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Proof step 194 from proof int2bytes-rec-neg-05 (previous step)

0 < 1, i→n(i) + 1 = # bits2bytes(restn(1 -1, int2bits(j % 2 ^ (i * 8)).rest)) + # bits2bytes(firstn(1, int2bits(j % 2 ^ (i * 8)))), 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), j % 2 ^ (i * 8) < 0, j + 2 ^ (i * 8) < i, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8 - 1) < 0, 0 < i, 7 < 8 * i→n(i) ⊦ bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = (bits2bytes(firstn(1, int2bits(j % 2 ^ (i * 8)))) + bits2bytes(restn(1 -1, int2bits(j % 2 ^ (i * 8)).rest))).rest, j % 2 ^ (i * 8) = 0, int2bits(j % 2 ^ (i * 8)).rest = [], i = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 195:
1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), i→n(i) + 1 = # bits2bytes(firstn(1, int2bits(j % 2 ^ (i * 8)))) + # bits2bytes(int2bits(j % 2 ^ (i * 8)).rest), j % 2 ^ (i * 8) < 0, j + 2 ^ (i * 8) < i, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8 - 1) < 0, 0 < i, 7 < 8 * i→n(i) ⊦ j % 2 ^ (i * 8) = 0, int2bits(j % 2 ^ (i * 8)).rest = [], i = 0, bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = (bits2bytes(firstn(1, int2bits(j % 2 ^ (i * 8)))) + bits2bytes(int2bits(j % 2 ^ (i * 8)).rest)).rest

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ restn(0, bits) = bits;