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Proof step 90 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(n, NODE_HEADER_SIZE), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf, true), buf2), n ≤ 2 * NODE_HEADER_SIZE + # buf + # buf0, # buf2 ≤ n, n ≤ # buf2 + #((buf + validtrailer) + 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)) ⊦ n = 0, abs-failed(buf2 + subarray((buf + validtrailer) + buf0, 0, n - # buf2))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 91:
# 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), NODE_HEADER_SIZE ≤ # buf0, 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)) ⊦ n = 0, abs-failed(buf2 + subarray(buf + validtrailer, 0, n - NODE_HEADER_SIZE))

Rule argument

Additional information

Used simplifier rules: abs-nodes-mkbuf0-empty-h: ⊦ abs-nodes(mkbuf(0), m, x, lax, weak) ↔ x = [] ∧ lax = [];%abs-nodes-headerspace: # buf ≠ 0 ⊦ abs-nodes(buf, m, x, lax, weak) → (NODE_HEADER_SIZE ≤ # buf + n ↔ NODE_HEADER_SIZE ≤ # buf);%m ≠ 0 ⊦ is-aligned(n, m) → (m ≤ n ↔ n ≠ 0); (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ' + x ≠ []; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)% ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m0 * 1 = m0; (s)%m1 ≠ 0 ⊦ m < (* m1) * m + n0 ↔ (m1 - 1) * m + n0 ≠ 0; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)% ⊦ m < n → m ≤ n; (s)% ⊦ m + m = 2 * m; (s)%n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0; (s)%m ≠ 0 ⊦ is-aligned(n, m) → (n < m ↔ n = 0); (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)