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Proof step 16 from proof coinduction (previous step)

monotone(f) ↔ (∀ S, S0. S ⊆ S0 → f(S) ⊆ f(S0)), φ(x), monotone(f), ν(f)(x0), ∀ x. φ(x) → f(λ x. ν(f)(x) ∨ φ(x))(x) ⊦ f(λ x. ν(f)(x) ∨ φ(x))(x0), φ(x0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
φ(x), monotone(f), ν(f)(x0), ∀ x. φ(x) → f(λ x. ν(f)(x) ∨ φ(x))(x), ∀ S, S0. S ⊆ S0 → f(S) ⊆ f(S0) ⊦ f(λ x. ν(f)(x) ∨ φ(x))(x0), φ(x0)

Proof step 16 from proof coinduction (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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