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Proof step 8 from proof rg2-not-pre1-unfair (previous step)

boolvar ∨ n = N + 1 ∧ N = N'' + 1 until Boolvar, [:S | Boolvar ::- [PL ¬ Pre1(pm, S)] ∥nf false ::- [PL S = s0]], \A ∀ N, Boolvar, Pre1, pm, S, Post2, s, G2, R2, R1, G1, Post1, I, Pre2. N < n → N = N'' +1 until Boolvar ∧ [:S | Boolvar ::- [PL ¬ Pre1(pm, S)] ∥nf false ::- [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(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) → (R1(pm, S', S'') ∧ R2(pm, S', S'')) -+-> (last ⊃ Post1(pm, s, S) ∧ Post2(pm, s, S);G1(pm, S, S') ∨ G2(pm, S, S')), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s1), Pre2(pm, s), I(pm, s1), I(pm, s), boolvar1 → s1 = s2 ∧ (boolvar ↔ boolvar0) ∧ n = n0, ¬ boolvar, G2(pm, s1, s2), ¬ R2(pm, s2, s0), ¬ boolvar1 ⊦ (G1(pm, s1, s2) ∨ G2(pm, s1, s2)) ∧ (R1(pm, s2, S) ∧ R2(pm, s2, S) → (R1(pm, S', S'') ∧ R2(pm, S', S'')) -+-> (last ⊃ Post1(pm, s, S) ∧ Post2(pm, s, S);G1(pm, S, S') ∨ G2(pm, S, S')))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
[:S | Boolvar ::- [PL ¬ Pre1(pm, S)] ∥nf false ::- [PL S = s0]], N = N'' + 1 until Boolvar, \A ∀ N, Boolvar, Pre1, pm, S, Post2, s, G2, R2, R1, G1, Post1, I, Pre2. N < n → N = N'' +1 until Boolvar ∧ [:S | Boolvar ::- [PL ¬ Pre1(pm, S)] ∥nf false ::- [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(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) → (R1(pm, S', S'') ∧ R2(pm, S', S'')) -+-> (last ⊃ Post1(pm, s, S) ∧ Post2(pm, s, S);G1(pm, S, S') ∨ G2(pm, S, S')), n = N + 1, R1(pm, s1, S), Pre1(pm, s2), I(pm, s2), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s1), Pre2(pm, s), I(pm, s1), I(pm, s), G2(pm, s1, s2), R1(pm, s2, S), R2(pm, s2, S), R1(pm, s1, s2), I(pm, S), Pre1(pm, S), ¬ R2(pm, s2, s0) ⊦ (R1(pm, S', S'') ∧ R2(pm, S', S'')) -+-> (last ⊃ Post1(pm, s, S) ∧ Post2(pm, s, S);G1(pm, S, S') ∨ G2(pm, S, S'))

Rule argument

Additional information

Used simplifier rules: 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);%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);%pre1-r1: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ R1(pm, s, s0) ∧ Pre1(pm, s) → Pre1(pm, s0);%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);%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);