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Proof step 157 from proof encode-node (previous step)

# buf2 = # buf, # buf0 = # buf, # buf = n0 + n + 2 * NODE_HEADER_SIZE + nd.alignedsize, # buf = n1 + (n + NODE_HEADER_SIZE) + node-size-headerless(nd), NODE_HEADER_SIZE + n0 + nd.alignedsize = node-size-headerless(nd) + n1, subarray(buf2, 0, n + NODE_HEADER_SIZE) = subarray(buf0, 0, n + NODE_HEADER_SIZE), subarray(buf2, (n + NODE_HEADER_SIZE) + node-size-headerless(nd), n1) = subarray(buf0, (n + NODE_HEADER_SIZE) + node-size-headerless(nd), n1), subarray(buf0, 0, n) = subarray(buf, 0, n), subarray(buf0, n + NODE_HEADER_SIZE, node-size-headerless(nd) + n1) = subarray(buf, n + NODE_HEADER_SIZE, node-size-headerless(nd) + n1), is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)), (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ # buf, ⌊err⌋ ⊦ subarray(buf2, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) = subarray(buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 158:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 159:
# buf = n1 + (n + NODE_HEADER_SIZE) + node-size-headerless(nd), # buf = n0 + n + 2 * NODE_HEADER_SIZE + nd.alignedsize, # buf0 = # buf, # buf2 = # buf, NODE_HEADER_SIZE + n0 + nd.alignedsize = node-size-headerless(nd) + n1, subarray(buf0, n + NODE_HEADER_SIZE, node-size-headerless(nd) + n1) = subarray(buf, n + NODE_HEADER_SIZE, node-size-headerless(nd) + n1), subarray(buf0, 0, n) = subarray(buf, 0, n), subarray(buf2, (n + NODE_HEADER_SIZE) + node-size-headerless(nd), n1) = subarray(buf0, (n + NODE_HEADER_SIZE) + node-size-headerless(nd), n1), subarray(buf2, 0, n + NODE_HEADER_SIZE) = subarray(buf0, 0, n + NODE_HEADER_SIZE), is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)), n + 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, ⌊err⌋ ⊦ # subarray(buf2, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) = # subarray(buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) ∧ (∀ n1. n1 < # subarray(buf2, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) → subarray(buf2, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0)[n1] = subarray(buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0)[n1])

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [subarray(buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0), subarray (buf2, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0)] flags: <all paths>

Additional information

Used terms: subarray(buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0), subarray(buf2, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0)