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Proof step 2 from proof unmodified-load-key-node (previous step)

iast[adr] = indexnode(brar, bv0, m), n < nused, nused < BRANCH_SIZE, unmodified(adr, mkznode(rp, zbrar, bv1, false, nused + 1), iast) ⊦ load(brar[n]).key = zbrar[n].key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
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

Rule argument

Additional information

Used simplifier rules: unmodified: ⊦ unmodified(adr, znd, iast) ↔ ¬ znd.dirty → adr ∈ iast ∧ iast[adr] = save(znd);%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ m +1 = m + 1; (s)% ⊦ BRANCH_SIZE ≠ 0; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ mkznode(r, zbrar, boolvar, boolvar0, m).usedsize = m; (s)% ⊦ mkznode(r, zbrar, boolvar, boolvar0, m).leaf ↔ boolvar; (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%save-properties: ⊦ save(znd) = indexnode(brar, bv, n) → (bv ↔ znd.leaf) ∧ n = znd.usedsize; (forward) from specification znode-ops% ⊦ mkznode(r, zbrar, boolvar, boolvar0, m).dirty ↔ boolvar0; (s)