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Proof step 18 from proof cont-iterate-fix (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
f(λ x0. ∃ n. ((f ^ n))(λ x. false)(x0))(x) ↔ (∃ n. f(((f ^ n))(λ x. false))(x)), ((f ^ n))(λ x. false)(x), monotone(f), ∀ x. f(λ x0. ∃ n. ((f ^ n))(λ x. false)(x0))(x) ↔ (∃ n. f(((f ^ n))(λ x. false))(x)) ⊦ f(λ x0. ∃ n. ((f ^ n))(λ x. false)(x0))(x)

Proof step 18 from proof cont-iterate-fix (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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