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Proof step 13 from proof lookup-range-rem-union (previous step)

adr ∈ ri ⊦ ∃ key. key ∈ ri \ ks ∧ (ri \ ks)[key] = adr, ∃ key. key ∈ ks ∧ key ∈ ri ∧ adr = ri[key]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr)
Proof step 15:
∃ key. key ∈ ri ∧ ri[key] = adr ⊦ ∃ key. key ∈ ks ∧ key ∈ ri ∧ adr = ri[key], ∃ key. key ∈ ri \ ks ∧ (ri \ ks)[key] = adr

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