[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 57 from proof decode-node (previous step)

err = ESUCCESS, m = m1, m0 = n, 2 * NODE_HEADER_SIZE ≤ m1, n + m1 ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, err = ESUCCESS → is-encoded(ndhd, subarray(buf, n, NODE_HEADER_SIZE)), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟪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)), err = ESUCCESS ∧ align↑(ndhd.size, 2 * NODE_HEADER_SIZE) + 2 * NODE_HEADER_SIZE ≠ m, err = ESUCCESS ∧ ndhd.ispadding

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
m = align↑(ndhd.size, 2 * NODE_HEADER_SIZE) + 2 * NODE_HEADER_SIZE, is-encoded(ndhd, subarray(buf, n, NODE_HEADER_SIZE)), n + align↑(ndhd.size, 2 * NODE_HEADER_SIZE) + 2 * NODE_HEADER_SIZE ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf, ¬ ndhd.ispadding ⊦ ⟪decode_node_headerless#(n + 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, n + 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) ∧ align↑(ndhd.size, 2 * NODE_HEADER_SIZE) = nd.alignedsize))

Rule argument

Additional information

Used simplifier rules: ⊦ 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 ≤ m + n; (s)% ⊦ # subarray(buf, m, n) = n; (s)%is-encoded-size: ⊦ is-encoded(ndhd, buf) → # buf = NODE_HEADER_SIZE; (forward) from specification encoding-fixed-size-nonempty[encoding-node-header]