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Proof step 22 from proof induction (previous step)

f(λ x. μ(f)(x) ∧ φ(x))(x0), μ(f)(x), φ(x0), ∀ x. f(μ(f))(x) → μ(f)(x), ∀ x. f(λ x. μ(f)(x) ∧ φ(x))(x) → φ(x) ⊦ (λ x. μ(f)(x) ∧ φ(x)) ⊆ μ(f), φ(x), μ(f)(x0), f(μ(f))(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] → [μ(f), λ x. μ(f)(x) ∧ φ(x)] flags: rewrite

Additional information

Used terms: μ(f), λ x. μ(f)(x) ∧ φ(x)