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Proof step 5 from proof induction (previous step)

μ(f)(x), monotone(f), ∀ x. f(λ x. μ(f)(x) ∧ φ(x))(x) → φ(x), ∀ S. f(S) ⊆ S → S(x) ⊦ φ(x)

User applied rule all left

And obtained the following new goals

Proof step 6:
μ(f)(x), monotone(f), ∀ x. f(λ x. μ(f)(x) ∧ φ(x))(x) → φ(x), f(λ x. μ(f)(x) ∧ φ(x)) ⊆ (λ x. μ(f)(x) ∧ φ(x)) → μ(f)(x) ∧ φ(x) ⊦ φ(x)

Rule argument

pos: left 4 terms: λ x. μ(f)(x) ∧ φ(x) abort: F discard: T computed: F

Additional information

Used terms: λ x. μ(f)(x) ∧ φ(x)