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Proof step 17 from proof iterate-is-fix (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ S ⊆ S0 ↔ (∀ x. S(x) → S0(x))
Proof step 19:
∀ x. ((f ^ n))(λ x. false)(x) → μ(f)(x), ((f ^ n))(λ x. false)(x), cont(f) ⊦ μ(f)(x)

Rule argument

spec: monotone-set-fixpoint inst: name: subseteq-def seq: ⊦ S ⊆ S0 ↔ (∀ x. S(x) → S0(x)) subst: [S0, S] → [μ(f), ((f ^ n))(λ x. false)] flags: rewrite

Additional information

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