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Proof step 1 from proof fixpoint (conclusion)

monotone(f) ⊦ f(μ(f)) = μ(f)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ S = S0 ↔ S ⊆ S0 ∧ S0 ⊆ S
Proof step 3:
monotone(f) ⊦ f(μ(f)) ⊆ μ(f) ∧ μ(f) ⊆ f(μ(f))

Rule argument

spec: inst: name: eq-bothsubset seq: ⊦ S = S0 ↔ S ⊆ S0 ∧ S0 ⊆ S subst: [S0, S] → [μ(f), f(μ(f))] flags: rewrite, current

Additional information

Used terms: μ(f), f(μ(f))