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Proof step 35 from proof btree-inv-format (previous step)

n0 ∈ (∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)] ⊦ (∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)][n0].ref-size = ((∅ ++ @(n, m0, m1)) | n0).size

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 36:
(∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)][n0] = indexblock(indlist, lax, m), n0 ∈ (∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)] ⊦ m = ((∅ ++ @(n, m0, m1)) | n0).size

Rule argument

spec: ablock, inst: index-store name: elim seq: ⊦ (indlist = iblock.indlist ∧ lax = iblock.ladrlist) ∧ m = iblock.ref-size ↔ iblock = indexblock(indlist, lax, m) subst: [iblock, indlist, lax, m] → [(∅ )[n, indexblock (indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1) ] [n0 ], indlist, lax, m]

Additional information

Used simplifier rules: ⊦ (indlist = iblock.indlist ∧ lax = iblock.ladrlist) ∧ m = iblock.ref-size ↔ iblock = indexblock(indlist, lax, m); (elim) Used terms: (∅ )[n, indexblock (indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1) ] [n0 ], indlist, lax, m