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Proof step 4 from proof rg2-lem1-term-unfair (previous step)

∃ N. □ (N = N' ∧ ¬ N' < N'') ∧ [:S | [PL N' = N'' +1 until ¬ R1(pm, S', S'') ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf [PL □ ¬ N' < N'' ∧ [:S | [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ (□ R2(pm, S', S'') → ◇ last)]]] ], □ (R1(pm, S', S'') ∧ R2(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) ⊦ ◇ last

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), □ (N = N' ∧ ¬ N' < N''), [:S | [PL N' = N'' + 1 until ¬ R1(pm, S', S'') ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf [PL □ ¬ N' < N'' ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ (□ R2(pm, S', S'') → ◇ last)] ], RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre1(pm, s), Pre2(pm, s), I(pm, S), I(pm, s) ⊦ ◇ last

Rule argument

Additional information

Used simplifier rules: succ: ⊦ m +1 = m + 1; from specification nat-basic2