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Proof step 167 from proof inv-read-gblock-nodes (previous step)

# lpt = # avol, # lpt0 = # avol, # gndx0 = # lax2, # gndx3 = # lax1, # buf2 = align↑(m2, 2 * NODE_HEADER_SIZE) + 2 * NODE_HEADER_SIZE, lax2.head = @(# buf0, # buf2), LEB_SIZE = n0 + # buf0 + # buf2 + # buf1, avol[m5] = mapped(buf0 + buf2 + buf1), align↑(m2, 2 * NODE_HEADER_SIZE) = gndx0.head.alignedsize, m5 < # avol, abs-node(buf2, gndx0.head), abs-nodes(buf0, gndx3, lax1, false), abs-nodes(buf1, # buf0 + # buf2, gndx0.tail, lax2.tail, true), awbuf-inv(avol, bleb), buf-ro-rw-mode(isbuf, bleb, lpt0, avol), bufs-log-only(bleb, log0, lpt0), is-aligned(# buf2, NODE_HEADER_SIZE), is-encoded(nodeheader(m2, false), subarray(buf2, 0, NODE_HEADER_SIZE)), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), range=(buf2 + buf1, NODE_HEADER_SIZE + align↑(m2, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), # buf0 + NODE_HEADER_SIZE ≤ LEB_SIZE, # buf0 + # buf2 + # buf1 ≤ LEB_SIZE, # buf0 + # buf2 ≤ LEB_SIZE ⊦ buf2 + buf1 = mkbuf(0), gndx0 = [], lax2 = [], isempty(buf2, 0, NODE_HEADER_SIZE), ∃ gndx5, lax4, buf4, buf3. buf0 + buf2 + buf1 = buf4 + buf3 ∧ # buf4 = # buf0 + # buf2 ∧ abs-nodes(buf4, gndx3 + gndx0.head ', lax1 + @(# buf0, # buf2) ', false) ∧ abs-nodes(buf3, # buf4, gndx5, lax4, true)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 168:
# buf2 = align↑(m2, 2 * NODE_HEADER_SIZE) + 2 * NODE_HEADER_SIZE, # gndx3 = # lax1, # gndx0 = # lax2, # lpt0 = # avol, # lpt = # avol, LEB_SIZE = n0 + # buf0 + # buf2 + # buf1, avol[m5] = mapped(buf0 + buf2 + buf1), align↑(m2, 2 * NODE_HEADER_SIZE) = gndx0.head.alignedsize, ladr = @(# buf0, # buf2), lax2 = ladr + lax0, m5 < # avol, abs-node(buf2, gndx0.head), abs-nodes(buf1, # buf0 + # buf2, gndx0.tail, lax0, true), abs-nodes(buf0, gndx3, lax1, false), awbuf-inv(avol, bleb), buf-ro-rw-mode(isbuf, bleb, lpt0, avol), bufs-log-only(bleb, log0, lpt0), is-aligned(# buf2, NODE_HEADER_SIZE), is-encoded(nodeheader(m2, false), subarray(buf2, 0, NODE_HEADER_SIZE)), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), range=(buf2 + buf1, NODE_HEADER_SIZE + align↑(m2, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), # buf0 + # buf2 ≤ LEB_SIZE, # buf0 + # buf2 + # buf1 ≤ LEB_SIZE, # buf0 + NODE_HEADER_SIZE ≤ LEB_SIZE ⊦ buf2 + buf1 = mkbuf(0), gndx0 = [], lax2 = [], isempty(buf2, 0, NODE_HEADER_SIZE), ∃ gndx5, lax4, buf4, buf3. buf0 + buf2 + buf1 = buf4 + buf3 ∧ # buf4 = # buf0 + # buf2 ∧ abs-nodes(buf4, gndx3 + gndx0.head ', lax1 + @(# buf0, # buf2) ', false) ∧ abs-nodes(buf3, # buf4, gndx5, lax4, true)

Rule argument

spec: list-data, inst: laddress-list name: elim-list-c seq: lax ≠ [] ⊦ ladr = lax.head ∧ lax0 = lax.tail ↔ lax = ladr + lax0 subst: [lax, ladr, lax0] → [lax2, ladr, lax]

Additional information

Used simplifier rules: lax ≠ [] ⊦ ladr = lax.head ∧ lax0 = lax.tail ↔ lax = ladr + lax0; (elim) Used terms: lax2, ladr, lax