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Proof step 17 from proof abs-nodes-crash-h (previous step)

n < # buf0, abs-nodes(buf1, m + # buf0, [], [], true), is-aligned(n, NODE_HEADER_SIZE), n ≤ # buf0 + # buf1, ∃ buf2, buf1. buf0 = buf2 + buf1 + validtrailer ∧ is-encoded(nodeheader(# buf1, true), buf2) ∧ is-aligned(# buf1, 2 * NODE_HEADER_SIZE), ∀ buf2, m, x, lax, n. # buf2 < #(buf0 + buf1) → abs-nodes(buf2, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf2 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf2, 0, n), m, x0, lax0, true)) ⊦ buf0 = mkbuf(0), abs-nodes(subarray(buf0, 0, n), m, [], [], true)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# buf2 = NODE_HEADER_SIZE, n < 2 * NODE_HEADER_SIZE + # buf, abs-nodes(buf1, 2 * NODE_HEADER_SIZE + m + # buf, [], [], 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 + # 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), abs-nodes(subarray(buf2 + buf + validtrailer, 0, n), m, [], [], true)

Rule argument

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ 2 * NODE_HEADER_SIZE + n ≠ 0; (s)% ⊦ m + m = 2 * m; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)%lfw-is-encoded-nodeheader-size: ⊦ is-encoded(ndhd, buf) → # buf = NODE_HEADER_SIZE; (forward) from specification abs-node%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%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)