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Proof step 6 from proof lookup-rem-inj-range-inter-empty (previous step)

ri-inj(ri), ri[key] ∈ ri \ ks, key ∈ ri, key ∈ ks ⊦ #(ri[ks] ∩ range(ri \ ks)) = 0, # ks = 0, ks = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr)
Proof step 8:
ri-inj(ri), key ∈ ks, key ∈ ri, ∃ key0. key0 ∈ ri \ ks ∧ (ri \ ks)[key0] = ri[key] ⊦ # ks = 0, #(ri[ks] ∩ range(ri \ ks)) = 0, ks = ∅

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, ri[key]] flags: <all paths>

Additional information

Used terms: ri \ ks, ri[key]