[elim (not_in_list_nil ? ? H1)
|elim H2
[simplify;rewrite > H;reflexivity
- |simplify;rewrite > H4;apply (bool_elim ? (equ a a1));intro;rewrite > H5;
- reflexivity]].
+ |simplify;rewrite > H4;apply (bool_elim ? (equ a a1));intro;reflexivity]].
qed.
lemma in_list_filter_to_p_true : \forall l,x,p.
[elim (not_in_list_nil ? ? H)
|elim (in_list_cons_case ? ? ? ? H1)
[rewrite < H3;simplify;rewrite > H2;simplify;apply in_list_head
- |simplify;apply (bool_elim ? (p t));intro;rewrite > H4;simplify
+ |simplify;apply (bool_elim ? (p t));intro;simplify;
[apply in_list_cons;apply H;assumption
|apply H;assumption]]]
qed.