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Proof step 4 from proof cont-iterate-fix (previous step)

monotone(f), cont(f) ⊦ (∃ n. ((f ^ n))(λ x. false)(x)) ↔ f(λ x0. ∃ n. ((f ^ n))(λ x. false)(x0))(x)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ cont(f) ↔ (∀ Sn. chain(Sn) → (∀ x. f(λ x0. ∃ n. Sn(n)(x0))(x) ↔ (∃ n. f(Sn(n))(x))))
Proof step 6:
monotone(f), ∀ Sn. chain(Sn) → (∀ x. f(λ x0. ∃ n. Sn(n)(x0))(x) ↔ (∃ n. f(Sn(n))(x))) ⊦ (∃ n. ((f ^ n))(λ x. false)(x)) ↔ f(λ x0. ∃ n. ((f ^ n))(λ x. false)(x0))(x)

Rule argument

spec: inst: name: cont-def seq: ⊦ cont(f) ↔ (∀ Sn. chain(Sn) → (∀ x. f(λ x0. ∃ n. Sn(n)(x0))(x) ↔ (∃ n. f(Sn(n))(x)))) subst: [f] → [f] flags: rewrite, current

Additional information

Used terms: f