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Proof step 33 from proof range-rem-in (previous step)

ri-cons(ri, nodes(gstore, ginval)), key0 ∈ ri, key ∈ ri ⊦ ri[key0] = ri[key], ri[key0] ∈ ri -- key

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr)
Proof step 35:
ri-cons(ri, nodes(gstore, ginval)), key ∈ ri, key0 ∈ ri ⊦ ri[key0] = ri[key], ∃ key1. key1 ∈ ri -- key ∧ (ri -- key)[key1] = ri[key0]

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[key0]] flags: <all paths>

Additional information

Used terms: ri -- key, ri[key0]