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Proof step 32 from proof abs-nodes-crash-h (previous step)

# buf2 = NODE_HEADER_SIZE, # buf < n0, n0 < NODE_HEADER_SIZE + # buf, abs-nodes(buf1, 2 * NODE_HEADER_SIZE + m + # buf, [], [], true), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-aligned(n0, 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), NODE_HEADER_SIZE = 1

User applied rule apply lemma

And obtained the following new goals

Proof step 33:
m ≠ 0 ⊦ is-aligned(m0, m) ∧ m0 < m1 ∧ m1 < m0 + m → ¬ is-aligned(m1, m)

Rule argument

spec: align name: between-is-aligned seq: m ≠ 0 ⊦ is-aligned(m0, m) ∧ m0 < m1 ∧ m1 < m0 + m → ¬ is-aligned(m1, m) subst: [m, m0, m1] → [NODE_HEADER_SIZE, # buf, n0]

Additional information

Used simplifier rules: mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%m ≠ 0, n0 ≠ 0 ⊦ is-aligned(n, n0 * m) → is-aligned(n, m); (ss)%c: ⊦ m + n = n + m; from specification nat-basic Used terms: NODE_HEADER_SIZE, # buf, n0