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Proof step 2 from proof no-progress-fw (previous step)

I(pm, s0), I(pm, s), R(pm, s, s0), P-restr(pm, ¬ P, I, R), P(pm, s0) ⊦ P(pm, s)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ P-restr(pm, P, I, R) ↔ (∀ s, s0. I(pm, s) ∧ I(pm, s0) ∧ P(pm, s) ∧ R(pm, s, s0) → P(pm, s0))
Proof step 4:
I(pm, s0), I(pm, s), R(pm, s, s0), ∀ s, s0. I(pm, s) ∧ I(pm, s0) ∧ (¬ P)(pm, s) ∧ R(pm, s, s0) → (¬ P)(pm, s0), P(pm, s0) ⊦ P(pm, s)

Rule argument

spec: inst: name: P-restr-def seq: ⊦ P-restr(pm, P, I, R) ↔ (∀ s, s0. I(pm, s) ∧ I(pm, s0) ∧ P(pm, s) ∧ R(pm, s, s0) → P(pm, s0)) subst: [R, I, P, pm] → [R, I, ¬ P, pm] flags: rewrite, current

Additional information

Used terms: R, I, ¬ P, pm