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Proof step 4 from proof rg2-not-pre1-unfair (previous step)

◇ Boolvar, [:S | Boolvar ::- [PL ¬ Pre1(pm, S)] ∥nf false ::- [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), 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 induction

And obtained the following new goals

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

Rule argument

indvar: ◇ Boolvar wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: ◇ Boolvar