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Proof step 8 from proof nu-is-UN (previous step)

monotone(f) ⊦ ¬ μ(compl(f))(x) ↔ (∃ S. S ⊆ f(S) ∧ S(x))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ monotone(f) → (μ(f)(x) ↔ (∀ S. f(S) ⊆ S → S(x)))
Proof step 10:
monotone(f) ⊦ ¬ μ(compl(f))(x) ↔ (∃ S. S ⊆ f(S) ∧ S(x)), monotone(compl(f))
Proof step 13:
monotone(f), monotone(compl(f)) ⊦ ¬(∀ S. compl(f)(S) ⊆ S → S(x)) ↔ (∃ S. S ⊆ f(S) ∧ S(x))

Rule argument

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

Additional information

Used terms: x, compl(f)