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 Th23:
  x in dom curry f implies (curry f).x is Function
proof
  assume
A1: x in dom curry f;
  dom curry f = proj1 dom f by Def1;
  then
  ex g st (curry f).x = g & dom g = proj2 (dom f /\ [:{x},proj2 dom f:] )
  & for y st y in dom g holds g.y = f.(x,y) by A1,Def1;
  hence thesis;
end;
