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Proof step 21 from proof rg2-sound-main-unfair (previous step)

R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')), Pre2(pm, s), Pre1(pm, s), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), I(pm, S), Post1(pm, s, 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'))

User applied rule induction

And obtained the following new goals

Proof step 22:
R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')), \A ∀ N0, R2, pm, S, Post2, s, G2, Pre2, Pre1, R1, G1, Post1, I, N. N0 < m → R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S')) ∧ Pre2(pm, s) ∧ Pre1(pm, s) ∧ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ I(pm, S) ∧ Post1(pm, s, S) → ((R1(pm, S', S'') ∧ R2(pm, S', S'') ∧ N = N'' + 1) ∧ N0 = N0'' +1) -+-> (last ⊃ Post1(pm, s, S) ∧ Post2(pm, s, S);G1(pm, S, S') ∨ G2(pm, S, S')), m = N0, Pre2(pm, s), Pre1(pm, s), RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), I(pm, S), Post1(pm, s, S) ⊦ ((R1(pm, S', S'') ∧ R2(pm, S', S'') ∧ N = N'' + 1) ∧ N0 = N0'' +1) -+-> (last ⊃ Post1(pm, s, S) ∧ Post2(pm, s, S);G1(pm, S, S') ∨ G2(pm, S, S'))

Rule argument

indvar: (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') ) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: (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') )