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Proof step 17 from proof refine-add-ind (previous step)

# lpt = # avol, # lpt0 = # avol, istore[m] = indexblock(indx, lax, m0), lpt[m] = mklp(m0, m1, LP_INDEX_NODES, m2), keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, m < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-leb(avol[m], indexblock(indx, lax, m0), mklp(m0, m1, LP_INDEX_NODES, m2)), awbuf-inv(avol, buffered(m)), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, buffered(m), lpt, avol), bufs-log-only(buffered(m), log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(indexblock(indx, lax, m0)), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log1), m ∈ istore, istore0 ⊑ istore, isbuf → synced(avol) ⊦ dups(log1), avol[m].mapped? ∧ (m1 + 2 * NODE_HEADER_SIZE + ind.alignedsize ≤ LEB_SIZE → m1 = # avol[m].data)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: abs-leb, inst: encoding-index-node name: abs-leb-def seq: ⊦ abs-leb(aleb, iblock, lp) ↔ aleb.mapped? ∧ abs-nodes (aleb.data, iblock.indlist, iblock.ladrlist, lp.size = LEB_SIZE) ∧ (lp.size ≠ LEB_SIZE → lp.size = # aleb.data) subst: [lp, iblock, aleb] → [mklp(m0, m1, LP_INDEX_NODES, m2), indexblock(indx, lax, m0), avol[m]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ indexblock(indx, lax, m).indlist = indx; (s)% ⊦ indexblock(indx, lax, m).ladrlist = lax; (s)% ⊦ mklp(n2, n3, lpf, m).size = n3; (s)% ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf)); (as)%abs-nodes-elems-adr-length: ⊦ abs-nodes(buf, indx, lax, weak) → # indx = # lax; (forward) from specification abs-list[encoding-index-node]% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)% ⊦ 2 * m = 0 ↔ m = 0; (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: mklp(m0, m1, LP_INDEX_NODES, m2), indexblock(indx, lax, m0), avol[m]