reserve a,b,c,h for Integer;
reserve k,m,n for Nat;
reserve i,j,z for Integer;
reserve p for Prime;

theorem
  for a1,a2 being Integer
  for n1,n2 being Nat st n1,n2 are_coprime & n1 > 0 & n2 > 0 holds
  { x where x is Nat: x solves_CRT a1,n1,a2,n2 } is infinite
  proof
    let a1,a2 be Integer;
    let n1,n2 be Nat;
    set X = { x where x is positive Nat: x solves_CRT a1,n1,a2,n2 };
    X c= { x where x is Nat: x solves_CRT a1,n1,a2,n2 }
    proof
      let e be object;
      assume e in X;
      then ex x being positive Nat st e = x & x solves_CRT a1,n1,a2,n2;
      hence thesis;
    end;
    hence thesis by Th28;
  end;
