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Proof step 110 from proof decode-node (previous step)

# buf = NODE_HEADER_SIZE, # buf1 = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), subarray(buf + buf1 + buf2, NODE_HEADER_SIZE + # buf1, NODE_HEADER_SIZE) = subarray(validtrailer, 0, NODE_HEADER_SIZE), is-encoded(nd, subarray(buf1 + buf2, 0, node-size-headerless(nd))), is-encoded(nodeheader(node-size-headerless(nd), false), buf), node-size-headerless(nd) ≤ # buf1 + # buf2, NODE_HEADER_SIZE ≤ # buf2, (NODE_HEADER_SIZE + # buf1) + NODE_HEADER_SIZE ≤ #(buf + buf1 + buf2), 0 + NODE_HEADER_SIZE ≤ # validtrailer ⊦ ∃ buf0, buf3. buf + buf1 + subarray(buf2, 0, NODE_HEADER_SIZE) = buf0 + buf3 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf0) ∧ is-encoded(nd, subarray(buf3, 0, node-size-headerless(nd))) ∧ # buf3 = # buf1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 111:
# buf1 = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), # buf = NODE_HEADER_SIZE, subarray(buf2, 0, NODE_HEADER_SIZE) = validtrailer, is-encoded(nodeheader(node-size-headerless(nd), false), buf), is-encoded(nd, subarray(buf1 + buf2, 0, node-size-headerless(nd))), NODE_HEADER_SIZE ≤ # buf2, node-size-headerless(nd) ≤ # buf1 + # buf2 ⊦ ∃ buf0, buf3. buf + buf1 = buf0 + buf3 ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf0) ∧ is-encoded(nd, subarray(buf3, 0, node-size-headerless(nd))) ∧ # buf3 = # buf1

Rule argument

Additional information

Used simplifier rules: ⊦ buf + buf0 = buf1 + buf0 ↔ buf = buf1; (s)% ⊦ m - m = 0; (s)% ⊦ n + 0 = n; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)% ⊦ m ≤ m; (s)% ⊦ m + n - m = n; (s)%# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m); (s)%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 ≤ m + n0 ↔ (m2 - 1) * m ≤ n0; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ m + m = 2 * m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m + n; (s)