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Proof step 35 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf2 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf = a.alignedsize, # buf0 = NODE_HEADER_SIZE, buf0 + subarray(buf + validtrailer, 0, n0) = buf2 + buf1, n0 < NODE_HEADER_SIZE + a.alignedsize, abs-nodes(buf1, m + # buf2, [], [], boolvar), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n0, NODE_HEADER_SIZE), is-encoded(nodeheader(node-size-headerless(a), false), buf0), is-encoded(a, subarray(buf, 0, node-size-headerless(a))), ∃ buf0, buf1. buf2 = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(a), false), buf0) ∧ is-encoded(a, subarray(buf1, 0, node-size-headerless(a))) ∧ # buf1 = a.alignedsize, ∀ buf, buf1, a, n, m, x, lax, boolvar. # buf < # mkbuf(0) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf + buf1, 0, n), m, x + a ', lax + @(m + # buf, # buf1) ', boolvar) ∧ abs-nodes(buf, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf + # buf1 ⊦ buf0 + buf + validtrailer = mkbuf(0), NODE_HEADER_SIZE + a.alignedsize = n0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
# buf3 = a.alignedsize, # buf0 = NODE_HEADER_SIZE, # buf = a.alignedsize, # buf4 = NODE_HEADER_SIZE, buf0 + subarray(buf + validtrailer, 0, n0) = (buf4 + buf3 + validtrailer) + buf1, n0 < NODE_HEADER_SIZE + a.alignedsize, abs-nodes(buf1, 2 * NODE_HEADER_SIZE + m + a.alignedsize, [], [], boolvar), is-aligned(n0, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), is-encoded(nodeheader(node-size-headerless(a), false), buf4), is-encoded(a, subarray(buf3, 0, node-size-headerless(a))), is-encoded(a, subarray(buf, 0, node-size-headerless(a))), is-encoded(nodeheader(node-size-headerless(a), false), buf0), ∀ buf, buf1, a, n, m, x, lax, boolvar. # buf < # mkbuf(0) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf + buf1, 0, n), m, x + a ', lax + @(m + # buf, # buf1) ', boolvar) ∧ abs-nodes(buf, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf + # buf1 ⊦ NODE_HEADER_SIZE + a.alignedsize = n0, buf0 + buf + validtrailer = mkbuf(0)

Rule argument

Additional information

Used simplifier rules: ⊦ m + m = 2 * m; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%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%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)