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Proof step 86 from proof inv-read-gblock-nodes (previous step)

# gndx3 = # lax1, # gndx0 = # lax2, # lpt0 = # avol, # lpt = # avol, LEB_SIZE = n0 + # buf0 + # buf, avol[m5] = mapped(buf0 + buf), m5 < # avol, # buf < 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), LEB_SIZE < # buf0 + 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), n0 + # buf < 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), abs-nodes(buf, # buf0, gndx0, lax2, 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-encoded(nodeheader(m, boolvar), subarray((buf0 + buf) + mkempbuf(n0), # buf0, NODE_HEADER_SIZE)), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), # buf0 + # buf ≤ LEB_SIZE, # buf0 + NODE_HEADER_SIZE ≤ LEB_SIZE ⊦ # buf + n0 = 0, gndx0 = [], isempty((buf0 + buf) + mkempbuf(n0), # buf0, NODE_HEADER_SIZE), gndx0 = [] ∧ lax2 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 87:
# gndx3 = # lax1, # gndx0 = # lax2, # lpt0 = # avol, # lpt = # avol, LEB_SIZE = n0 + # buf0 + # buf, avol[m5] = mapped(buf0 + buf), m5 < # avol, # buf < 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), LEB_SIZE < # buf0 + 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), n0 + # buf < 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), abs-nodes(buf, # buf0, gndx0, lax2, 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-encoded(nodeheader(m, boolvar), subarray(buf, 0, NODE_HEADER_SIZE)), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), # buf0 + # buf ≤ LEB_SIZE, # buf0 + NODE_HEADER_SIZE ≤ LEB_SIZE ⊦ # buf + n0 = 0, gndx0 = [], isempty(buf + mkempbuf(n0), 0, NODE_HEADER_SIZE)

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 = # buf0, m ≤ # buf1 ⊦ isempty(buf0 + buf1, n, m) ↔ isempty(buf1, 0, m); (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)% ⊦ 0 < m ↔ m ≠ 0; (s)%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)%m ≤ # buf ⊦ subarray(buf0 + buf, # buf0, m) = subarray(buf, 0, m); (s)%# buf < NODE_HEADER_SIZE ⊦ abs-nodes(buf, m, gndx, lax, boolvar) ↔ gndx = [] ∧ lax = [] ∧ buf = mkbuf(0); (ws)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%# buf ≠ 0 ⊦ abs-nodes(buf, m, gndx, lax, weak) → (NODE_HEADER_SIZE ≤ # buf + n ↔ NODE_HEADER_SIZE ≤ # buf); (s)% ⊦ abs-nodes(mkbuf(0), m, gndx, lax, weak) ↔ gndx = [] ∧ lax = []; (s)% ⊦ buf + mkbuf(0) = buf; (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)% ⊦ # mkbuf(n) = n; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkempbuf(n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)