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Proof step 6 from proof band-mod256-neg (previous step)

0 < i % 256, 127 < i % 256, 0 ≤ i ⊦ 255 + (~255 + i % 256) % 256 = i % 256

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ abs(i) < j → i % j = i
Proof step 8:
¬ abs(~255 + i % 256) < 256, 0 < i % 256, 127 < i % 256, 0 ≤ i ⊦ 255 + (~255 + i % 256) % 256 = i % 256

Rule argument

seq: ⊦ abs(i) < j → i % j = i subst: [j, i] → [256, ~255 + i % 256] rotate: F spec: int-div inst: name: mod-zero-05

Additional information

Used simplifier rules: ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: 256, ~255 + i % 256