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Proof step 6 from proof rg2-not-pre1-unfair (previous step)

boolvar ∨ n = N +1 ∧ N = N'' +1 until Boolvar, ( ( ((false ⊃ Post2(pm, s, s1);G2(pm, s1, s2)) ∧ ¬ Pre1(pm, s1)) ∧ ¬ R2(pm, s2, S) ∨ (((false ⊃ Post2(pm, s, s1);G2(pm, s1, s2)) ∧ R2(pm, s2, S)) ∧ ¬ Pre1(pm, s1)) ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))) ∨ (¬ false ∧ ¬ Pre1(pm, s1)) ∧ ¬ boolvar1 ∧ [:S | Boolvar ::- [PL true ∧ true] ∥nf false ::- [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))]] ∨ (∃ s0. (((false ⊃ Post2(pm, s, s1);G2(pm, s1, s2)) ∧ ¬ Pre1(pm, s1)) ∧ ¬ R2(pm, s2, s0)) ∧ [:S | Boolvar ::- [PL true ∧ true] ∥nf false ::- [PL S = s0 ∧ true]]) ∨ (∃ s0. (((false ⊃ Post2(pm, s, s1);G2(pm, s1, s2)) ∧ R2(pm, s2, s0)) ∧ ¬ Pre1(pm, s1)) ∧ [:S | Boolvar ::- [PL true ∧ true] ∥nf false ::- [PL S = s0 ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))]])) ∨ ( ((true ⊃ Post2(pm, s, s1);G2(pm, s1, s1)) ∧ ¬ R2(pm, s1, s1)) ∧ ¬ Pre1(pm, s1) ∨ (∃ s0. (¬ boolvar ∧ (false ⊃ Post2(pm, s, s1);G2(pm, s1, s2)) ∧ ¬ R2(pm, s2, s0)) ∧ ¬ boolvar1 ∧ [:S | Boolvar ::- [PL ¬ Pre1(pm, S)] ∥nf false ::- [PL S = s0 ∧ true]]) ∨ (∃ s0. (((false ⊃ Post2(pm, s, s1);G2(pm, s1, s1)) ∧ ¬ R2(pm, s1, s0)) ∧ ¬ Pre1(pm, s1)) ∧ [:S | Boolvar ::- [PL true ∧ true] ∥nf false ::- [PL S = s0 ∧ true]])) ∨ ((true ⊃ Post2(pm, s, s1);G2(pm, s1, s1)) ∧ R2(pm, s1, s1)) ∧ ¬ Pre1(pm, s1) ∨ (∃ s0. (¬ boolvar ∧ (false ⊃ Post2(pm, s, s1);G2(pm, s1, s2)) ∧ R2(pm, s2, s0)) ∧ ¬ boolvar1 ∧ [:S | Boolvar ::- [PL ¬ Pre1(pm, S)] ∥nf false ::- [PL S = s0 ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))]]) ∨ (∃ s0. (((false ⊃ Post2(pm, s, s1);G2(pm, s1, s1)) ∧ R2(pm, s1, s0)) ∧ ¬ Pre1(pm, s1)) ∧ [:S | Boolvar ::- [PL true ∧ true] ∥nf false ::- [PL S = s0 ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))]]), \A ∀ N, Boolvar, Pre1, pm, S, Post2, s, G2, R2, R1, G1, Post1, I, Pre2. N < m → 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')), m = n, RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s1), Pre2(pm, s), I(pm, s1), I(pm, s), ¬ false, boolvar1 → s1 = s2 ∧ (boolvar ↔ boolvar0) ∧ n = n0 ⊦ (false ⊃ Post1(pm, s, s1) ∧ Post2(pm, s, s1);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 7:
boolvar ∨ n = N + 1 ∧ N = N'' + 1 until Boolvar, ¬ boolvar ∧ G2(pm, s1, s2) ∧ ¬ R2(pm, s2, s0) ∧ ¬ boolvar1 ∧ [:S | Boolvar ::- [PL ¬ Pre1(pm, S)] ∥nf false ::- [PL S = s0]] ∨ ¬ boolvar ∧ G2(pm, s1, s2) ∧ R2(pm, s2, s3) ∧ ¬ boolvar1 ∧ [:S | Boolvar ::- [PL ¬ Pre1(pm, S)] ∥nf false ::- [PL S = s3 ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))]], \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 ⊦ (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')))

Rule argument

Additional information

Used simplifier rules: pre2-i: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ Pre2(pm, s) → I(pm, s);%pre1-i: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ Pre1(pm, s) → I(pm, s);%succ: ⊦ m +1 = m + 1; from specification nat-basic2