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Proof step 1 from proof inv-propagate (conclusion)

Pelem(a), ∀ a, b. Pelem(a) ∧ p(a, b) → Pelem(b) ⊦ inv(a, Pelem)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ inv(a, Pelem) ↔ (∀ b. p*(a, b) → Pelem(b))
Proof step 3:
Pelem(a), ∀ a, b. Pelem(a) ∧ p(a, b) → Pelem(b) ⊦ ∀ b. p*(a, b) → Pelem(b)

Rule argument

spec: inst: name: inv seq: ⊦ inv(a, Pelem) ↔ (∀ b. p*(a, b) → Pelem(b)) subst: [Pelem, a] → [Pelem, a] flags: rewrite, current

Additional information

Used terms: Pelem, a