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Proof step 198 from proof inv-read-gblock-nodes (previous step)

# gndx0 = # lax2, # gndx3 = # lax1, # lpt0 = # avol, # lpt = # avol, LEB_SIZE = n0 + # buf0 + # buf, avol[m5] = mapped(buf0 + buf), m5 < # avol, 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(# buf, NODE_HEADER_SIZE), is-encoded(nodeheader(m, true), subarray(buf, 0, NODE_HEADER_SIZE)), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), range=(buf, NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), # buf0 + 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ≤ LEB_SIZE, # buf0 + # buf ≤ LEB_SIZE, # buf0 + NODE_HEADER_SIZE ≤ LEB_SIZE, 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ≤ # buf, ∃ buf2, buf1. buf = buf2 + buf1 ∧ ( true ∧ abs-padding(buf2) ∧ abs-nodes(buf1, # buf0 + # buf2, gndx0, lax2, true) ∨ # buf2 = gndx0.head.flashsize ∧ gndx0 ≠ [] ∧ lax2 ≠ [] ∧ lax2.head = @(# buf0, # buf2) ∧ ¬ true ∧ abs-node(buf2, gndx0.head) ∧ abs-nodes(buf1, # buf0 + # buf2, gndx0.tail, lax2.tail, true)) ⊦ # buf + n0 = 0, buf = mkbuf(0), isempty(buf, 0, NODE_HEADER_SIZE), ∃ gndx5, lax4, buf1, buf2. buf0 + buf = buf1 + buf2 ∧ # buf1 = # buf0 + 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ∧ abs-nodes(buf1, gndx3, lax1, false) ∧ abs-nodes(buf2, # buf1, gndx5, lax4, true)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 199:
# gndx0 = # lax2, # gndx3 = # lax1, # lpt0 = # avol, # lpt = # avol, LEB_SIZE = n0 + # buf0 + (2 * NODE_HEADER_SIZE + m) + # buf1, avol[m5] = mapped(buf0 + buf2 + buf1), m5 < # avol, abs-nodes(buf0, gndx3, lax1, false), abs-nodes(buf1, # buf0 + 2 * NODE_HEADER_SIZE + m, gndx0, lax2, true), abs-padding(buf2), awbuf-inv(avol, bleb), buf-ro-rw-mode(isbuf, bleb, lpt0, avol), bufs-log-only(bleb, log0, lpt0), is-aligned(m, NODE_HEADER_SIZE), is-encoded(nodeheader(m, true), 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 + m, validtrailer, 0, NODE_HEADER_SIZE), # buf0 + 2 * NODE_HEADER_SIZE + m ≤ LEB_SIZE, # buf0 + (2 * NODE_HEADER_SIZE + m) + # buf1 ≤ LEB_SIZE, # buf0 + NODE_HEADER_SIZE ≤ LEB_SIZE ⊦ buf2 + buf1 = mkbuf(0), isempty(buf2, 0, NODE_HEADER_SIZE), ∃ gndx, lax, buf, buf3. buf0 + buf2 + buf1 = buf + buf3 ∧ # buf = # buf0 + 2 * NODE_HEADER_SIZE + m ∧ abs-nodes(buf, gndx3, lax1, false) ∧ abs-nodes(buf3, # buf, gndx, lax, true)

Rule argument

Additional information

Used simplifier rules: ⊦ # subarray(buf, m, n) = n; (s)%lfw-is-encoded-nodeheader-size: ⊦ is-encoded(ndhd, buf) → # buf = NODE_HEADER_SIZE; (forward) from specification abs-node[encoding-index-node]%n + m ≤ # buf0, n + m ≤ # buf0 + # buf1 ⊦ isempty(buf0 + buf1, n, m) ↔ isempty(buf0, n, m); (s)%m1 ≠ 0 ⊦ m ≤ (* m1) * m + n0; (s)% ⊦ m ≤ m + n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%⊦ abs-padding(buf) ∧ is-encoded (nodeheader(m, true), subarray(buf, 0, NODE_HEADER_SIZE)) → align↑(m, 2 * NODE_HEADER_SIZE) = m; (s)%n ≠ 0 ⊦ is-aligned(n0 * n, n); (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%⊦ abs-nodes(buf, m, gndx, lax, weak) → is-aligned(# buf, NODE_HEADER_SIZE); (ss)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ 2 * NODE_HEADER_SIZE + n ≠ 0; (s)%⊦ abs-padding(buf) ∧ is-encoded (nodeheader(m, true), subarray(buf, 0, NODE_HEADER_SIZE)) → # buf = 2 * NODE_HEADER_SIZE + m; (s)%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)% ⊦ # buf < NODE_HEADER_SIZE → ¬ abs-padding(buf); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)