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 Th53:
  compose(<*f,g,h*>,X) = h*g*f*id X
proof
  <*f,g,h*> = <*f,g*>^<*h*> by FINSEQ_1:43;
  hence compose(<*f,g,h*>,X) = h*compose(<*f,g*>,X) by Th40
    .= h*(g*f*id X) by Th50
    .= h*(g*f)*id X by RELAT_1:36
    .= h*g*f*id X by RELAT_1:36;
end;
