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Proof step 6 from proof cont-iterate-fix (previous step)

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)

User applied rule all left

And obtained the following new goals

Proof step 7:
monotone(f), chain(λ 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))) ⊦ (∃ n. ((f ^ n))(λ x. false)(x)) ↔ f(λ x0. ∃ n. ((f ^ n))(λ x. false)(x0))(x)

Rule argument

pos: left 2 terms: λ n. ((f ^ n))(λ x. false) abort: F discard: T computed: F

Additional information

Used terms: λ n. ((f ^ n))(λ x. false)