reserve i,j,n,k,m for Nat,
     a,b,x,y,z for object,
     F,G for FinSequence-yielding FinSequence,
     f,g,p,q for FinSequence,
     X,Y for set,
     D for non empty set;
reserve
  B,A,M for BinOp of D,
  F,G for D* -valued FinSequence,
  f for FinSequence of D,
  d,d1,d2 for Element of D;
reserve
  F,G for non-empty non empty FinSequence of D*,
  f for non empty FinSequence of D;
reserve f,g for FinSequence of D,
        a,b,c for set,
        F,F1,F2 for finite set;

theorem Th109:
   for E be Enumeration of F, p be Permutation of dom E holds
    E*p is Enumeration of F
proof
  let E be Enumeration of F,p be Permutation of dom E;
  reconsider Ep = E*p as FinSequence;
  dom p = dom E = rng p by FUNCT_2:52,def 3;
  then rng Ep = rng E =F by RELAT_1:28,RLAFFIN3:def 1;
  hence thesis by RLAFFIN3:def 1;
end;
