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Proof step 16 from proof compl-monotone (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 17:
f(λ x0. ¬ S(x0))(x), S0 ⊆ S, (λ x0. ¬ S(x0)) ⊆ (λ x0. ¬ S0(x0)) → f(λ x0. ¬ S(x0)) ⊆ f(λ x0. ¬ S0(x0)) ⊦ f(λ x0. ¬ S0(x0))(x)

Rule argument

pos: left 3 terms: λ x0. ¬ S(x0), λ x0. ¬ S0(x0) abort: F discard: T computed: F

Additional information

Used terms: λ x0. ¬ S(x0), λ x0. ¬ S0(x0)