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Proof step 2 from proof compl-monotone (previous step)

monotone(f) ⊦ monotone(compl(f))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ monotone(f) ↔ (∀ S, S0. S ⊆ S0 → f(S) ⊆ f(S0))
Proof step 4:
monotone(f) ⊦ ∀ S, S0. S ⊆ S0 → compl(f)(S) ⊆ compl(f)(S0)

Rule argument

spec: inst: name: monotone-def seq: ⊦ monotone(f) ↔ (∀ S, S0. S ⊆ S0 → f(S) ⊆ f(S0)) subst: [f] → [compl(f)] flags: rewrite, current

Additional information

Used terms: compl(f)