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At: mod mul

x,y:, n:. ((xy) mod n) = (((x mod n)(y mod n)) mod n)

By:
Auto
THEN
Inst Thm* a:, n:. a = (a n)n+(a mod n) & (a mod n) < n [x;n]
THEN
Inst Thm* a:, n:. a = (a n)n+(a mod n) & (a mod n) < n [y;n]
THEN
Inst Thm* a:, n:. a = (a n)n+(a mod n) & (a mod n) < n [(x mod n)(y mod n);n]
THEN
RepDHyps


Generated subgoal:

11. x:
2. y:
3. n:
4. x = (x n)n+(x mod n)
5. (x mod n) < n
6. y = (y n)n+(y mod n)
7. (y mod n) < n
8. (x mod n)(y mod n) = (((x mod n)(y mod n)) n)n+(((x mod n)(y mod n)) mod n)
9. (((x mod n)(y mod n)) mod n) < n
((xy) mod n) = (((x mod n)(y mod n)) mod n)
2 steps

About:
intaddmultiplyless_thanequalandall

(3steps total) PrintForm Definitions Lemmas graph 1 1 Sections Graphs Doc