reserve Al for QC-alphabet;
reserve p,q,p1,p2,q1 for Element of CQC-WFF(Al),
  k for Element of NAT,
  f,f1,f2,g for FinSequence of CQC-WFF(Al),
  a,b,b1,b2,c,i,n for Nat;
reserve P for Permutation of dom f;

theorem Th19:
  dom Per(f,P) = dom f
proof
  rng P = dom f by FUNCT_2:def 3;
  then dom (P*f) = dom P by RELAT_1:27;
  hence thesis by FUNCT_2:52;
end;
