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Proof step 4 from proof prefixpoint-aux (previous step)

monotone(f), μ(f)(x), f(S) ⊆ S ⊦ S(x)

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

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

Additional information

Used terms: x, f