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Proof step 9 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 ⊦ (∀ 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ save(znd) = indexnode(save(znd.zbranches, 0, znd.usedsize), znd.leaf, znd.usedsize)
Proof step 11:
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)

Rule argument

spec: znode-ops name: save-node seq: ⊦ save(znd) = indexnode (save(znd.zbranches, 0, znd.usedsize), znd.leaf, znd.usedsize) subst: [znd] → [mkznode(rp, zbrar, bv1, false, nused + 1)] flags: <all paths>

Additional information

Used terms: mkznode(rp, zbrar, bv1, false, nused + 1)