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HITs-Examples
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trailing white spaces

This commit is contained in:
Leon Gondelman 2017-05-26 12:28:07 +02:00
parent 140b02e9f4
commit f8ed41e5fe
2 changed files with 41 additions and 39 deletions
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10
FiniteSets/operations.v
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@ -19,7 +19,6 @@ hrecursion.
- intros a'. compute. destruct (A_deceq a a'); reflexivity. - intros a'. compute. destruct (A_deceq a a'); reflexivity.
Defined. Defined.
Infix "∈" := isIn (at level 9, right associativity).
Definition comprehension : Definition comprehension :
(A -> Bool) -> FSet A -> FSet A. (A -> Bool) -> FSet A -> FSet A.
@ -54,15 +53,16 @@ Proof.
intros X Y. intros X Y.
hrecursion X. hrecursion X.
- exact true. - exact true.
- exact (fun a => (a ∈ Y)). - exact (fun a => (isIn a Y)).
- exact andb. - exact andb.
- intros. compute. destruct x; reflexivity. - intros. compute. destruct x; reflexivity.
- intros x y; compute; destruct x, y; reflexivity. - intros x y; compute; destruct x, y; reflexivity.
- intros x; compute; destruct x; reflexivity. - intros x; compute; destruct x; reflexivity.
- intros x; compute; destruct x; reflexivity. - intros x; compute; destruct x; reflexivity.
- intros x; cbn; destruct (x ∈ Y); reflexivity. - intros x; cbn; destruct (isIn x Y); reflexivity.
Defined. Defined.
Notation "⊆" := subset.
End operations. End operations.
Infix "∈" := isIn (at level 9, right associativity).
Infix "⊆" := subset (at level 10, right associativity).

4
FiniteSets/properties.v
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@ -439,7 +439,7 @@ Admitted.
(* Properties about subset relation. *) (* Properties about subset relation. *)
Lemma subsect_intersection `{Funext} (X Y : FSet A) : Lemma subsect_intersection `{Funext} (X Y : FSet A) :
subset X Y = true -> U X Y = Y. X ⊆ Y = true -> U X Y = Y.
Proof. Proof.
hinduction X; try (intros; apply path_forall; intro; apply set_path2). hinduction X; try (intros; apply path_forall; intro; apply set_path2).
- intros. apply nl. - intros. apply nl.
@ -479,4 +479,6 @@ hinduction X; try (intros; apply path_forall; intro; apply set_path2).
rewrite <- assoc. rewrite IH2. rewrite IH1. reflexivity. rewrite <- assoc. rewrite IH2. rewrite IH1. reflexivity.
Defined. Defined.
Theorem
End properties. End properties.