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Proof step 2 from proof cont-iterate-fix (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
cont(f) ⊦ monotone(f)
Proof step 4:
monotone(f), cont(f) ⊦ (∃ n. ((f ^ n))(λ x. false)(x)) ↔ f(λ x0. ∃ n. ((f ^ n))(λ x. false)(x0))(x)

Rule argument

spec: inst: name: cont-monotone seq: cont(f) ⊦ monotone(f) subst: [f] → [f] flags: current, []

Additional information

Used terms: f