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Proof step 169 from proof refine-sync (previous step)

# lpt0 = # avol0, # lpt1 = # avol0, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, lpt1[pstate.lnum] = mklp(m0, # buf0, LP_INDEX_NODES, m3), istore2[pstate.lnum] = indexblock(indx, lax, m0), avol0[pstate.lnum] = mapped(buf0), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, ginval < # avol0, pstate.lnum < # avol0, abs-gstore(avol0, lpt1, gstore2, ginval), abs-leb(mapped(buf0), indexblock(indx, lax, m0), mklp(m0, # buf0, LP_INDEX_NODES, m3)), abs-padding(buf1), awbuf-inv(avol0[pstate.lnum, mapped(buf0 + buf1)], buffered(pstate.lnum)), awbuf-inv(avol0, buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol0), bufs-log-only(buffered(pstate.lnum), log1, lpt1), flash-lpt-cons(lpt0, istore1, gstore1), freelist-cons(lpt1, freelist), inv(gstore2 \ ginval), inv(gstore1), inv(istore2), inv(istore1), inv(indexblock(indx, lax, m0)), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), log-group-block(log1, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1[pstate.lnum, mklp(m0, # buf0 + # buf1, LP_INDEX_NODES, m3)], lpt0, log1), lpt-ram-flash(lpt1, lpt0, log1), pstate.lnum ∈ istore2, EB_PAGE_SIZE + # buf0 ≤ LEB_SIZE + # buf0 % EB_PAGE_SIZE, # buf0 ≤ LEB_SIZE, # buf0 + # buf1 ≤ LEB_SIZE, istore1 ⊑ istore2, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? ∨ pstate.journal? ⊦ buf1 = mkbuf(0), pstate = readonly, pstate = unbuffered, abs-leb(mapped(buf0 + buf1), indexblock(indx, lax, m0), mklp(m0, # buf0 + # buf1, LP_INDEX_NODES, m3)), dups(log1), is-aligned(# buf0, EB_PAGE_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 170:
⊦ 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 171:
# lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, avol0[pstate.lnum] = mapped(buf0), istore2[pstate.lnum] = indexblock(indx, lax, m0), lpt1[pstate.lnum] = mklp(m0, # buf0, LP_INDEX_NODES, m3), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, mapped(buf0).mapped?, pstate.lnum < # avol0, ginval < # avol0, abs-gstore(avol0, lpt1, gstore2, ginval), abs-nodes (mapped(buf0).data, indexblock(indx, lax, m0).indlist, indexblock(indx, lax, m0).ladrlist, mklp(m0, # buf0, LP_INDEX_NODES, m3).size = LEB_SIZE), abs-padding(buf1), awbuf-inv(avol0, buffered(pstate.lnum)), awbuf-inv(avol0[pstate.lnum, mapped(buf0 + buf1)], buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol0), bufs-log-only(buffered(pstate.lnum), log1, lpt1), flash-lpt-cons(lpt0, istore1, gstore1), freelist-cons(lpt1, freelist), inv(indexblock(indx, lax, m0)), inv(istore1), inv(istore2), inv(gstore1), inv(gstore2 \ ginval), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), log-group-block(log1, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log1), lpt-ram-flash(lpt1[pstate.lnum, mklp(m0, # buf0 + # buf1, LP_INDEX_NODES, m3)], lpt0, log1), pstate.lnum ∈ istore2, # buf0 + # buf1 ≤ LEB_SIZE, # buf0 ≤ LEB_SIZE, EB_PAGE_SIZE + # buf0 ≤ LEB_SIZE + # buf0 % EB_PAGE_SIZE, istore1 ⊑ istore2, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, mklp(m0, # buf0, LP_INDEX_NODES, m3).size ≠ LEB_SIZE → mklp(m0, # buf0, LP_INDEX_NODES, m3).size = # mapped(buf0).data, pstate.index? ∨ pstate.journal? ⊦ buf1 = mkbuf(0), pstate = unbuffered, pstate = readonly, abs-leb(mapped(buf0 + buf1), indexblock(indx, lax, m0), mklp(m0, # buf0 + # buf1, LP_INDEX_NODES, m3)), dups(log1), is-aligned(# buf0, EB_PAGE_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(m0, # buf0, LP_INDEX_NODES, m3), indexblock(indx, lax, m0), mapped(buf0)] flags: <all paths>

Additional information

Used terms: mklp(m0, # buf0, LP_INDEX_NODES, m3), indexblock(indx, lax, m0), mapped(buf0)