reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r,s for Real;
reserve p,p1,p2,p3 for Prime;

theorem Th77:
  p1 <> p2 implies not p1*p2 is having_exactly_one_prime_divisor
  proof
    assume
A1: p1 <> p2;
    given p being Prime such that
    p divides p1*p2 and
A2: for r being Prime st r <> p holds not r divides p1*p2;
    p1 divides p1*p2 & p2 divides p1*p2;
    then p1 = p & p2 = p by A2;
    hence thesis by A1;
  end;
