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Proof step 1 from proof prefixpoint-aux2 (conclusion)

monotone(f), ∀ S. f(S) ⊆ S → S0 ⊆ S ⊦ S0 ⊆ μ(f)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ S ⊆ S0 ↔ (∀ x. S(x) → S0(x))
Proof step 3:
monotone(f), ∀ S. f(S) ⊆ S → S0 ⊆ S ⊦ ∀ x. S0(x) → μ(f)(x)

Rule argument

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

Additional information

Used terms: μ(f), S0