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 u being integer-valued FinSequence
  for m being CR_Sequence st dom u = dom m holds
  { z where z is Nat: z solves_CRT u,m } is infinite
  proof
    let u be integer-valued FinSequence;
    let m be CR_Sequence;
    set X = { x where x is positive Nat: x solves_CRT u,m };
    X c= { x where x is Nat: x solves_CRT u,m }
    proof
      let a be object;
      assume a in X;
      then ex x being positive Nat st a = x & x solves_CRT u,m;
      hence thesis;
    end;
    hence thesis by Th31;
  end;
