[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 42 from proof decode-node (previous step)

align↑(ndhd.size, 2 * NODE_HEADER_SIZE) + 2 * NODE_HEADER_SIZE ≠ m1, is-encoded(ndhd, subarray(buf, n, NODE_HEADER_SIZE)), n + NODE_HEADER_SIZE ≤ # buf, n + m1 ≤ # buf, 2 * NODE_HEADER_SIZE ≤ m1, ¬ ndhd.ispadding ⊦ ⟪debug#("persistence: decode_node node of wrong size"); err := EIO; m0 := n; m := m1; 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))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 43:
¬ boolvar, ndhd = nodeheader(m2, boolvar), is-encoded(ndhd, subarray(buf, n, NODE_HEADER_SIZE)), 2 * NODE_HEADER_SIZE ≤ m1, n + m1 ≤ # buf, n + NODE_HEADER_SIZE ≤ # buf ⊦ ⟪debug#("persistence: decode_node node of wrong size"); err := EIO; m0 := n; m := m1; 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 ≠ m2 then {debug#("persistence: decode_node size of node unexpected"); err := EINVAL}}; if err = ESUCCESS ∧ ¬ range=(buf, m0 + NODE_HEADER_SIZE + align↑(m2, 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)), align↑(m2, 2 * NODE_HEADER_SIZE) + 2 * NODE_HEADER_SIZE = m1

Rule argument

spec: node-header name: elim seq: ⊦ m = ndhd.size ∧ (boolvar ↔ ndhd.ispadding) ↔ ndhd = nodeheader(m, boolvar) subst: [ndhd, m, boolvar] → [ndhd, m2, boolvar]

Additional information

Used simplifier rules: ⊦ m = ndhd.size ∧ (boolvar ↔ ndhd.ispadding) ↔ ndhd = nodeheader(m, boolvar); (elim) Used terms: ndhd, m2, boolvar