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Proof step 27 from proof btree-inv-format (previous step)

⊦ nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)])[@(n, m0, m1)] = indexnode(mkbrarray(BRANCH_SIZE), true, 0), r = null

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ adr ∈ istore → nodes(istore)[adr] = istore[adr]
Proof step 29:
@(n, m0, m1) ∈ (∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)] ⊦ (∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)][@(n, m0, m1)] = indexnode(mkbrarray(BRANCH_SIZE), true, 0), r = null

Rule argument

spec: ablock-nodes, inst: index-store name: at-nodes seq: ⊦ adr ∈ istore → nodes(istore)[adr] = istore[adr] subst: [adr, istore] → [@(n, m0, m1), (∅ )[n, indexblock (indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1) ]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ @(n, n0, n1) ∈ istore[n, iblock] ↔ @(n0, n1) ∈ iblock.ladrlist; (s)% ⊦ indexblock(indlist, lax, m).ladrlist = lax; (s)%in-17: ⊦ ladr ∈ ladr0 ' ↔ ladr = ladr0; from specification list[laddress-list] Used terms: @(n, m0, m1), (∅ )[n, indexblock (indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1) ]