reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r for Real;
reserve p,p1,p2 for Prime;

theorem Th1:
  m gcd (m*n) = m
  proof
A1: m divides m*n;
    for d being Nat st d divides m & d divides m*n holds d divides m;
    hence thesis by A1,NAT_D:def 5;
  end;
