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Proof step 17 from proof coinduction (previous step)

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)

User applied rule all left

And obtained the following new goals

Proof step 18:
φ(x), monotone(f), ν(f)(x0), ∀ x. φ(x) → f(λ x. ν(f)(x) ∨ φ(x))(x), ν(f) ⊆ (λ x. ν(f)(x) ∨ φ(x)) → f(ν(f)) ⊆ f(λ x. ν(f)(x) ∨ φ(x)) ⊦ f(λ x. ν(f)(x) ∨ φ(x))(x0), φ(x0)

Rule argument

pos: left 5 terms: ν(f), λ x. ν(f)(x) ∨ φ(x) abort: F discard: T computed: F

Additional information

Used terms: ν(f), λ x. ν(f)(x) ∨ φ(x)