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Proof step 37 from proof abs-nodes-notrailer-h (previous step)

# buf = nd.alignedsize, # buf2 = NODE_HEADER_SIZE, nd.alignedsize < node-size-headerless(nd), abs-nodes(buf0, 2 * NODE_HEADER_SIZE + n + nd.alignedsize, x0, lax0, weak), is-encoded(nodeheader(node-size-headerless(nd), false), buf2), is-encoded(nd, subarray(buf, 0, node-size-headerless(nd))), align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ nd.alignedsize + # buf0 ⊦ subarray((buf2 + buf + validtrailer) + buf0, NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), NODE_HEADER_SIZE) = validtrailer

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: encoding-node-base name: alignedsize seq: ⊦ nd.alignedsize = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) subst: [nd] → [nd] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + m = 2 * m; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m); (s)% ⊦ m + n - m = n; (s)% ⊦ m ≤ m; (s)% ⊦ m - m = 0; (s)% ⊦ n + 0 = n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n < n; (s)%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)% ⊦ 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 ≠ 0 ⊦ align↑(n, m) < n ↔ false; (s) Used terms: nd