Definition lex_prod_dec: 
  (forall a1 a2 : A, {a1 = a2} + {a1 <> a2}) ->
  (forall a1 a2, {ltA a1 a2} + {~ltA a1 a2}) ->
  (forall b1 b2, {ltB b1 b2} + {~ltB b1 b2}) ->
  (forall x y, {lexprod x y} + {~ lexprod x y}).

Lemma skipn_incl {A:Type} (l:list A) n: incl (skipn n l) l.