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Proof step 82 from proof abs-nodes-crash-h (previous step)

# buf2 = NODE_HEADER_SIZE, n < 2 * NODE_HEADER_SIZE + # buf, abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + # buf, nd ' + x1, @(m0, m1) ' + lax0, true), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), is-encoded(nodeheader(# buf, true), buf2), n ≤ 2 * NODE_HEADER_SIZE + # buf + # buf0, ∀ 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)) ⊦ abs-nodes(subarray((buf2 + buf + validtrailer) + buf0, 0, n), m, [], [], true)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 83:
⊦ abs-nodes(buf, m, [], lax, weak) ↔ # buf = 0 ∧ lax = [] ∨ (∃ buf0, buf1. buf = buf0 + buf1 ∧ abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, [], lax, weak)) ∨ weak ∧ abs-failed(buf) ∧ lax = []
Proof step 84:
# buf2 = NODE_HEADER_SIZE, n < 2 * NODE_HEADER_SIZE + # buf, abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + # buf, nd ' + x1, @(m0, m1) ' + lax0, true), is-aligned(n, NODE_HEADER_SIZE), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf, true), buf2), n ≤ 2 * NODE_HEADER_SIZE + # buf + # buf0, ∀ 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)) ⊦ ∃ buf3, buf1. subarray((buf2 + buf + validtrailer) + buf0, 0, n) = buf3 + buf1 ∧ abs-padding(buf3) ∧ abs-nodes(buf1, m + # buf3, [], [], true), # subarray((buf2 + buf + validtrailer) + buf0, 0, n) = 0 ∧ [] = [], true ∧ abs-failed(subarray((buf2 + buf + validtrailer) + buf0, 0, n)) ∧ [] = []

Rule argument

spec: <toplevel> name: abs-nodes-base seq: ⊦ abs-nodes(buf, m, [], lax, weak) ↔ # buf = 0 ∧ lax = [] ∨ (∃ buf0, buf1. buf = buf0 + buf1 ∧ abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, [], lax, weak)) ∨ weak ∧ abs-failed(buf) ∧ lax = [] subst: [weak, lax, m, buf] → [true, [], m, subarray((buf2 + buf + validtrailer) + buf0, 0, n)] flags: <all paths>

Additional information

Used terms: true, [], m, subarray((buf2 + buf + validtrailer) + buf0, 0, n)