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Proof step 38 from proof fix-bits2bytes (previous step)

# bits = m * 8 + n0, # bits2bytes(bits) < n, m * 8 + n0 ≤ 8 * (n - 1), m * 8 + n0 < n * 8, n0 < 8, m < n ⊦ bits = [], mklist(i2b(0), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(false, n * 8 - m * 8 + n0) + bits), n * 8 = m * 8 + n0, n0 = 0, bits.first

User applied rule cut formula

And obtained the following new goals

Proof step 39:
n * 8 - m * 8 + n0 = (n - 1 - m) * 8 + (8 - n0), # bits = m * 8 + n0, # bits2bytes(bits) < n, m * 8 + n0 ≤ 8 * (n - 1), m * 8 + n0 < n * 8, n0 < 8, m < n ⊦ bits = [], mklist(i2b(0), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(false, n * 8 - m * 8 + n0) + bits), n * 8 = m * 8 + n0, n0 = 0, bits.first
Proof step 75:
# bits = m * 8 + n0, # bits2bytes(bits) < n, m * 8 + n0 ≤ 8 * (n - 1), m * 8 + n0 < n * 8, n0 < 8, m < n ⊦ n * 8 - m * 8 + n0 = (n - 1 - m) * 8 + (8 - n0), bits = [], mklist(i2b(0), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(false, n * 8 - m * 8 + n0) + bits), n * 8 = m * 8 + n0, n0 = 0, bits.first

Rule argument

fma: n * 8 - m * 8 + n0 = (n - 1 - m) * 8 + (8 - n0)

Additional information

Used formulas: n * 8 - m * 8 + n0 = (n - 1 - m) * 8 + (8 - n0)