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Proof step 36 from proof nu-is-UN (previous step)

S(x0), S(x), monotone(compl(f)), monotone(f), S ⊆ f(S) ⊦ f(S)(x0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ S ⊆ S0 ↔ (∀ x. S(x) → S0(x))
Proof step 38:
S(x), S(x0), monotone(f), monotone(compl(f)), ∀ x. S(x) → f(S)(x) ⊦ f(S)(x0)

Rule argument

spec: <toplevel> name: subseteq-def seq: ⊦ S ⊆ S0 ↔ (∀ x. S(x) → S0(x)) subst: [S0, S] → [f(S), S] flags: <all paths>

Additional information

Used terms: f(S), S