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Proof step 12 from proof abs-nodes-notrailer-h (previous step)

abs-nodes(buf1, n + # buf0, [], [], weak), is-encoded(nodeheader(m, boolvar0), subarray(buf0, 0, NODE_HEADER_SIZE)), 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ≤ # buf0 + # buf1, ∃ buf2, buf1. buf0 = buf2 + buf1 + validtrailer ∧ is-encoded(nodeheader(# buf1, true), buf2) ∧ is-aligned(# buf1, 2 * NODE_HEADER_SIZE) ⊦ buf0 + buf1 = mkbuf(0), range=(buf0 + buf1, NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
# buf2 = NODE_HEADER_SIZE, abs-nodes(buf1, 2 * NODE_HEADER_SIZE + n + # buf, [], [], weak), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf, true), buf2) ⊦ (buf2 + buf + validtrailer) + buf1 = mkbuf(0), range=((buf2 + buf + validtrailer) + buf1, NODE_HEADER_SIZE + # buf, validtrailer, 0, NODE_HEADER_SIZE)

Rule argument

Additional information

Used simplifier rules: ⊦ m + m = 2 * m; (s)% ⊦ m ≤ m + n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)%m ≠ 0 ⊦ is-aligned(n, m) → n % m = 0; (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)% ⊦ 2 * m = 0 ↔ m = 0; (s)%⊦ nodeheader(m, boolvar) = nodeheader(m0, boolvar0) ↔ m = m0 ∧ (boolvar ↔ boolvar0); (ws)% ⊦ is-encoded(ndhd, buf) → (is-encoded(ndhd0, buf) ↔ ndhd = ndhd0); (s)%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)%lfw-is-encoded-nodeheader-size: ⊦ is-encoded(ndhd, buf) → # buf = NODE_HEADER_SIZE; (forward) from specification abs-node%c: ⊦ m + n = n + m; from specification nat-basic%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m0 * 1 = m0; (s)%m2 ≠ 0 ⊦ (* m2) * m + n ≤ m + n0 ↔ (m2 - 1) * m + n ≤ n0; (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]% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)