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Proof step 9 from proof range-del-in (previous step)

ri-inj(ri), key ∈ ri ⊦ (∃ key0. key0 ≠ key ∧ key0 ∈ ri ∧ ri[key0] = adr) ↔ adr ≠ ri[key] ∧ adr ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr)
Proof step 11:
ri-inj(ri), key ∈ ri ⊦ (∃ key0. key0 ≠ key ∧ key0 ∈ ri ∧ ri[key0] = adr) ↔ adr ≠ ri[key] ∧ (∃ key. key ∈ ri ∧ ri[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