reserve d,i,j,k,m,n,p,q,x,k1,k2 for Nat,
  a,c,i1,i2,i3,i5 for Integer;

theorem Th3:
  for k,m,n being Nat holds k divides n*m & n,k are_coprime implies k divides m
proof
  let k,m,n be Nat;
  assume that
A1: k divides n*m and
A2: n,k are_coprime;
  reconsider k,m,n as Element of NAT by ORDINAL1:def 12;
  n gcd k = 1 by A2,INT_2:def 3;
  then
A3: (n*m gcd k*m) = m by EULER_1:5;
  k divides k*m;
  hence thesis by A1,A3,NEWTON:50;
end;
