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Proof step 3 from proof progress-right (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), [:S | [PL □ ◇ P(pm, S) ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ∥ [PL R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ], RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), I(pm, S), Pre1(pm, s), Pre2(pm, s), P-restr(pm, P, I, R2) ⊦ □ ◇ P(pm, S)

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name: progress-left seq: RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), I(pm, S), Pre1(pm, s), Pre2(pm, s), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), P-restr(pm, P, I, R1), [:S | [PL □ ◇ P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S')) ] ∥ [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ] ] ⊦ □ ◇ P(pm, S) subst: [pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2, S, s, P] → [pm, R2, G2, Pre2, Post2, I, R1, G1, Pre1, Post1, S, s, P] 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); from specification RG-I-2-Theory Used terms: pm, R2, G2, Pre2, Post2, I, R1, G1, Pre1, Post1, S, s, P