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Proof step 4 from proof nu-is-UN (previous step)

monotone(f) ⊦ ν(f)(x) ↔ UN(λ S. S ⊆ f(S))(x)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ monotone(f) → (ν(f)(x) ↔ ¬ μ(compl(f))(x))
Proof step 6:
monotone(f) ⊦ ¬ μ(compl(f))(x) ↔ UN(λ S. S ⊆ f(S))(x)

Rule argument

spec: <toplevel> name: greatest-prefixpoint-def seq: ⊦ monotone(f) → (ν(f)(x) ↔ ¬ μ(compl(f))(x)) subst: [x, f] → [x, f] flags: <all paths>

Additional information

Used terms: x, f