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Proof step 20 from proof compl-monotone (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
S0(x0), f(λ x0. ¬ S(x0))(x), S0 ⊆ S ⊦ S(x0), f(λ x0. ¬ S0(x0))(x)

Rule argument

Additional information