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Proof step 7 from proof coinduction (previous step)

φ(x), monotone(f), ∀ x. φ(x) → f(λ x. ν(f)(x) ∨ φ(x))(x) ⊦ ∃ S. S ⊆ f(S) ∧ S(x)

User applied rule exists right

And obtained the following new goals

Proof step 8:
φ(x), monotone(f), ∀ x. φ(x) → f(λ x. ν(f)(x) ∨ φ(x))(x) ⊦ (λ x. ν(f)(x) ∨ φ(x)) ⊆ f(λ x. ν(f)(x) ∨ φ(x)) ∧ (ν(f)(x) ∨ φ(x))

Rule argument

pos: right 1 terms: λ x. ν(f)(x) ∨ φ(x) abort: F discard: T computed: F

Additional information

Used terms: λ x. ν(f)(x) ∨ φ(x)