reserve x,y,z for Real,
  a,b,c,d,e,f,g,h for Nat,
  k,l,m,n,m1,n1,m2,n2 for Integer,
  q for Rational;

theorem Th17:
  k<>0 implies (k divides l iff l/k is Integer)
proof
  assume
A1: k<>0;
  hence k divides l implies l/k is Integer by XCMPLX_1:89;
  assume l/k is Integer;
  then reconsider m=l/k as Integer;
  l=k*m by A1,XCMPLX_1:87;
  hence k divides l;
end;
