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Proof step 350 from proof int2bytes-rec-pos-any (previous step)

i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = m * 8 + n, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), m * 8 + n < i→n(i * 8), 0 < i, 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), n < 8, m < i→n(i) ⊦ mklist(false, i→n(i * 8) - m * 8 + n) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i * 8) + 1 = m * 8 + n, m * 8 + n = i→n(i * 8), i = 0, bits2bytes(mklist(false, i→n(i * 8) - m * 8 + n) + int2bits(j % 2 ^ (i * 8))) = mklist(i2b(0), i→n(i) - m + 1) + bits2bytes(int2bits(j % 2 ^ (i * 8))), n = 0, (i→n(i) - 1) * 8 + 8 = i→n(i * 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, 1, i→n(i)] rotate: F spec: nat-mult inst: name: dist-sub

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;%0 ≤ i ⊦ (* m) ≤ i→n(i) ↔ n→i(m) ≤ i;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j); Used terms: 8, 1, i→n(i)