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Proof step 27 from proof compl-monotone (previous step)

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

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: x

Additional information

Used terms: x