reserve X,Y,Z,X1,X2,Y1,Y2 for set, x,y,z,t,x1,x2 for object,
  f,g,h,f1,f2,g1,g2 for Function;

theorem Th18:
  dom f c= [:X,Y:] implies dom curry f c= X & dom curry' f c= Y
proof
  assume
A1: dom f c= [:X,Y:];
  dom curry f = proj1 dom f by Def1;
  hence dom curry f c= X by A1,Th5;
A2: dom curry' f = proj1 dom ~f by Def1;
  dom ~f c= [:Y,X:] by A1,FUNCT_4:45;
  hence thesis by A2,Th5;
end;
