theorem
  (curry f in Funcs(X,Funcs(Y,Z)) or curry' f in Funcs(Y,Funcs(X,Z))) &
  dom f c= [:V1,V2:] implies f in Funcs([:X,Y:],Z)
proof
  assume curry f in Funcs(X,Funcs(Y,Z)) or curry' f in Funcs(Y,Funcs(X,Z));
  then
A1: uncurry curry f in Funcs([:X,Y:],Z) or uncurry' curry' f in Funcs([:X,Y
  :],Z) by Th11;
  assume dom f c= [:V1,V2:];
  hence thesis by A1,FUNCT_5:50;
end;
