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Proof step 40 from proof abs-nodes-notrailer-h (previous step)

# buf = nd.alignedsize, # buf2 = NODE_HEADER_SIZE, 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, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ nd.alignedsize + # buf0 ⊦ subarray(buf + validtrailer, 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: array-splice, inst: buffer name: subarray-append-elim-left seq: # buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m) subst: [m, n0, buf0, buf] → [NODE_HEADER_SIZE, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), validtrailer, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # validtrailer = NODE_HEADER_SIZE; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m - m = 0; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s) Used terms: NODE_HEADER_SIZE, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), validtrailer, buf