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Proof step 1 from proof coinduction (conclusion)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
φ(x), monotone(f), ∀ x. φ(x) → f(λ x. ν(f)(x) ∨ φ(x))(x) ⊦ ν(f)(x)

Rule argument

Additional information