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Proof step 44 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, i % 256 ≤ 127 ⊦ 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 45:
0 ≤ i, i ≤ 127 ⊦ int2bytes(i) = i2b(i) '
Proof step 46:
0 ≤ i % 256 ∧ i % 256 ≤ 127, uint2bits(i) = uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest, # uint2bits(i % 256) ≤ 9, 255 < i, 0 < i, 0 ≤ i, i % 256 ≤ 127 ⊦ fillsgn(9, uint2bits(i % 256)) = [], i2b(bits2int(fillsgn(9, uint2bits(i % 256)).rest)) = i2b(i % 256) '.last

Rule argument

name: int2bytes-le127 rotate: F subst: [i] → [i % 256]

Additional information

Used simplifier rules: ⊦ 0 < j ∧ 0 ≤ i → 0 ≤ i % j;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: i % 256