reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;

theorem Th27:
  for f being Function st rng p c= dom f & q = f*p holds len q = len p
proof
  let f be Function;
  assume rng p c= dom f;
  then dom(f*p) = dom p by RELAT_1:27;
  then dom(f*p) = Seg len p by FINSEQ_1:def 3;
  hence thesis by FINSEQ_1:def 3;
end;
