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Proof step 147 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf3 = NODE_HEADER_SIZE, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf0 = a0.alignedsize, 2 * NODE_HEADER_SIZE + a0.alignedsize = # buf4, subarray(buf3 + buf0 + validtrailer, 0, n) = buf4 + buf2, n < 2 * NODE_HEADER_SIZE + a0.alignedsize + # buf + # buf1, n < # buf4, abs-node(buf1, a), abs-nodes(buf2, m + # buf4, x0 + a ', lax0 + @(2 * NODE_HEADER_SIZE + m + a0.alignedsize + # buf, # buf1) ', boolvar), abs-nodes(buf, 2 * NODE_HEADER_SIZE + m + a0.alignedsize, x0, lax0, false), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), is-encoded(a0, subarray(buf0, 0, node-size-headerless(a0))), is-encoded(nodeheader(node-size-headerless(a0), false), buf3), ∃ buf0, buf1. buf4 = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(a0), false), buf0) ∧ is-encoded(a0, subarray(buf1, 0, node-size-headerless(a0))) ∧ # buf1 = a0.alignedsize, ∀ buf4, buf1, a, n, m, x, lax, boolvar. # buf4 < #((buf3 + buf0 + validtrailer) + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf4 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf4 + buf1, 0, n), m, x + a ', lax + @(m + # buf4, # buf1) ', boolvar) ∧ abs-nodes(buf4, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf4 + # buf1 ⊦ buf3 + buf0 + validtrailer = mkbuf(0), buf4 = mkbuf(0), n = 2 * NODE_HEADER_SIZE + a0.alignedsize + # buf + # buf1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 148:
# buf0 = a0.alignedsize, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf3 = NODE_HEADER_SIZE, # buf5 = a0.alignedsize, # buf6 = NODE_HEADER_SIZE, subarray(buf3 + buf0 + validtrailer, 0, n) = (buf6 + buf5 + validtrailer) + buf2, n < 2 * NODE_HEADER_SIZE + a0.alignedsize + # buf + # buf1, n < 2 * NODE_HEADER_SIZE + a0.alignedsize, abs-node(buf1, a), abs-nodes(buf, 2 * NODE_HEADER_SIZE + m + a0.alignedsize, x0, lax0, false), abs-nodes (buf2, 2 * NODE_HEADER_SIZE + m + a0.alignedsize, x0 + a ', lax0 + @(2 * NODE_HEADER_SIZE + m + a0.alignedsize + # buf, # buf1) ', boolvar), is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), is-encoded(nodeheader(node-size-headerless(a0), false), buf6), is-encoded(a0, subarray(buf5, 0, node-size-headerless(a0))), is-encoded(nodeheader(node-size-headerless(a0), false), buf3), is-encoded(a0, subarray(buf0, 0, node-size-headerless(a0))), ∀ buf4, buf1, a, n, m, x, lax, boolvar. # buf4 < #((buf3 + buf0 + validtrailer) + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf4 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf4 + buf1, 0, n), m, x + a ', lax + @(m + # buf4, # buf1) ', boolvar) ∧ abs-nodes(buf4, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf4 + # buf1 ⊦ buf6 + buf5 + validtrailer = mkbuf(0), buf3 + buf0 + validtrailer = mkbuf(0), n = 2 * NODE_HEADER_SIZE + a0.alignedsize + # buf + # buf1

Rule argument

Additional information

Used simplifier rules: ⊦ m + m = 2 * m; (s)% ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%lfw-is-encoded-nodeheader-size: ⊦ is-encoded(ndhd, buf) → # buf = NODE_HEADER_SIZE; (forward) from specification abs-node%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%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)