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Proof step 9 from proof abs-node-abs-node-append-subarray (previous step)

# buf = nd1.alignedsize, # buf2 = nd0.alignedsize, # buf1 = NODE_HEADER_SIZE, # buf3 = NODE_HEADER_SIZE, buf1 + subarray((buf2 + validtrailer) + buf0, 0, 2 * NODE_HEADER_SIZE + nd1.alignedsize - # buf1) = buf3 + buf + validtrailer, is-encoded(nodeheader(node-size-headerless(nd1), false), buf3), is-encoded(nd1, subarray(buf, 0, node-size-headerless(nd1))), is-encoded(nodeheader(node-size-headerless(nd0), false), buf1), is-encoded(nd0, subarray(buf2, 0, node-size-headerless(nd0))), nd1.alignedsize ≤ nd0.alignedsize + # buf0, # buf1 ≤ 2 * NODE_HEADER_SIZE + nd1.alignedsize, 2 * NODE_HEADER_SIZE + nd1.alignedsize ≤ # buf1 + #((buf2 + validtrailer) + buf0) ⊦ nd0 = nd1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# buf = nd1.alignedsize, # buf2 = nd0.alignedsize, # buf1 = NODE_HEADER_SIZE, # buf3 = NODE_HEADER_SIZE, buf1 + subarray((buf2 + validtrailer) + buf0, 0, 2 * NODE_HEADER_SIZE + nd1.alignedsize - NODE_HEADER_SIZE) = buf3 + buf + validtrailer, is-encoded(nodeheader(node-size-headerless(nd1), false), buf3), is-encoded(nd1, subarray(buf, 0, node-size-headerless(nd1))), is-encoded(nodeheader(node-size-headerless(nd0), false), buf1), is-encoded(nd0, subarray(buf2, 0, node-size-headerless(nd0))), nd1.alignedsize ≤ nd0.alignedsize + # buf0 ⊦ nd0 = nd1

Rule argument

Additional information

Used simplifier rules: m1 ≠ 0 ⊦ m ≤ (* m1) * m + n0; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%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)