reserve
   a,b,c,x,y,z,A,B,C,X,Y for set,
   f,g for Function,
   V for SetValuation,
   P for Permutation of V,
   p,q,r,s for Element of HP-WFF,
   n for Element of NAT;

theorem Th8:
  for f being Function st f*f = id dom f holds f is involutive
  proof
    let f be Function such that
A1: f*f = id dom f;
    let x be set;
    assume
A2: x in dom f;
    hence f.(f.x) = (f*f).x by FUNCT_1:13
    .= x by A1,A2,FUNCT_1:18;
  end;
