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Proof step 35 from proof prepost-encode-padding (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
# 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)

Rule argument

Additional information

Used simplifier rules: ⊦ NODE_HEADER_SIZE ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m0 * 1 = m0; (s)%m1 ≠ 0 ⊦ m + n < (* m1) * m ↔ n < (m1 - 1) * m; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m ≤ m + n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ 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 = n; (s)