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

ri-cons(ri, nodes(gstore, ginval)), key ∈ ri ⊦ range(ri -- key) = range ri -- ri[key]

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-cons(ri, nodes(gstore, ginval)), key ∈ ri ⊦ ∀ adr. adr ∈ range(ri -- key) ↔ adr ∈ range ri -- ri[key]

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], range(ri -- key)] flags: <all paths>

Additional information

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