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Proof step 112 from proof rg2-lem2-term-unfair (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL N = n22 ∧ S = s22 ∧ N' = N'' + 1 until last ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL S = s23 ∧ N = n23 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ◇ last] ], □ (N = N' ∧ ¬ N' < N''), boolvar ∨ n2 = N0 + 1 ∧ N0 = N0'' + 1 until Boolvar, INDHYP-nat(n3) ∧ 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 ≤ n3, I(pm, s), boolvar1 → s2 = s3 ∧ (boolvar ↔ boolvar0) ∧ n2 = n4, n3 = n22 + 1, G1(pm, s2, s2), R1(pm, s2, s22), G2(pm, s2, s3), R2(pm, s3, s23), ¬ n22 + 1 < n23 ⊦ ◇ last

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 113:
□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | Boolvar ::- [PL N = n22 ∧ S = s22 ∧ N' = N'' + 1 until last ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf false ::- [PL S = s23 ∧ N = n23 ∧ □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ ◇ last] ], □ (N = N' ∧ ¬ N' < N''), boolvar ∨ n2 = N0 + 1 ∧ N0 = N0'' + 1 until Boolvar, INDHYP-nat(n22 + 1) ∧ INDHYP-nat0(n2), 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), N ≤ n22 + 1, I(pm, s), G1(pm, s2, s2), R1(pm, s2, s22), G2(pm, s2, s3), R2(pm, s3, s23), n23 ≤ n22 + 1, R2(pm, s2, s2), R1(pm, s2, s3), I(pm, s22), I(pm, S), I(pm, s23), boolvar1 → s2 = s3 ∧ (boolvar ↔ boolvar0) ∧ n2 = n4 ⊦ ◇ last

Rule argument

Additional information

Used simplifier rules: i-r1-i: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R1(pm, s, s0) ∧ I(pm, s) → I(pm, s0);%g2-r1: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ G2(pm, s, s0) ∧ I(pm, s) → R1(pm, s, s0);%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);%r1-trans: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R1(pm, s, s0) ∧ R1(pm, s0, s1) ∧ I(pm, s) → R1(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);%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat