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Proof step 11 from proof unmodified-sorted-node (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
BRANCH_SIZE = # zbrar, iast[adr] = indexnode(save(zbrar, 0, nused + 1), bv1, nused + 1), m + 1 < BRANCH_SIZE, 2 + m < BRANCH_SIZE, m < nused, m0 < nused, m < m0, nused < BRANCH_SIZE, m0 + 1 < BRANCH_SIZE, m0 < BRANCH_SIZE, m + 1 < nused, m < BRANCH_SIZE, adr ∈ iast, ∀ m, m0. m < m0 ∧ m0 < nused → zbrar[m].key < zbrar[m0].key ⊦ zbrar[m].key < zbrar[m0].key

Rule argument

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ load(save(zbrar[n])).key = zbrar[n].key; (s)%n < nused, nused ≤ BRANCH_SIZE ⊦ save(zbrar, 0, nused)[n] = save(zbrar[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 + 1 ≤ n ↔ m < n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)%⊦ indexnode(brar, boolvar, m) = indexnode(brar0, boolvar0, m0) ↔ brar = brar0 ∧ (boolvar ↔ boolvar0) ∧ m = m0; (ws)% ⊦ mkznode(r, zbrar, boolvar, boolvar0, m).leaf ↔ boolvar; (s)% ⊦ mkznode(r, zbrar, boolvar, boolvar0, m).usedsize = m; (s)% ⊦ mkznode(r, zbrar, boolvar, boolvar0, m).zbranches = zbrar; (s)