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Proof step 182 from proof encode-node (previous step)

# buf0 = # buf, # buf = n0 + n + 2 * NODE_HEADER_SIZE + nd.alignedsize, subarray(buf0, 0, n) = subarray(buf, 0, n), subarray(buf0, n + NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0 + nd.alignedsize) = subarray(buf, n + NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0 + nd.alignedsize), n + NODE_HEADER_SIZE ≤ # buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ # buf, ⌊err⌋ ⊦ subarray(buf0, 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 183:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 184:
# buf = n0 + n + 2 * NODE_HEADER_SIZE + nd.alignedsize, # buf0 = # buf, subarray(buf0, n + NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0 + nd.alignedsize) = subarray(buf, n + NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0 + nd.alignedsize), subarray(buf0, 0, n) = subarray(buf, 0, n), n + 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, ⌊err⌋ ⊦ # subarray(buf0, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) = # subarray(buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) ∧ (∀ n1. n1 < # subarray(buf0, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) → subarray(buf0, 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 (buf0, 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(buf0, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0)