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Proof step 3 from proof unmodified-load-key-node (previous step)

iast[adr] = indexnode(brar, bv1, nused + 1), indexnode(brar, bv1, nused + 1) = save(mkznode(rp, zbrar, bv1, false, nused + 1)), n + 1 < BRANCH_SIZE, nused < BRANCH_SIZE, n < nused, n < BRANCH_SIZE, adr ∈ iast ⊦ load(brar[n]).key = zbrar[n].key

User applied rule insert rewrite lemma

And obtained the following new goals

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 simplifier rules: ⊦ mkznode(r, zbrar, boolvar, boolvar0, m).zbranches = zbrar; (s)% ⊦ mkznode(r, zbrar, boolvar, boolvar0, m).usedsize = m; (s)% ⊦ mkznode(r, zbrar, boolvar, boolvar0, m).leaf ↔ boolvar; (s)%⊦ indexnode(brar, boolvar, m) = indexnode(brar0, boolvar0, m0) ↔ brar = brar0 ∧ (boolvar ↔ boolvar0) ∧ m = m0; (ws)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m < n → ¬ n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)%n < nused, nused ≤ BRANCH_SIZE ⊦ save(zbrar, 0, nused)[n] = save(zbrar[n]); (s)% ⊦ load(save(zbrar[n])).key = zbrar[n].key; (s) Used terms: mkznode(rp, zbrar, bv1, false, nused + 1)