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Proof step 2 from proof rg2-not-pre2-unfair (previous step)

[:S | [PL R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥nf [PL ¬ Pre2(pm, S)]], RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre2(pm, S), Pre1(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'))

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name: rg2-not-pre1-unfair seq: [:S | [PL ¬ Pre1(pm, S)] ∥nf [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) ⊦ (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') ) subst: [Pre1, pm, S, Post2, s, G2, R2, R1, G1, Post1, I, Pre2] → [Pre2, pm, S, Post1, s, G1, R1, R2, G2, Post2, I, Pre1] flags: current, []

Additional information

Used simplifier rules: RG-restr-sym: ⊦ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) → ( ¬ RG-restr(pm, R2, G2, Pre2, Post2, I, R1, G1, Pre1, Post1) ↔ false); Used terms: Pre2, pm, S, Post1, s, G1, R1, R2, G2, Post2, I, Pre1