reserve x,y,y1,y2,z,a,b for object, X,Y,Z,V1,V2 for set,
  f,g,h,h9,f1,f2 for Function,
  i for Nat,
  P for Permutation of X,
  D,D1,D2,D3 for non empty set,
  d1 for Element of D1,
  d2 for Element of D2,
  d3 for Element of D3;

theorem Th11:
  f in Funcs(X,Funcs(Y,Z)) implies uncurry f in Funcs([:X,Y:],Z) &
  uncurry' f in Funcs([:Y,X:],Z)
proof
  assume f in Funcs(X,Funcs(Y,Z));
  then
A1: ex g st f = g & dom g = X & rng g c= Funcs(Y,Z) by FUNCT_2:def 2;
  then
A2: dom uncurry f = [:X,Y:] & dom uncurry' f = [:Y,X:] by FUNCT_5:26;
  rng uncurry f c= Z & rng uncurry' f c= Z by A1,FUNCT_5:41;
  hence thesis by A2,FUNCT_2:def 2;
end;
