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Proof step 118 from proof int2bytes-rec-pos-any (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 119:
# int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8), i→n(i * 8) % 8 = 0, 2 ^ (i * 8) ≤ j, 0 < i, # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8), 0 ≤ j % 2 ^ (i * 8) ⊦ i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], bits2bytes(mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest
Proof step 145:
# int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8), i→n(i * 8) % 8 = 0, 2 ^ (i * 8) ≤ j, 0 < i, # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8), 0 ≤ j % 2 ^ (i * 8) ⊦ # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], bits2bytes(mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest

Rule argument

fma: # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8)

Additional information

Used formulas: # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8)