reserve x,x1,x2,x3,x4,y,y1,y2,y3,y4,z,z1,z2,z2,z4 for object;
reserve X,X1,X2,X3,X4,Y for set;

theorem Th7:
 [x,y] in X implies y in union union X
  proof assume
A1: [x,y] in X;
   {x,y} in {{x},{x,y}} by TARSKI:def 2;
   then
A2: {x,y} in union X by A1,TARSKI:def 4;
    y in {x,y} by TARSKI:def 2;
   hence y in union union X by A2,TARSKI:def 4;
  end;
