theorem Th12:
  k gcd l = 1 implies k gcd l|^b = 1 & k|^a gcd l|^b = 1
proof
  assume k gcd l=1;
  then k,l are_coprime by INT_2:def 3;
  then k,l|^b are_coprime & k|^a,l|^b are_coprime by Th10,Th11;
  hence thesis by INT_2:def 3;
end;
