reserve A for RelStr;
reserve X for non empty set;
reserve PX,PY,PZ,Y,a,b,c,x,y for set;
reserve S1,S2 for Subset of Y;

theorem Th3:
  for C,x be set st C is Classification of X & x in union C holds x c= X
proof
  let C,x be set such that
A1: C is Classification of X and
A2: x in union C;
  consider Y be set such that
A3: x in Y and
A4: Y in C by A2,TARSKI:def 4;
  reconsider Y9 = Y as a_partition of X by A1,A4,PARTIT1:def 3;
  let a be object;
  assume a in x;
  then a in union Y9 by A3,TARSKI:def 4;
  hence thesis;
end;
