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Proof step 13 from proof induction (previous step)

f(λ x. μ(f)(x) ∧ φ(x))(x0), f(μ(f)) ⊆ μ(f), μ(f)(x), monotone(f), f(λ x. μ(f)(x) ∧ φ(x))(x0) → φ(x0), ∀ x. f(λ x. μ(f)(x) ∧ φ(x))(x) → φ(x) ⊦ φ(x), μ(f)(x0) ∧ φ(x0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
f(λ x. μ(f)(x) ∧ φ(x))(x0), f(μ(f)) ⊆ μ(f), μ(f)(x), monotone(f), φ(x0), ∀ x. f(λ x. μ(f)(x) ∧ φ(x))(x) → φ(x) ⊦ φ(x), μ(f)(x0)

Proof step 13 from proof induction (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information