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Proof step 8 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 ≤ # zbrar ⊦ (∀ m, m0. m < m0 ∧ m0 < nused → load(brar[m]).key < load(brar[m0]).key) ↔ (∀ m0, m1. m0 < m1 ∧ m1 < nused → zbrar[0 + m0].key < zbrar[0 + m1].key)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
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) ↔ (∀ m, m0. m < m0 ∧ m0 < nused → zbrar[m].key < zbrar[m0].key)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (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)