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Proof step 131 from proof encode-node (previous step)

# buf2 = # buf, # buf0 = # buf, # buf = n0 + n + 2 * NODE_HEADER_SIZE + nd.alignedsize, err = ESUCCESS, m0 = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), subarray(buf2, 0, n + NODE_HEADER_SIZE) = subarray(buf0, 0, n + NODE_HEADER_SIZE), 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(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)), (n + NODE_HEADER_SIZE) + node-size-headerless(nd) ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, n + 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ # buf, (n + NODE_HEADER_SIZE + node-size-headerless(nd)) + (m0 - node-size-headerless(nd)) ≤ # buf2, m0 ≥ node-size-headerless(nd), err = ESUCCESS → is-encoded(nd, subarray(buf2, n + NODE_HEADER_SIZE, node-size-headerless(nd))) ∧ m = node-size-headerless(nd), err = ESUCCESS ∨ ⌊err⌋ ⊦ ( 0 + NODE_HEADER_SIZE ≤ # validtrailer ∧ (n + NODE_HEADER_SIZE + m0) + NODE_HEADER_SIZE ≤ # fill(buf2, empty, n + NODE_HEADER_SIZE + node-size-headerless(nd), m0 - node-size-headerless(nd))) ∧ (n + NODE_HEADER_SIZE + node-size-headerless(nd)) + (m0 - node-size-headerless(nd)) ≤ # buf2 ∧ m0 ≥ node-size-headerless(nd)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%n ≠ 0, is-aligned(m, n) ⊦ m < align↑(m0, n) ↔ m < m0; (s)% ⊦ is-aligned(nd.alignedsize, 2 * NODE_HEADER_SIZE); (s)% ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)%m1 ≠ 0 ⊦ m < (* m1) * m + n0 ↔ (m1 - 1) * m + n0 ≠ 0; (s)% ⊦ m0 * 1 = m0; (s)%m1 ≠ 0 ⊦ m + n < (* m1) * m + n0 ↔ n < (m1 - 1) * m + n0; (s)% ⊦ NODE_HEADER_SIZE < 2 * NODE_HEADER_SIZE; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ 2 * NODE_HEADER_SIZE + n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ # fill(buf, d, m, n) = # buf; (s)% ⊦ m + m = 2 * m; (s)% ⊦ m ≤ m; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)% ⊦ n + 0 = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)%m ≠ 0 ⊦ align↑(n, m) < n ↔ false; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%m ≠ 0 ⊦ n0 ≤ align↑(n0, m); (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ NODE_HEADER_SIZE ≠ 0; (s)% ⊦ 2 * m = 0 ↔ m = 0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)