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 Th8:
  dom uncurry (X --> f) = [:X,dom f:] & rng uncurry (X --> f) c=
rng f & dom uncurry' (X --> f) = [:dom f,X:] & rng uncurry' (X --> f) c= rng f
proof
  f in Funcs(dom f, rng f) by FUNCT_2:def 2;
  then rng (X --> f) c= {f} & {f} c= Funcs(dom f, rng f) by FUNCOP_1:13
,ZFMISC_1:31;
  then dom (X --> f) = X & rng (X --> f) c= Funcs(dom f, rng f);
  hence thesis by FUNCT_5:26,41;
end;
