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Proof step 19 from proof coinduction (previous step)

φ(x), monotone(f), ν(f)(x0), ∀ x. φ(x) → f(λ x. ν(f)(x) ∨ φ(x))(x) ⊦ ν(f) ⊆ (λ x. ν(f)(x) ∨ φ(x)), f(λ x. ν(f)(x) ∨ φ(x))(x0), φ(x0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: monotone-set-fixpoint inst: name: subseteq-def seq: ⊦ S ⊆ S0 ↔ (∀ x. S(x) → S0(x)) subst: [S0, S] → [λ x. ν(f)(x) ∨ φ(x), ν(f)] flags: rewrite

Additional information

Used terms: λ x. ν(f)(x) ∨ φ(x), ν(f)