[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 105 from proof abs-nodes-crash-h (previous step)

# buf2 = NODE_HEADER_SIZE, abs-nodes(subarray(buf0, 0, n0), 2 * NODE_HEADER_SIZE + m + # buf, x, lax, true), abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + # buf, nd ' + x1, @(m0, m1) ' + lax0, true), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-aligned(n0, NODE_HEADER_SIZE), is-encoded(nodeheader(# buf, true), buf2), n0 ≤ # buf0, x ⊑ nd ' + x1, lax ⊑ @(m0, m1) ' + lax0, ∀ buf3, m, x, lax, n. # buf3 < #((buf2 + buf + validtrailer) + buf0) → abs-nodes(buf3, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf3 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf3, 0, n), m, x0, lax0, true)) ⊦ ∃ x, lax. x ⊑ nd ' + x1 ∧ lax ⊑ @(m0, m1) ' + lax0 ∧ abs-nodes(buf2 + buf + validtrailer + subarray(buf0, 0, n0), m, x, lax, true)

User applied rule exists right

And obtained the following new goals

Proof step 106:
# buf2 = NODE_HEADER_SIZE, abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + # buf, nd ' + x1, @(m0, m1) ' + lax0, true), abs-nodes(subarray(buf0, 0, n0), 2 * NODE_HEADER_SIZE + m + # buf, x, lax, true), is-aligned(n0, NODE_HEADER_SIZE), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf, true), buf2), n0 ≤ # buf0, lax ⊑ @(m0, m1) ' + lax0, x ⊑ nd ' + x1, ∀ buf3, m, x, lax, n. # buf3 < #((buf2 + buf + validtrailer) + buf0) → abs-nodes(buf3, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf3 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf3, 0, n), m, x0, lax0, true)) ⊦ x ⊑ nd ' + x1 ∧ lax ⊑ @(m0, m1) ' + lax0 ∧ abs-nodes(buf2 + buf + validtrailer + subarray(buf0, 0, n0), m, x, lax, true)

Rule argument

pos: right 1 terms: x, lax abort: F discard: T computed: T

Additional information

Used terms: x, lax