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Proof step 2 from proof iterate-is-fix (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ monotone(f) → (μ(f)(x) ↔ (∀ S. f(S) ⊆ S → S(x)))
Proof step 4:
cont(f), μ(f)(x) ⊦ monotone(f), ∃ n. ((f ^ n))(λ x. false)(x)
Proof step 7:
cont(f), monotone(f), ∀ S. f(S) ⊆ S → S(x) ⊦ ∃ n. ((f ^ n))(λ x. false)(x)

Rule argument

spec: monotone-set-fixpoint name: least-prefixpoint-def seq: ⊦ monotone(f) → (μ(f)(x) ↔ (∀ S. f(S) ⊆ S → S(x))) subst: [x, f] → [x, f] flags: <all paths>

Additional information

Used terms: x, f