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Proof step 5 from proof rg2-sound-main-unfair (previous step)

\A ∀ N, Post1, pm, s, S, G1, R1, Post2, G2, R2, Pre1, I, Pre2. N < m → [:S | [PL R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, 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) ∧ I(pm, S) → ((R1(pm, S', S'') ∧ R2(pm, S', S'')) ∧ N = N'' +1) -+-> (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, s), Pre2(pm, s), I(pm, s0), I(pm, s), Post1(pm, s, s0) ∧ Post2(pm, s, s0) ∧ ¬ R1(pm, s0, s0) ∧ ¬ R2(pm, s0, s0) ∨ Post1(pm, s, s0) ∧ Post2(pm, s, s0) ∧ R2(pm, s0, s0) ∧ ¬ R1(pm, s0, s0) ∨ Post1(pm, s, s0) ∧ R1(pm, s0, s0) ∧ Post2(pm, s, s0) ∧ ¬ R2(pm, s0, s0) ∨ Post1(pm, s, s0) ∧ R1(pm, s0, s0) ∧ Post2(pm, s, s0) ∧ R2(pm, s0, s0) ∨ Post2(pm, s, s0) ∧ Post1(pm, s, s0) ∧ ¬ R2(pm, s0, s0) ∧ ¬ R1(pm, s0, s0) ∨ Post2(pm, s, s0) ∧ Post1(pm, s, s0) ∧ R1(pm, s0, s0) ∧ ¬ R2(pm, s0, s0) ∨ Post2(pm, s, s0) ∧ R2(pm, s0, s0) ∧ Post1(pm, s, s0) ∧ ¬ R1(pm, s0, s0) ∨ Post2(pm, s, s0) ∧ R2(pm, s0, s0) ∧ Post1(pm, s, s0) ∧ R1(pm, s0, s0), ¬ Post1(pm, s, s0) ∨ ¬ Post2(pm, s, s0) ⊦

User applied rule case distinction

And closed the goal!

Rule argument

pos: left 8

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