reserve a,x,y for object, A,B for set,
  l,m,n for Nat;
reserve X,Y for set, x for object,
  p,q for Function-yielding FinSequence,
  f,g,h for Function;

theorem Th50:
  compose(<*f,g*>,X) = g*f*id X
proof
  <*f,g*> = <*f*>^<*g*> by FINSEQ_1:def 9;
  hence compose(<*f,g*>,X) = g*compose(<*f*>,X) by Th40
    .= g*(f*id X) by Th44
    .= g*f*id X by RELAT_1:36;
end;
