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Proof step 170 from proof inv-read-gblock-nodes (previous step)

# gndx3 = # lax1, # buf2 = align↑(m2, 2 * NODE_HEADER_SIZE) + 2 * NODE_HEADER_SIZE, # lpt = # avol, # lpt0 = # avol, # gndx0 = # lax0 + 1, # gndx0 - 1 = # lax0, LEB_SIZE = n0 + # buf0 + # buf2 + # buf1, avol[m5] = mapped(buf0 + buf2 + buf1), align↑(m2, 2 * NODE_HEADER_SIZE) = gnd.alignedsize, gndx0 = gnd + gndx1, m5 < # avol, abs-node(buf2, gnd), abs-nodes(buf0, gndx3, lax1, false), abs-nodes(buf1, # buf0 + # buf2, gndx1, lax0, 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 = [], isempty(buf2, 0, NODE_HEADER_SIZE), ∃ gndx5, lax4, buf4, buf3. buf0 + buf2 + buf1 = buf4 + buf3 ∧ # buf4 = # buf0 + # buf2 ∧ abs-nodes(buf4, gndx3 + gnd ', lax1 + @(# buf0, # buf2) ', false) ∧ abs-nodes(buf3, # buf4, gndx5, lax4, true)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 171:
# lpt0 = # avol, # lpt = # avol, # buf2 = gnd.alignedsize + 2 * NODE_HEADER_SIZE, # gndx3 = # lax1, # gndx1 = # lax0, LEB_SIZE = n0 + # buf0 + # buf2 + # buf1, avol[m5] = mapped(buf0 + buf2 + buf1), align↑(m2, 2 * NODE_HEADER_SIZE) = gnd.alignedsize, m5 < # avol, abs-node(buf2, gnd), abs-nodes(buf1, # buf0 + # buf2, gndx1, 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 + gnd.alignedsize, validtrailer, 0, NODE_HEADER_SIZE), # buf0 + # buf2 ≤ LEB_SIZE, # buf0 + # buf2 + # buf1 ≤ LEB_SIZE, # buf0 + NODE_HEADER_SIZE ≤ LEB_SIZE ⊦ buf2 + buf1 = mkbuf(0), isempty(buf2, 0, NODE_HEADER_SIZE), ∃ gndx5, lax4, buf4, buf3. buf0 + buf2 + buf1 = buf4 + buf3 ∧ # buf4 = # buf0 + # buf2 ∧ abs-nodes(buf4, gndx3 + gnd ', lax1 + @(# buf0, # buf2) ', false) ∧ abs-nodes(buf3, # buf4, gndx5, lax4, true)

Rule argument

Additional information

Used simplifier rules: abs-nodes-elems-adr-length-h: ⊦ abs-nodes(buf, m, gndx, lax, weak) → # gndx = # lax; (forward) from specification abs-list[encoding-group-node]% ⊦ gnd ' + gndx ≠ []; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ m +1 = m + 1; (s)% ⊦ #(gnd ' + gndx) = (# gndx)+1; (s)% ⊦ gnd + gndx = gnd ' + gndx; (s)