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Proof step 2 from proof rg2-lem2-term-unfair (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | [PL R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S')) ∧ ◇ last] ∥nf [PL 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) ⊦ ◇ last

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | [PL R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S')) ∧ ◇ last] ∥nf [PL 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: pre2-i: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ Pre2(pm, s) → I(pm, s);