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Proof step 45 from proof refine-sync (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 46:
⊦ 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)
Proof step 47:
# lpt = # avol, # lpt0 = # avol, lpt[m2] = mklp(m, m0, LP_INDEX_NODES, m1), istore[m2] = indexblock(indx, lax, m), keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, avol[m2].mapped?, ginval < # avol, m2 < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-nodes(avol[m2].data, indexblock(indx, lax, m).indlist, indexblock(indx, lax, m).ladrlist, mklp(m, m0, LP_INDEX_NODES, m1).size = LEB_SIZE), awbuf-inv(avol, buffered(m2)), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, buffered(m2), lpt, avol), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(indexblock(indx, lax, m)), 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), m2 ∈ istore, istore0 ⊑ istore, isbuf → synced(avol), mklp(m, m0, LP_INDEX_NODES, m1).size ≠ LEB_SIZE → mklp(m, m0, LP_INDEX_NODES, m1).size = # avol[m2].data ⊦ dups(log1), # avol[m2].data ≤ LEB_SIZE ∧ avol[m2].mapped? ∧ m0 = # avol[m2].data ∧ is-aligned(# avol[m2].data, 2 * NODE_HEADER_SIZE)

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(m, m0, LP_INDEX_NODES, m1), indexblock(indx, lax, m), avol[m2]] flags: <all paths>

Additional information

Used terms: mklp(m, m0, LP_INDEX_NODES, m1), indexblock(indx, lax, m), avol[m2]