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Proof step 15 from proof unmodified-payload (previous step)

BRANCH_SIZE = # zbrar, zbrar[n] = mkzentry(key, adr0), iast[adr] = indexnode(brar, bv1, nused), indexnode(brar, bv1, nused) = save(mkznode(rp, zbrar, bv1, false, nused)), n < nused, n < BRANCH_SIZE, sorted(zbrar, 0, nused), adr ∈ iast, key ∈ payload(load(brar, 0, nused), 0, nused), nused ≤ BRANCH_SIZE ⊦ payload(load(brar, 0, nused), 0, nused)[key] = payload(zbrar, 0, nused)[key], 0 + nused ≤ # zbrar ∧ n < nused ∧ zbrar[0 + n] = mkzentry(key, adr0) ∧ (∀ n0. n0 < n ∧ zbrar[0 + n0].entry? → zbrar[0 + n0].key ≠ key)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
BRANCH_SIZE = # zbrar, zbrar[n] = mkzentry(zbrar[n0].key, adr0), iast[adr] = indexnode(brar, bv1, nused), indexnode(brar, bv1, nused) = save(mkznode(rp, zbrar, bv1, false, nused)), zbrar[n0].entry?, n0 + 1 < BRANCH_SIZE, n0 + 1 < nused, n < nused, n < BRANCH_SIZE, n0 < n, n0 < nused, n0 < BRANCH_SIZE, sorted(zbrar, 0, nused), adr ∈ iast, zbrar[n0].key ∈ payload(load(brar, 0, nused), 0, nused), nused ≤ BRANCH_SIZE ⊦ payload(load(brar, 0, nused), 0, nused)[zbrar[n0].key] = payload(zbrar, 0, nused)[zbrar[n0].key]

Rule argument

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)