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Proof step 32 from proof prepost-encode-padding (previous step)

# buf = 2 * NODE_HEADER_SIZE + n0, # buf1 = # buf, subarray(buf1, NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0) = subarray(buf, NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0), NODE_HEADER_SIZE < # buf, n < NODE_HEADER_SIZE + n0, n < # buf, is-aligned(n0, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(n0, true), subarray(buf1, 0, NODE_HEADER_SIZE)), NODE_HEADER_SIZE ≤ n ⊦ buf1[n] = subarray(buf1, NODE_HEADER_SIZE, n0)[n - NODE_HEADER_SIZE], buf = mkbuf(0), n0 = 0

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, NODE_HEADER_SIZE, n1]

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ m < n → n ≠ 0; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, NODE_HEADER_SIZE, n1