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Proof step 15 from proof compl-monotone (previous step)

S0 ⊆ S, ∀ S, S0. S ⊆ S0 → f(S) ⊆ f(S0) ⊦ ¬ f(λ x0. ¬ S(x0))(x), f(λ x0. ¬ S0(x0))(x)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
f(λ x0. ¬ S(x0))(x), S0 ⊆ S, ∀ S, S0. S ⊆ S0 → f(S) ⊆ f(S0) ⊦ f(λ x0. ¬ S0(x0))(x)

Rule argument

Additional information