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Proof step 30 from proof btree-inv-format (previous step)

⊦ (∅)[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

Rule argument

spec: ablock-store-inv, inst: index-store name: at seq: ⊦ adr ∈ istore → istore[adr] = istore[adr.lnum].indlist [pos(@(adr.pos, adr.size), istore[adr.lnum].ladrlist) ] 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: ⊦ @(m, m0, m1).lnum = m; (s)%At-same: ⊦ istore[n, iblock][n] = iblock; from specification store[index-store-ablock-store-nat-store]% ⊦ indexblock(indlist, lax, m).indlist = indlist; (s)% ⊦ @(m, m0, m1).pos = m0; (s)% ⊦ @(m, m0, m1).size = m1; (s)% ⊦ indexblock(indlist, lax, m).ladrlist = lax; (s)%pos-one: ⊦ pos(ladr, ladr ') = 0; from specification list-del[laddress-list]%one-03: ⊦ ind '[0] = ind; from specification list-del[index-store]% ⊦ @(n, n0, n1) ∈ istore[n, iblock] ↔ @(n0, n1) ∈ iblock.ladrlist; (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) ]