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Proof step 5 from proof unmodified-sorted-node (previous step)

BRANCH_SIZE = # zbrar, iast[adr] = indexnode(brar, bv1, nused + 1), indexnode(brar, bv1, nused + 1) = save(mkznode(rp, zbrar, bv1, false, nused + 1)), nused < BRANCH_SIZE, adr ∈ iast, 0 + nused ≤ # load(brar, 0, nused + 1) ⊦ (∀ m0, m1. m0 < m1 ∧ m1 < nused → load(brar, 0, nused + 1)[0 + m0].key < load(brar, 0, nused + 1)[0 + m1].key) ↔ sorted(zbrar, 0, nused)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
BRANCH_SIZE = # zbrar, iast[adr] = indexnode(brar, bv1, nused + 1), indexnode(brar, bv1, nused + 1) = save(mkznode(rp, zbrar, bv1, false, nused + 1)), nused < BRANCH_SIZE, adr ∈ iast ⊦ (∀ m, m0. m < m0 ∧ m0 < nused → load(brar[m]).key < load(brar[m0]).key) ↔ sorted(zbrar, 0, nused)

Rule argument

Additional information

Used simplifier rules: n < nused, nused ≤ BRANCH_SIZE ⊦ load(brar, 0, nused)[n] = load(brar[n]); (s)% ⊦ m < n → ¬ n < m; (s)% ⊦ 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% ⊦ m < n → m ≤ n; (s)% ⊦ # load(brar, m, nused) = BRANCH_SIZE; (s)% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)