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Proof step 103 from proof decode-node (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 104:
# buf = NODE_HEADER_SIZE, 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) = n0 + NODE_HEADER_SIZE, is-encoded(nodeheader(node-size-headerless(nd), false), buf), is-encoded(nd, subarray(buf0, 0, node-size-headerless(nd))), range=(buf + buf0, NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ # buf0, node-size-headerless(nd) ≤ # buf0, NODE_HEADER_SIZE ≤ 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ⊦ ∃ buf2, buf3. buf + subarray(buf0, 0, n0) = buf2 + buf3 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf2) ∧ is-encoded(nd, subarray(buf3, 0, node-size-headerless(nd))) ∧ # buf3 = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [ 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), NODE_HEADER_SIZE, n]

Additional information

Used simplifier rules: ⊦ 2 * m = 0 ↔ m = 0; (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m * n + n0 < n ↔ m = 0 ∧ n0 < n; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)%m2 ≠ 0 ⊦ ¬ (* m2) * m + n < m; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), NODE_HEADER_SIZE, n