reserve a,b,c for Integer;
reserve i,j,k,l for Nat;
reserve n for Nat;
reserve a,b,c,d,a1,b1,a2,b2,k,l for Integer;
reserve p,p1,q,l for Nat;

theorem
  p is prime & q is prime implies p,q are_coprime or p = q
proof
  assume that
A1: p is prime and
A2: q is prime;
A3: (p gcd q) divides q by Def2;
  assume
A4: not p,q are_coprime;
  (p gcd q) divides p by Def2;
  then p gcd q = p by A1,A4;
  hence thesis by A2,A4,A3;
end;
