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Proof step 8 from proof range-rem-in (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr)
Proof step 10:
ri-cons(ri, nodes(gstore, ginval)), key ∈ ri, ∃ key0. key0 ∈ ri -- key ∧ (ri -- key)[key0] = ri[key] ⊦

Rule argument

spec: store+set, inst: node-index name: Data-in seq: ⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr) subst: [ri, adr] → [ri -- key, ri[key]] flags: <all paths>

Additional information

Used terms: ri -- key, ri[key]