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Proof step 4 from proof prefixpoint-aux2 (previous step)

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