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Proof step 35 from proof encode-node (previous step)

# buf = n0 + n + 2 * NODE_HEADER_SIZE + nd.alignedsize, # buf0 = # buf, # buf2 = # 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), subarray(buf2, (n + NODE_HEADER_SIZE) + node-size-headerless(nd), # buf - (n + NODE_HEADER_SIZE) + node-size-headerless(nd)) = subarray(buf0, (n + NODE_HEADER_SIZE) + node-size-headerless(nd), # buf - (n + NODE_HEADER_SIZE) + node-size-headerless(nd)), subarray(buf2, 0, n + NODE_HEADER_SIZE) = subarray(buf0, 0, n + NODE_HEADER_SIZE), is-encoded(nd, subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd))), is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)), align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) + n + NODE_HEADER_SIZE ≤ # buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, 2 * NODE_HEADER_SIZE + n + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ # buf ⊦ subarray (fill (buf2, empty, n + NODE_HEADER_SIZE + node-size-headerless(nd), align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) - node-size-headerless(nd)), 0, n) = subarray(buf, 0, n) ∧ subarray (fill (buf2, empty, n + NODE_HEADER_SIZE + node-size-headerless(nd), align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) - node-size-headerless(nd)), n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) = subarray(buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) ∧ (∃ buf, buf1. subarray (copy (validtrailer, 0, fill (buf2, empty, n + NODE_HEADER_SIZE + node-size-headerless(nd), align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) - node-size-headerless(nd)), n + NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), NODE_HEADER_SIZE), n, 2 * NODE_HEADER_SIZE + nd.alignedsize) = buf + buf1 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf) ∧ is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd))) ∧ # buf1 = nd.alignedsize) ∧ align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) = nd.alignedsize

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 36:
# buf2 = # buf, # buf0 = # buf, # buf = n0 + n + 2 * NODE_HEADER_SIZE + nd.alignedsize, # buf = n1 + (n + NODE_HEADER_SIZE) + node-size-headerless(nd), 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_HEADER_SIZE + n0 + nd.alignedsize) = subarray(buf, n + NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0 + nd.alignedsize), is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf0, n, NODE_HEADER_SIZE)), is-encoded(nd, subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd))), 2 * NODE_HEADER_SIZE + n + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ # buf, (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ # buf, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) + n + NODE_HEADER_SIZE ≤ # buf ⊦ subarray (fill (buf2, empty, n + NODE_HEADER_SIZE + node-size-headerless(nd), align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) - node-size-headerless(nd)), 0, n) = subarray(buf, 0, n) ∧ subarray (fill (buf2, empty, n + NODE_HEADER_SIZE + node-size-headerless(nd), align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) - node-size-headerless(nd)), n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) = subarray(buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize, n0) ∧ (∃ buf, buf1. subarray (copy (validtrailer, 0, fill (buf2, empty, n + NODE_HEADER_SIZE + node-size-headerless(nd), align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) - node-size-headerless(nd)), n + NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), NODE_HEADER_SIZE), n, 2 * NODE_HEADER_SIZE + nd.alignedsize) = buf + buf1 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf) ∧ is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd))) ∧ # buf1 = nd.alignedsize) ∧ align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) = nd.alignedsize

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# buf, (n + NODE_HEADER_SIZE) + node-size-headerless(nd), n1]

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # buf, (n + NODE_HEADER_SIZE) + node-size-headerless(nd), n1