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Proof step 7 from proof lookup-range-rem-union (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr)
Proof step 9:
⊦ (∃ key. key ∈ ks ∧ key ∈ ri ∧ adr = ri[key]) ∨ (∃ key. key ∈ ri \ ks ∧ (ri \ ks)[key] = adr) ↔ adr ∈ ri

Rule argument

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

Additional information

Used terms: ri \ ks, adr