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Proof step 1 from proof prefixpoint (conclusion)

monotone(f) ⊦ f(μ(f)) ⊆ μ(f)

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

spec: <toplevel> name: prefixpoint-aux2 seq: monotone(f), ∀ S. f(S) ⊆ S → S0 ⊆ S ⊦ S0 ⊆ μ(f) subst: [f, S0] → [f, f(μ(f))] flags: <all paths>

Additional information

Used terms: f, f(μ(f))