At:
div floor mod properties3
1.
a:
2.
n:
3.
a < 0
4.
((-a) rem n) = 0
a = (-((-a) n)+-1)n+n-((-a) rem n) & n-((-a) rem n) < n
By:
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)
[-a;n]
THEN
MoveToConcl -3
THEN
Unfold `absval` 0
THEN
RepeatFor 2 SplitOnConclITE
THEN
ThinTrivial
Generated subgoals:
((-a) rem n) = 0
a = (-((-a) 
n)+-1)
n+n-((-a) rem n) & n-((-a) rem n) < n
a:
. a = (a 
a < 0) & ((a rem n) > 0