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Proof step 9 from proof prefixpoint-aux2 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ S ⊆ S0 ↔ (∀ x. S(x) → S0(x))
Proof step 11:
S0(x), monotone(f), f(S) ⊆ S, ∀ x. S0(x) → S(x) ⊦ S(x)

Rule argument

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

Additional information

Used terms: S, S0