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;
reserve fs,fs1,fs2,fs3 for FinSequence;
reserve D for non empty set,
  v,v1,v2,v3 for object,
  fp for FinSequence of NAT,
  fr,fr1,fr2 for FinSequence of INT,
  ft for FinSequence of REAL;

theorem Th29:
  m divides n*k & m gcd n=1 implies m divides k
proof
  assume that
A1: m divides n*k and
A2: (m gcd n)=1;
  consider m1,n1 such that
A3: m*m1+n*n1=1 by A2,Th28;
  k=(m*m1+n*n1)*k by A3
    .=m*(m1*k)+(n*k)*n1;
  hence thesis by A1,Th5;
end;
