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Proof step 3 from proof range-write-in (previous step)

ri-inj(ri), key ∈ ri ⊦ range ri[key, adr] = (range ri -- ri[key]) ++ adr

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0)
Proof step 5:
ri-inj(ri), key ∈ ri ⊦ ∀ adr0. adr0 ∈ range ri[key, adr] ↔ adr0 ∈ (range ri -- ri[key]) ++ adr

Rule argument

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

Additional information

Used terms: (range ri -- ri[key]) ++ adr, range ri[key, adr]