reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;

theorem
  a,b are_coprime implies (a+b),(a*b) are_coprime
  proof
    assume a,b are_coprime; then
    a + 1*b gcd b = 1 & b+1*a gcd a = 1 by Th5;
    hence thesis by WSIERP_1:7;
  end;
