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Proof step 4 from proof least-fixpoint (previous step)

f(S) = S, μ(f)(x), monotone(f) ⊦ S(x)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ μ(f)(x) ↔ (∀ S. f(S) ⊆ S → S(x))
Proof step 6:
f(S) = S, ∀ S. f(S) ⊆ S → S(x), monotone(f) ⊦ S(x)

Rule argument

spec: monotone-set inst: name: least-prefixpoint-def seq: ⊦ μ(f)(x) ↔ (∀ S. f(S) ⊆ S → S(x)) subst: [x, f] → [x, f] flags: rewrite, current

Additional information

Used terms: x, f