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Proof step 187 from proof encode-node (previous step)

# 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]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 188:
# buf = n0 + n + 2 * NODE_HEADER_SIZE + nd.alignedsize, # buf0 = # buf, subarray(buf0, 0, n) = subarray(buf, 0, n), n1 < n0, n + 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, ⌊err⌋ , ∀ n2. n2 < NODE_HEADER_SIZE + n0 + nd.alignedsize → buf0[(n + NODE_HEADER_SIZE) + n2] = buf[(n + NODE_HEADER_SIZE) + n2] ⊦ buf0[(n + 2 * NODE_HEADER_SIZE + nd.alignedsize) + n1] = buf[(n + 2 * NODE_HEADER_SIZE + nd.alignedsize) + n1]

Rule argument

Additional information

Used simplifier rules: ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ # subarray(buf, m, n) = n; (s)