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Proof step 13 from proof iterate-is-fix (previous step)

((f ^ n))(λ x. false)(x), cont(f) ⊦ μ(f)(x)

User applied rule insert lemma

And obtained the following new goals

Proof step 14:
monotone(f) ⊦ ((f ^ n))(λ x. false) ⊆ μ(f)
Proof step 15:
((f ^ n))(λ x. false)(x), cont(f) ⊦ monotone(f), μ(f)(x)
Proof step 17:
((f ^ n))(λ x. false) ⊆ μ(f), ((f ^ n))(λ x. false)(x), cont(f) ⊦ μ(f)(x)

Rule argument

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

Additional information

Used terms: f, n