(5steps total) PrintForm Definitions Lemmas graph 1 1 Sections Graphs Doc

At: rem mul
x,y:, n:. ((xy) rem n) = (((x rem n)(y rem n)) rem n)
By:
Auto
THEN
Inst Thm* a:, n:. a = (a n)n+(a rem n) & |a rem n| < |n| & ((a rem n) < 0 a < 0) & ((a rem n) > 0 a > 0) [x;n]
THEN
Inst Thm* a:, n:. a = (a n)n+(a rem n) & |a rem n| < |n| & ((a rem n) < 0 a < 0) & ((a rem n) > 0 a > 0) [y;n]
THEN
Inst Thm* a:, n:. a = (a n)n+(a rem n) & |a rem n| < |n| & ((a rem n) < 0 a < 0) & ((a rem n) > 0 a > 0) [(x rem n)(y rem n);n]
THEN
RepDHyps
Generated subgoal:

11. x:
2. y:
3. n:
4. x = (x n)n+(x rem n)
5. |x rem n| < |n|
6. (x rem n) < 0 x < 0
7. (x rem n) > 0 x > 0
8. y = (y n)n+(y rem n)
9. |y rem n| < |n|
10. (y rem n) < 0 y < 0
11. (y rem n) > 0 y > 0
12. (x rem n)(y rem n) = (((x rem n)(y rem n)) n)n+(((x rem n)(y rem n)) rem n)
13. |((x rem n)(y rem n)) rem n| < |n|
14. (((x rem n)(y rem n)) rem n) < 0 (x rem n)(y rem n) < 0
15. (((x rem n)(y rem n)) rem n) > 0 (x rem n)(y rem n) > 0
((xy) rem n) = (((x rem n)(y rem n)) rem n)		4 steps

About:
intnatural_numberaddmultiplydivideremainderless_thanequalimpliesandall

(5steps total) PrintForm Definitions Lemmas graph 1 1 Sections Graphs Doc