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 Th38:
  dom f1 = [:X,Y:] & dom f2 = [:X,Y:] & curry' f1 = curry' f2 implies f1 = f2
proof
  assume that
A1: dom f1 = [:X,Y:] and
A2: dom f2 = [:X,Y:] and
A3: curry' f1 = curry' f2;
  dom ~f1 = [:Y,X:] & dom ~f2 = [:Y,X:] by A1,A2,FUNCT_4:46;
  then
A4: ~f1 = ~f2 by A3,Th37;
  ~~f1 = f1 by A1,FUNCT_4:52;
  hence thesis by A2,A4,FUNCT_4:52;
end;
