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Proof step 19 from proof lebs-write (previous step)

@(n, m3, m4) ∈ ri ⊦ key ∈ ri, ∃ adr. adr.lnum = n ∧ adr ∈ ri[key, @(m, m0, m1)]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr)
Proof step 21:
∃ key. key ∈ ri ∧ ri[key] = @(n, m3, m4) ⊦ key ∈ ri, ∃ adr. adr.lnum = n ∧ adr ∈ ri[key, @(m, m0, m1)]

Rule argument

spec: store+set, inst: node-index name: Data-in seq: ⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr) subst: [ri, adr] → [ri, @(n, m3, m4)] flags: <all paths>

Additional information

Used terms: ri, @(n, m3, m4)