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Proof step 17 from proof decode-node (previous step)

n + m1 ≤ # buf, 2 * NODE_HEADER_SIZE ≤ m1 ⊦ ⟪decode_header#(n, buf; ndhd; err); if err = ESUCCESS ∧ ndhd.ispadding then {debug#("persistence: decode_node got padding node"); err := EIO}; m := m1; if err = ESUCCESS ∧ align↑(ndhd.size, 2 * NODE_HEADER_SIZE) + 2 * NODE_HEADER_SIZE ≠ m then {debug#("persistence: decode_node node of wrong size"); err := EIO}; m0 := n; if err = ESUCCESS then {decode_node_headerless#(m0 + NODE_HEADER_SIZE, buf; nd, m; err); if err ≠ ESUCCESS then debug#("persistence: decode_node decoding failed") else if m ≠ ndhd.size then {debug#("persistence: decode_node size of node unexpected"); err := EINVAL}}; if err = ESUCCESS ∧ ¬ range=(buf, m0 + NODE_HEADER_SIZE + align↑(ndhd.size, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE) then {debug#("persistence: decode_node no validtrailer"); err := EIO}⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → (∃ buf0, buf1. subarray(buf, n, 2 * NODE_HEADER_SIZE + nd.alignedsize) = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf0) ∧ is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd))) ∧ # buf1 = nd.alignedsize) ∧ m1 = 2 * NODE_HEADER_SIZE + nd.alignedsize))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: encoding-fixed-size-nonempty, inst: encoding-node-header name: decode-contract seq: n + NODE_HEADER_SIZE ≤ # buf ⊦ ⟪decode_header#(n, buf; ndhd; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → is-encoded(ndhd, subarray(buf, n, NODE_HEADER_SIZE)))) subst: [buf, n, ndhd, err] → [buf, n, ndhd, err] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → (n * n0 ≤ m ↔ n0 = 0); (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult