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This commit is contained in:
Thomas Baruchel 2023-12-02 18:25:32 +01:00
parent 890eccba4d
commit a550b5aa8f
1 changed files with 28 additions and 2 deletions
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30
src/mapping.v
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@ -19,11 +19,11 @@ Definition permutation_mapping {X: Type} (u v base : list X) :=
(*
Definition incl_without_eq {X: Type} (u v : list X) := Definition incl_without_eq {X: Type} (u v : list X) :=
exists l, map Some u = map (nth_error v) l. exists l, map Some u = map (nth_error v) l.
Lemma incl_without_eq_incl {X: Type}: Lemma incl_without_eq_incl {X: Type}:
forall (u v : list X), incl_without_eq u v -> incl u v. forall (u v : list X), incl_without_eq u v -> incl u v.
Proof. Proof.
@ -43,7 +43,7 @@ Proof.
apply In_nth_error in H. destruct H. exists (x0 :: x). apply In_nth_error in H. destruct H. exists (x0 :: x).
simpl. rewrite H. rewrite H0. reflexivity. simpl. rewrite H. rewrite H0. reflexivity.
Qed. Qed.
*)
Lemma permutation_mapping_self {X: Type} : Lemma permutation_mapping_self {X: Type} :
@ -57,3 +57,29 @@ Proof.
Qed. Qed.
Lemma permutation_mapping_length {X: Type} :
forall (u v base : list X),
permutation_mapping u v base -> length u = length v.
Proof.
intros u v base. intro H. destruct H. destruct H. destruct H. destruct H0.
replace (length u) with (length (map Some u)). rewrite H0.
replace (length v) with (length (map Some v)). rewrite H1.
rewrite map_length. rewrite map_length. reflexivity.
apply map_length. apply map_length.
Qed.
Lemma permutation_mapping_swap {X: Type} :
forall (u v base : list X),
permutation_mapping u v base -> permutation_mapping v u base.
Proof.
intro u. induction u; intros v base; intro H.