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Proof step 11 from proof cont-iterate-fix (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
monotone(f) ⊦ (∃ n. ((f ^ n))(λ x. false)(x)) ↔ f(λ x0. ∃ n. ((f ^ n))(λ x. false)(x0))(x), ((f ^ m))(λ x. false) ⊆ ((f ^ n))(λ x. false), ((f ^ n))(λ x. false) ⊆ ((f ^ m))(λ x. false)

Proof step 11 from proof cont-iterate-fix (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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