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Proof step 2 from proof coinduction (previous step)

φ(x), monotone(f), ∀ x. φ(x) → f(λ x. ν(f)(x) ∨ φ(x))(x) ⊦ ν(f)(x)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 3:
⊦ ν(f) = UN(λ S. S ⊆ f(S))
Proof step 4:
ν(f) = UN(λ S. S ⊆ f(S)), φ(x), monotone(f), ∀ x. φ(x) → f(λ x. ν(f)(x) ∨ φ(x))(x) ⊦ ν(f)(x)

Rule argument

spec: monotone-set-fixpoint inst: name: nu-is-UN seq: ⊦ ν(f) = UN(λ S. S ⊆ f(S)) subst: [f] → [f] flags: []

Additional information

Used terms: f