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Proof step 41 from proof int2bytes-rec-pos (previous step)

uint2bits(i) = uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest, # uint2bits(i % 256) ≤ 9, 255 < i, 0 < i, 0 ≤ i ⊦ fillsgn(9, uint2bits(i % 256)) = [], i2b(bits2int(fillsgn(9, uint2bits(i % 256)).rest)) = int2bytes(i % 256).last

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
127 < i, i ≤ 255 ⊦ int2bytes(i) = i2b(0) ' + i2b(i - 256) '
Proof step 43:
¬(127 < i % 256 ∧ i % 256 ≤ 255), uint2bits(i) = uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest, # uint2bits(i % 256) ≤ 9, 255 < i, 0 < i, 0 ≤ i ⊦ fillsgn(9, uint2bits(i % 256)) = [], i2b(bits2int(fillsgn(9, uint2bits(i % 256)).rest)) = int2bytes(i % 256).last
Proof step 58:
127 < i % 256 ∧ i % 256 ≤ 255, uint2bits(i) = uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest, # uint2bits(i % 256) ≤ 9, 255 < i, 0 < i, 0 ≤ i ⊦ fillsgn(9, uint2bits(i % 256)) = [], i2b(bits2int(fillsgn(9, uint2bits(i % 256)).rest)) = (i2b(0) ' + i2b(i % 256 - 256) ').last

Rule argument

name: int2bytes-le255 rotate: F subst: [i] → [i % 256]

Additional information

Used terms: i % 256