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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ S ⊆ S0 ↔ (∀ x. S(x) → S0(x))
Proof step 8:
cont(f) ⊦ ∀ x. f(λ x. ∃ n. ((f ^ n))(λ x. false)(x))(x) → (∃ n. ((f ^ n))(λ x. false)(x)), ∃ n. ((f ^ n))(λ x. false)(x)

Rule argument

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

Additional information

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