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Proof step 99 from proof decode-node (previous step)

is-encoded(nd, subarray(buf1, NODE_HEADER_SIZE, node-size-headerless(nd))), is-encoded(nodeheader(node-size-headerless(nd), false), subarray(buf1, 0, NODE_HEADER_SIZE)), range=(buf1, NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), NODE_HEADER_SIZE + node-size-headerless(nd) ≤ # buf1, NODE_HEADER_SIZE ≤ # buf1, align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) + 2 * NODE_HEADER_SIZE ≤ # buf1, 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE) ≤ # buf1, NODE_HEADER_SIZE ≤ # buf1 → (∃ buf0, buf2. buf1 = buf0 + buf2 ∧ # buf0 = NODE_HEADER_SIZE) ⊦ ∃ buf2, buf3. subarray(buf1, 0, 2 * NODE_HEADER_SIZE + align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)) = buf2 + buf3 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf2) ∧ is-encoded(nd, subarray(buf3, 0, node-size-headerless(nd))) ∧ # buf3 = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ n = # buf ∧ m ≤ # buf0 → subarray(buf + buf0, n, m) = subarray(buf0, 0, m); (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; 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)%m2 ≠ 0 ⊦ (* m2) * m + n ≤ m + n0 ↔ (m2 - 1) * m + n ≤ n0; (s)%is-encoded-size: ⊦ is-encoded(ndhd, buf) → # buf = NODE_HEADER_SIZE; (forward) from specification encoding-fixed-size-nonempty[encoding-node-header]% ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)