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Proof step 235 from proof fix-bits2bytes-01 (previous step)

# bits = m * 8 + n0, n0 < 8, bits.first, # bits2bytes(bits) < n, m < n ⊦ mklist(i2b(~1), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(true, n * 8 - # bits) + bits), bits = [], n * 8 = # bits, n0 = 0, n * 8 = m * 8 + 8 + (n - 1 - m) * 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: [n, m0, m] → [8, m, n - 1] rotate: F spec: nat-mult inst: name: dist-sub

Additional information

Used simplifier rules: ⊦ m + 1 ≤ n ↔ m < n;%n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n;% ⊦ m + n = n + m;% ⊦ m * n = n * m;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m < n → (n ≤ m ↔ false);% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n + 1 ↔ ¬ n < m;%n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0;% ⊦ m < 1 ↔ m = 0;% ⊦ m < n → n ≠ 0;% ⊦ m0 * m < m0 * n ↔ m0 ≠ 0 ∧ m < n;% ⊦ ¬ m ≤ n ↔ n < m;%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1;% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ m * n + n = m1 * n ↔ ¬ ¬(m + 1 = m1 ∨ n = 0); Used terms: 8, m, n - 1