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Proof step 50 from proof int2bytes-rec-neg-05 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
# bits2bytes(firstn(# int2bits(j) % 8, int2bits(j))) + # bits2bytes(restn(# int2bits(j) % 8, int2bits(j))) = i→n(i) + 1, j < 0, 0 < 2 ^ (i * 8) + j, 0 < j + 2 ^ (i * 8), j + 2 ^ (i * 8 - 1) < 0, 0 < i, 8 < # int2bits(j) ⊦ # int2bits(j) % 8 = 0, bits2bytes(firstn(# int2bits(j) % 8, int2bits(j))) + bits2bytes(restn(# int2bits(j) % 8, int2bits(j))) = i2b(~1) ' + (bits2bytes(firstn(# int2bits(j) % 8, int2bits(j))) + bits2bytes(restn(# int2bits(j) % 8, int2bits(j)))).rest, j = 0

Rule argument

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → n ≠ 0; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ #(bytes + bytes0) = # bytes + # bytes0;