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Proof step 13 from proof coinduction (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information