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Proof step 10 from proof compl-monotone (previous step)

compl(f)(S0)(x), S0 ⊆ S, ∀ S, S0. S ⊆ S0 → f(S) ⊆ f(S0) ⊦ compl(f)(S)(x)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ compl(f)(S)(x) ↔ ¬ f(λ x0. ¬ S(x0))(x)
Proof step 12:
¬ f(λ x0. ¬ S0(x0))(x), S0 ⊆ S, ∀ S, S0. S ⊆ S0 → f(S) ⊆ f(S0) ⊦ compl(f)(S)(x)

Rule argument

spec: inst: name: compl-def seq: ⊦ compl(f)(S)(x) ↔ ¬ f(λ x0. ¬ S(x0))(x) subst: [x, S, f] → [x, S0, f] flags: rewrite, current

Additional information

Used terms: x, S0, f