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 Th18:
 x in proj1_4 X implies ex x1,x2,x3 st [x,x1,x2,x3] in X
proof assume x in proj1_4 X;
  then consider x1 such that
A1: [x,x1] in proj1_3 X by Def12;
  consider x2 such that
A2: [[x,x1],x2] in proj1 X by A1,Def12;
  consider x3 such that
A3: [[[x,x1],x2],x3] in X by A2,Def12;
 take x1,x2,x3;
 thus thesis by A3;
end;
