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Proof step 52 from proof int2bytes-rec-pos (previous step)

9 ≤ # uint2bits(i % 256), # uint2bits(i % 256) = 9, uint2bits(i) = uint2bits(i / 256) + uint2bits(i % 256).rest, i % 256 ≤ 127, 0 ≤ i, 0 < i, 255 < i ⊦ bits2int(uint2bits(i % 256).rest) = i % 256, i2b(bits2int(uint2bits(i % 256).rest)) = i2b(i % 256), uint2bits(i % 256) = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
uint2bits(i) = uint2bits(i / 256) + uint2bits(i % 256).rest, # uint2bits(i % 256) = 9, 255 < i, 0 < i, 0 ≤ i, i % 256 ≤ 127 ⊦ i2b(bits2int(uint2bits(i % 256).rest)) = i2b(i % 256), bits2int(uint2bits(i % 256).rest) = i % 256

Rule argument

Additional information

Used simplifier rules: ⊦ i2b(i) ≠ i2b(j) → i ≠ j; (forward)%0 ≤ i ⊦ uint2bits(i) ≠ [];% ⊦ 0 < j ∧ 0 ≤ i → 0 ≤ i % j;