lemma eq_map : ∀A,B,f,g,l. (∀x.f x = g x) → map A B f l = map A B g l.
intros (A B f g l Efg); elim l; simplify; [1: reflexivity ];
-rewrite > (Efg t); rewrite > H; reflexivity;
+rewrite > (Efg a); rewrite > H; reflexivity;
qed.
lemma le_length_filter : \forall A,l,p.length A (filter A l p) \leq length A l.
intros;elim l
[simplify;apply le_n
- |simplify;apply (bool_elim ? (p t));intro
+ |simplify;apply (bool_elim ? (p a));intro
[simplify;apply le_S_S;assumption
|simplify;apply le_S;assumption]]
qed.
\ No newline at end of file