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Proof step 9 from proof coinduction (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ S ⊆ S0 ↔ (∀ x. S(x) → S0(x))
Proof step 11:
φ(x), monotone(f), ∀ x. φ(x) → f(λ x. ν(f)(x) ∨ φ(x))(x) ⊦ ∀ x. ν(f)(x) ∨ φ(x) → f(λ x. ν(f)(x) ∨ φ(x))(x)

Rule argument

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

Additional information

Used terms: f(λ x. ν(f)(x) ∨ φ(x)), λ x. ν(f)(x) ∨ φ(x)