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Proof step 6 from proof iterate-subseq-mu (previous step)

monotone(f), ∀ f. monotone(f) → ((f ^ n0))(λ x. false) ⊆ μ(f) ⊦ ((f ^ (n0 + 1)))(λ x. false) ⊆ μ(f)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
monotone(f) ⊦ f(μ(f)) = μ(f)
Proof step 8:
monotone(f), monotone(f), ∀ f. monotone(f) → ((f ^ n0))(λ x. false) ⊆ μ(f) ⊦ ((f ^ (n0 + 1)))(λ x. false) ⊆ f(μ(f))

Rule argument

spec: monotone-set-fixpoint inst: name: fixpoint seq: monotone(f) ⊦ f(μ(f)) = μ(f) subst: [f] → [f] flags: rewrite

Additional information

Used terms: f