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Proof step 116 from proof decode-node (previous step)

# buf = NODE_HEADER_SIZE, # buf1 = align↑(node-size-headerless(nd), 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(node-size-headerless(nd), false), buf), is-encoded(nd, subarray(buf1 + validtrailer + buf0, 0, node-size-headerless(nd))), node-size-headerless(nd) ≤ # buf1 + NODE_HEADER_SIZE + # buf0 ⊦ is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd)))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: subarray-elim-right seq: n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m) subst: [m, n, buf0, buf] → [node-size-headerless(nd), 0, validtrailer + buf0, buf1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ 2 * m = 0 ↔ m = 0; (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%m ≠ 0 ⊦ align↑(n, m) < n ↔ false; (s) Used terms: node-size-headerless(nd), 0, validtrailer + buf0, buf1