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Proof step 10 from proof abs-node-abs-node-append-subarray (previous step)

# buf = nd1.alignedsize, # buf2 = nd0.alignedsize, # buf1 = NODE_HEADER_SIZE, # buf3 = NODE_HEADER_SIZE, buf1 + subarray((buf2 + validtrailer) + buf0, 0, 2 * NODE_HEADER_SIZE + nd1.alignedsize - NODE_HEADER_SIZE) = buf3 + buf + validtrailer, is-encoded(nodeheader(node-size-headerless(nd1), false), buf3), is-encoded(nd1, subarray(buf, 0, node-size-headerless(nd1))), is-encoded(nodeheader(node-size-headerless(nd0), false), buf1), is-encoded(nd0, subarray(buf2, 0, node-size-headerless(nd0))), nd1.alignedsize ≤ nd0.alignedsize + # buf0 ⊦ nd0 = nd1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
# buf3 = NODE_HEADER_SIZE, # buf1 = NODE_HEADER_SIZE, # buf2 = nd0.alignedsize, # buf = nd1.alignedsize, buf1 + subarray((buf2 + validtrailer) + buf0, 0, n0) = buf3 + buf + validtrailer, 2 * NODE_HEADER_SIZE + nd1.alignedsize = n0 + NODE_HEADER_SIZE, is-encoded(nd0, subarray(buf2, 0, node-size-headerless(nd0))), is-encoded(nodeheader(node-size-headerless(nd0), false), buf1), is-encoded(nd1, subarray(buf, 0, node-size-headerless(nd1))), is-encoded(nodeheader(node-size-headerless(nd1), false), buf3), nd1.alignedsize ≤ nd0.alignedsize + # buf0, NODE_HEADER_SIZE ≤ 2 * NODE_HEADER_SIZE + nd1.alignedsize ⊦ nd0 = nd1

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [2 * NODE_HEADER_SIZE + nd1.alignedsize, NODE_HEADER_SIZE, n]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m * n + n0 < n ↔ m = 0 ∧ n0 < n; (ws)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)%m2 ≠ 0 ⊦ ¬ (* m2) * m + n < m; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: 2 * NODE_HEADER_SIZE + nd1.alignedsize, NODE_HEADER_SIZE, n