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Proof step 5 from proof compl-monotone (previous step)

S0 ⊆ S, monotone(f) ⊦ compl(f)(S0) ⊆ compl(f)(S)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ monotone(f) ↔ (∀ S, S0. S ⊆ S0 → f(S) ⊆ f(S0))
Proof step 7:
S0 ⊆ S, ∀ S, S0. S ⊆ S0 → f(S) ⊆ f(S0) ⊦ compl(f)(S0) ⊆ compl(f)(S)

Rule argument

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

Additional information

Used terms: f