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Proof step 6 from proof nu-is-UN (previous step)

monotone(f) ⊦ ¬ μ(compl(f))(x) ↔ UN(λ S. S ⊆ f(S))(x)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ UN(SS)(x) ↔ (∃ S. SS(S) ∧ S(x))
Proof step 8:
monotone(f) ⊦ ¬ μ(compl(f))(x) ↔ (∃ S. S ⊆ f(S) ∧ S(x))

Rule argument

spec: <toplevel> name: union-def seq: ⊦ UN(SS)(x) ↔ (∃ S. SS(S) ∧ S(x)) subst: [x, SS] → [x, λ S. S ⊆ f(S)] flags: <all paths>

Additional information

Used terms: x, λ S. S ⊆ f(S)