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Proof step 36 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), n1 < NODE_HEADER_SIZE, n1 + NODE_HEADER_SIZE + n0 < # buf, NODE_HEADER_SIZE + n0 < # buf, is-aligned(n0, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(n0, true), subarray(buf1, 0, NODE_HEADER_SIZE)) ⊦ (validtrailer)[n1] = (subarray(buf1, NODE_HEADER_SIZE, n0) + validtrailer)[n1 + n0], buf = mkbuf(0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: append-at seq: ⊦ n < # buf + # buf0 → (buf + buf0)[n] = (n < # buf ⊃ buf[n];buf0[n - # buf]) subst: [n, buf0, buf] → [n1 + n0, validtrailer, subarray(buf1, NODE_HEADER_SIZE, n0)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # subarray(buf, m, n) = n; (s)% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n - m = n; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s) Used terms: n1 + n0, validtrailer, subarray(buf1, NODE_HEADER_SIZE, n0)