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Proof step 3 from proof prefixpoint-aux-nu (previous step)

monotone(f), S ⊆ f(S) ⊦ S ⊆ UN(λ S. S ⊆ f(S))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ S ⊆ S0 ↔ (∀ x. S(x) → S0(x))
Proof step 5:
monotone(f), S ⊆ f(S) ⊦ ∀ x. S(x) → UN(λ S. S ⊆ f(S))(x)

Rule argument

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

Additional information

Used terms: UN(λ S. S ⊆ f(S)), S