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 Th15:
 for x,y being object holds
  [x,y] in dom f & g = (curry' f).y implies x in dom g & g.x = f.(x,y)
proof let x,y be object;
  assume [x,y] in dom f;
  then
A1: [y,x] in dom ~f by FUNCT_4:42;
  assume
A2: g = (curry' f).y;
  then g.x = (~f).(y,x) by A1,Th13;
  hence thesis by A1,A2,Th13,FUNCT_4:43;
end;
