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Proof step 4 from proof fair-never-violates-left-rely (previous step)

□ (R1(pm, S', S'') ∧ R2(pm, S', S'')), ◇ Boolvar, [:S | Boolvar ::- [PL S = s] ∥ false ::- [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s1, S);G2(pm, S, S'))]], RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre2(pm, s1), I(pm, s0), R1(pm, s0, S), I(pm, S), I(pm, s1), ¬ R1(pm, s0, s) ⊦

User applied rule induction

And obtained the following new goals

Proof step 5:
[:S | Boolvar ::- [PL S = s] ∥ false ::- [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s1, S);G2(pm, S, S'))]], N = N'' +1 until Boolvar, □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), \A ∀ N, R1, pm, S, R2, Boolvar, s, Post2, s1, G2, G1, Pre1, Post1, I, Pre2, s0. N < m → □ (R1(pm, S', S'') ∧ R2(pm, S', S'')) ∧ N = N'' +1 until Boolvar ∧ [:S | Boolvar ::- [PL S = s] ∥ false ::- [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s1, S);G2(pm, S, S'))]] ∧ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ Pre2(pm, s1) ∧ I(pm, s0) ∧ R1(pm, s0, S) ∧ I(pm, S) ∧ I(pm, s1) ∧ ¬ R1(pm, s0, s) → false, m = N, RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), Pre2(pm, s1), I(pm, s0), R1(pm, s0, S), I(pm, S), I(pm, s1), ¬ R1(pm, s0, s) ⊦

Rule argument

indvar: ◇ Boolvar wfpred: <

Additional information

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