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Proof step 12 from proof cont-iterate-fix (previous step)

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)

User applied rule insert lemma

And obtained the following new goals

Proof step 13:
monotone(f), m ≤ n ⊦ ((f ^ m))(λ x. false) ⊆ ((f ^ n))(λ x. false)
Proof step 14:
monotone(f) ⊦ m ≤ n, (∃ 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)

Rule argument

spec: inst: name: iterate-subseq-leq seq: monotone(f), m ≤ n ⊦ ((f ^ m))(λ x. false) ⊆ ((f ^ n))(λ x. false) subst: [f, m, n] → [f, m, n] flags: current, []

Additional information

Used terms: f, m, n