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Proof step 60 from proof int2bytes-rec-neg-05 (previous step)

# bits2bytes(restn(i→n(i * 8) % 8, int2bits(j).rest)) = i→n(i), 0 ≤ 2 ^ (i * 8) + j, 0 < i, j + 2 ^ (i * 8 - 1) < 0, 0 < j + 2 ^ (i * 8), 0 < 2 ^ (i * 8) + j, j < 0 ⊦ (i→n(i * 8) + 1) % 8 = 0, j = 0, bits2int(true ' + firstn(i→n(i * 8) % 8, int2bits(j).rest)) = ~1, i2b(bits2int(true ' + firstn(i→n(i * 8) % 8, int2bits(j).rest))) = i2b(~1)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: 0 ≤ i, 0 ≤ j ⊦ i→n(i) * i→n(j) = i→n(i * j) subst: [j, i] → [8, i] rotate: T spec: intnat inst: name: i2np

Additional information

Used simplifier rules: ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;%n ≠ 0 ⊦ (m * n) % n = 0;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;% ⊦ restn(0, bits) = bits;%n ≠ 0 ⊦ (m + n0 * n) % n = m % n;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ firstn(0, bits) = [];% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits2int(true ') = ~1; Used terms: 8, i