[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 12 from proof band-mod256-neg (previous step)

0 < i % 256, 127 < i % 256, 0 ≤ i, 511 ≤ i % 256, 255 ≤ i % 256 ⊦ 255 + (~255 + i % 256) % 256 = i % 256

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 13:
⊦ 0 < j → i % j < j
Proof step 14:
0 < 256 → i % 256 < 256, 0 < i % 256, 127 < i % 256, 0 ≤ i, 511 ≤ i % 256, 255 ≤ i % 256 ⊦ 255 + (~255 + i % 256) % 256 = i % 256

Rule argument

seq: ⊦ 0 < j → i % j < j subst: [j, i] → [256, i] rotate: F spec: int-div inst: name: mod-less-01

Additional information

Used terms: 256, i