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 Lm2:
  Perm(P,q) is with_fixpoint implies Perm(P,p=>q) is with_fixpoint
  proof
    given x being object such that
A1: x is_a_fixpoint_of Perm(P,q);
    reconsider xx=x as set by TARSKI:1;
    take SetVal(V,p) --> xx;
    thus thesis by A1,Th14;
  end;
