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Proof step 39 from proof unmodified-payload (previous step)

BRANCH_SIZE = # zbrar, iast[adr] = indexnode(brar, bv1, nused), indexnode(brar, bv1, nused) = save(mkznode(rp, zbrar, bv1, false, nused)), zbrar[n].entry?, n < nused, n < BRANCH_SIZE, sorted(zbrar, 0, nused), adr ∈ iast, nused ≤ BRANCH_SIZE ⊦ ∃ n0. n0 < nused ∧ load(brar[n0]).entry? ∧ load(brar[n0]).key = zbrar[n].key

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 40:
BRANCH_SIZE = # zbrar, iast[adr] = indexnode(brar, bv1, nused), zbrar[n] = mkzentry(key, adr0), indexnode(brar, bv1, nused) = save(mkznode(rp, zbrar, bv1, false, nused)), zbrar[n].entry?, n < BRANCH_SIZE, n < nused, sorted(zbrar, 0, nused), adr ∈ iast, nused ≤ BRANCH_SIZE ⊦ ∃ n0. n0 < nused ∧ load(brar[n0]).entry? ∧ load(brar[n0]).key = key

Rule argument

spec: zbranch name: elim-03 seq: ⊦ zbr.entry? → (key = zbr.key ∧ adr = zbr.adr ↔ zbr = mkzentry(key, adr)) subst: [zbr, key, adr] → [zbrar[n], key, adr0]

Additional information

Used simplifier rules: ⊦ zbr.entry? → (key = zbr.key ∧ adr = zbr.adr ↔ zbr = mkzentry(key, adr)); (elim) Used terms: zbrar[n], key, adr0