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Proof step 185 from proof encode-node (previous step)

# 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), n1 < n0, n + 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, ⌊err⌋ ⊦ buf0[(n + 2 * NODE_HEADER_SIZE + nd.alignedsize) + n1] = buf[(n + 2 * NODE_HEADER_SIZE + nd.alignedsize) + n1]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 186:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 187:
# subarray(buf0, n + NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0 + nd.alignedsize) = # subarray(buf, n + NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0 + nd.alignedsize), # buf0 = # buf, # buf = n0 + n + 2 * NODE_HEADER_SIZE + nd.alignedsize, subarray(buf0, 0, n) = subarray(buf, 0, n), n1 < n0, n + NODE_HEADER_SIZE ≤ # buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ # buf, ⌊err⌋ , ∀ n1. n1 < # subarray(buf0, n + NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0 + nd.alignedsize) → subarray(buf0, n + NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0 + nd.alignedsize)[n1] = subarray(buf, n + NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0 + nd.alignedsize)[n1] ⊦ buf0[(n + 2 * NODE_HEADER_SIZE + nd.alignedsize) + n1] = buf[(n + 2 * NODE_HEADER_SIZE + nd.alignedsize) + 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 + NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0 + nd.alignedsize), subarray (buf0, n + NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0 + nd.alignedsize)] flags: <all paths>

Additional information

Used terms: subarray (buf, n + NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0 + nd.alignedsize), subarray (buf0, n + NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0 + nd.alignedsize)