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This commit is contained in:
Thomas Baruchel 2023-01-03 18:07:57 +01:00
parent 2d33df42b6
commit c7bef286df
1 changed files with 2 additions and 11 deletions
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13
thue-morse.v
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@ -23,15 +23,6 @@ Fixpoint tm_step (n: nat) : list bool :=
end. end.
(* ad hoc more or less general lemmas *) (* ad hoc more or less general lemmas *)
Lemma negb_map_explode : forall (l1 l2 : list bool),
map negb (l1 ++ l2) = map negb l1 ++ map negb l2.
Proof.
intros l1 l2.
induction l1.
- reflexivity.
- simpl. rewrite IHl1. reflexivity.
Qed.
Lemma negb_double_map : forall (l : list bool), Lemma negb_double_map : forall (l : list bool),
map negb (map negb l) = l. map negb (map negb l) = l.
Proof. Proof.
@ -117,7 +108,7 @@ Lemma tm_morphism_rev : forall (l : list bool),
Proof. Proof.
intro l. induction l. intro l. induction l.
- reflexivity. - reflexivity.
- simpl. rewrite negb_map_explode. - simpl. rewrite map_app.
rewrite IHl. rewrite tm_morphism_concat. rewrite IHl. rewrite tm_morphism_concat.
rewrite <- app_assoc. simpl. rewrite <- app_assoc. simpl.
rewrite negb_involutive. reflexivity. rewrite negb_involutive. reflexivity.
@ -306,7 +297,7 @@ Proof.
- reflexivity. - reflexivity.
- simpl. rewrite tm_step_lemma. rewrite IHn. rewrite tm_morphism_concat. - simpl. rewrite tm_step_lemma. rewrite IHn. rewrite tm_morphism_concat.
simpl in IHn. rewrite IHn. rewrite tm_build_negb. rewrite IHn. simpl in IHn. rewrite IHn. rewrite tm_build_negb. rewrite IHn.
rewrite negb_map_explode. rewrite negb_double_map. rewrite map_app. rewrite negb_double_map.
reflexivity. reflexivity.
Qed. Qed.