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Proof step 29 from proof abs-nodes-crash-h (previous step)

# buf2 = NODE_HEADER_SIZE, n0 < NODE_HEADER_SIZE + # buf, abs-nodes(buf1, 2 * NODE_HEADER_SIZE + m + # buf, [], [], true), is-aligned(n0, NODE_HEADER_SIZE), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf, true), buf2), n0 ≤ NODE_HEADER_SIZE + # buf + # buf1, ∀ buf3, m, x, lax, n. # buf3 < #((buf2 + buf + validtrailer) + buf1) → 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)) ⊦ buf2 + buf + validtrailer = mkbuf(0), #(buf2 + subarray(buf + validtrailer, 0, n0)) ≥ NODE_HEADER_SIZE ∧ is-aligned(#(buf2 + subarray(buf + validtrailer, 0, n0)), NODE_HEADER_SIZE) ∧ (∃ buf0, buf1. buf2 + subarray(buf + validtrailer, 0, n0) = buf0 + buf1 ∧ # buf0 = NODE_HEADER_SIZE ∧ (is-garbage-header(buf0) ∨ (∃ ndhd. is-encoded(ndhd, buf0) ∧ # buf1 ≤ align↑(ndhd.size, 2 * NODE_HEADER_SIZE))))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
# buf2 = NODE_HEADER_SIZE, n0 < NODE_HEADER_SIZE + # buf, abs-nodes(buf1, 2 * NODE_HEADER_SIZE + m + # buf, [], [], true), is-aligned(n0, NODE_HEADER_SIZE), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf, true), buf2), n0 ≤ NODE_HEADER_SIZE + # buf + # buf1, ∀ buf3, m, x, lax, n. # buf3 < #((buf2 + buf + validtrailer) + buf1) → 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)) ⊦ buf2 + buf + validtrailer = mkbuf(0), ∃ buf0, buf1. buf2 + subarray(buf + validtrailer, 0, n0) = buf0 + buf1 ∧ # buf0 = NODE_HEADER_SIZE ∧ (is-garbage-header(buf0) ∨ (∃ ndhd. is-encoded(ndhd, buf0) ∧ # buf1 ≤ align↑(ndhd.size, 2 * NODE_HEADER_SIZE)))

Rule argument

Additional information

Used simplifier rules: n ≠ 0 ⊦ is-aligned(n, n); (s)% ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)