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Proof step 1 from proof lookup-range-rem-union (conclusion)

⊦ ri[ks] ∪ range(ri \ ks) = range ri

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0)
Proof step 3:
⊦ ∀ adr. adr ∈ ri[ks] ∪ range(ri \ ks) ↔ adr ∈ range ri

Rule argument

spec: set-basic, inst: node-store name: Extension seq: ⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0) subst: [as0, as] → [range ri, ri[ks] ∪ range(ri \ ks)] flags: <all paths>

Additional information

Used terms: range ri, ri[ks] ∪ range(ri \ ks)