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Proof step 256 from proof fix-bits2bytes-01 (previous step)

(n * 8 - n0 * 8) % 8 = 0, # bits = n0 * 8, bits.first, n0 < n ⊦ n = n0, n * 8 - n0 * 8 = 0, bits = [], n - n0 = (n * 8 - n0 * 8) / 8

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ m0 ≤ m → (m - m0) * n = m * n - m0 * n subst: [m0, n, m] → [n0, 8, n] rotate: T spec: nat-mult inst: name: dist-sub

Additional information

Used simplifier rules: ⊦ m < n → ¬ n < m;% ⊦ ¬ m ≤ n ↔ n < m;%n ≠ 0 ⊦ (m * n) % n = 0;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;% ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0;% ⊦ n < m → m - n ≠ 0;%n ≠ 0 ⊦ (m * n) / n = m; Used terms: n0, 8, n