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Proof step 27 from proof abs-nodes-nospace-header-h (previous step)

# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, # buf1 + # buf0 < 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), abs-nodes(buf0, n + # buf1, x0, lax0, weak), is-encoded(nodeheader(m, boolvar0), subarray(buf1, 0, NODE_HEADER_SIZE)), NODE_HEADER_SIZE ≤ # buf1 + # buf0, ∃ buf0, buf2. buf1 = buf0 + buf2 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf0) ∧ is-encoded(nd, subarray(buf2, 0, node-size-headerless(nd))) ∧ # buf2 = nd.alignedsize ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
# buf2 = NODE_HEADER_SIZE, # buf = nd.alignedsize, nd.alignedsize + # buf0 < align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), abs-nodes(buf0, 2 * NODE_HEADER_SIZE + n + nd.alignedsize, x0, lax0, weak), is-encoded(nd, subarray(buf, 0, node-size-headerless(nd))), is-encoded(nodeheader(node-size-headerless(nd), false), buf2) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m + m = 2 * m; (s)% ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%m1 ≠ 0 ⊦ m + n < (* m1) * m + n0 ↔ n < (m1 - 1) * m + n0; (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% ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; 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)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)