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Proof step 30 from proof range-rem-in (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr)
Proof step 32:
ri-cons(ri, nodes(gstore, ginval)), key ∈ ri, ∃ key. key ∈ ri ∧ ri[key] = adr ⊦ adr = ri[key], adr ∈ 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, adr] flags: <all paths>

Additional information

Used terms: ri, adr