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Proof step 166 from proof inv-read-gblock-nodes (previous step)

# lpt = # avol, # lpt0 = # avol, # gndx0 = # lax2, # gndx3 = # lax1, n0 + # buf = gnd.alignedsize + 2 * NODE_HEADER_SIZE + n1, LEB_SIZE = n1 + # buf0 + 2 * NODE_HEADER_SIZE + gnd.alignedsize, LEB_SIZE = n0 + # buf0 + # buf, avol[m5] = mapped(buf0 + buf), align↑(m2, 2 * NODE_HEADER_SIZE) = gnd.alignedsize, m5 < # avol, abs-node(subarray(buf + mkempbuf(n0), 0, 2 * NODE_HEADER_SIZE + gnd.alignedsize), gnd), 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(m2, false), 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 + gnd.alignedsize, validtrailer, 0, NODE_HEADER_SIZE), range=(buf, NODE_HEADER_SIZE + align↑(m2, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), # buf0 + NODE_HEADER_SIZE ≤ LEB_SIZE, # buf0 + # buf ≤ LEB_SIZE, # buf0 + 2 * NODE_HEADER_SIZE + gnd.alignedsize ≤ LEB_SIZE, 2 * NODE_HEADER_SIZE + align↑(m2, 2 * NODE_HEADER_SIZE) ≤ # buf, ∃ buf2, buf1. buf = buf2 + buf1 ∧ ( false ∧ abs-padding(buf2) ∧ abs-nodes(buf1, # buf0 + # buf2, gndx0, lax2, true) ∨ # buf2 = gndx0.head.flashsize ∧ gndx0 ≠ [] ∧ lax2 ≠ [] ∧ lax2.head = @(# buf0, # buf2) ∧ ¬ false ∧ abs-node(buf2, gndx0.head) ∧ abs-nodes(buf1, # buf0 + # buf2, gndx0.tail, lax2.tail, true)) ⊦ buf = mkbuf(0), isempty(buf, 0, NODE_HEADER_SIZE), ∃ gndx5, lax4, buf1, buf2. buf0 + buf = buf1 + buf2 ∧ # buf1 = # buf0 + 2 * NODE_HEADER_SIZE + gnd.alignedsize ∧ abs-nodes(buf1, gndx3 + gnd ', lax1 + @(# buf0, 2 * NODE_HEADER_SIZE + gnd.alignedsize) ', false) ∧ abs-nodes(buf2, # buf1, gndx5, lax4, true)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 167:
# 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)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%⊦ abs-node(buf, gnd) ∧ 2 * NODE_HEADER_SIZE + gnd0.alignedsize ≤ # buf + # buf0 → ( abs-node (subarray (buf + buf0, 0, 2 * NODE_HEADER_SIZE + gnd0.alignedsize), gnd0) ↔ gnd = gnd0); (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%n + m ≤ # buf0, n + m ≤ # buf0 + # buf1 ⊦ isempty(buf0 + buf1, n, m) ↔ isempty(buf0, n, m); (s)% ⊦ # 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]%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ 2 * m = 0 ↔ m = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)% ⊦ # mkbuf(n) = n; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)%m ≠ 0 ⊦ is-aligned(n, m) → (m ≤ n ↔ n ≠ 0); (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)%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m * n + n0 < n ↔ m = 0 ∧ n0 < n; (ws)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)% ⊦ lax ≠ [] → # lax.tail = (# lax)-1; (s)% ⊦ n -1 = n - 1; (s)% ⊦ gndx ≠ [] → # gndx.tail = (# gndx)-1; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%abs-nodes-elems-adr-length-h: ⊦ abs-nodes(buf, m, gndx, lax, weak) → # gndx = # lax; (forward) from specification abs-list[encoding-group-node]%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ gnd.flashsize = 2 * NODE_HEADER_SIZE + gnd.alignedsize; (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)