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Proof step 12 from proof iterate-subseq-mu (previous step)

monotone(f), ((f ^ n0))(λ x. false) ⊆ μ(f) ⊦ f(((f ^ n0))(λ x. false)) ⊆ f(μ(f))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ monotone(f) ↔ (∀ S, S0. S ⊆ S0 → f(S) ⊆ f(S0))
Proof step 14:
((f ^ n0))(λ x. false) ⊆ μ(f), ∀ S, S0. S ⊆ S0 → f(S) ⊆ f(S0) ⊦ f(((f ^ n0))(λ x. false)) ⊆ f(μ(f))

Rule argument

spec: monotone-set-fixpoint name: monotone-def seq: ⊦ monotone(f) ↔ (∀ S, S0. S ⊆ S0 → f(S) ⊆ f(S0)) subst: [f] → [f] flags: <all paths>

Additional information

Used terms: f