(pm, s), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), I(pm, s2), I(pm, s3), R2(pm, s2, S), I(pm, S), I(pm, s48), I(pm, s47), R1(pm, s2, s2), R2(pm, s2, s3), n47 ≤ n48 + 1, R1(pm, s3, s48), G1(pm, s2, s3), R2(pm, s2, s47), G2(pm, s2, s2), I(pm, s), boolvar1 → s2 = s3 ∧ boolvar0 ∧ n2 = n4 ⊦ ◇ last

Rule argument

Additional information

Used simplifier rules: ref-1: ⊦ ¬ n < n; from specification nat-basic1%lep-02: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; from specification nat%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2%le-one: ⊦ m ≤ n + 1 ∧ n < n0 → m ≤ n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic1%eqle-one: ⊦ m = n + 1 ∧ n < n0 → m ≤ n0; (forward) from specification nat%les: ⊦ m < n → (n ≤ m + 1 ↔ n = m + 1); 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