(** The purpose of this file is to test functional properties of the Definition swap {A B} '((x,y) : A*B) := (y,x).(** Tests the use of patterns in [fun] and [Definition] *) Section TestFun.Variables A B : Type .Goal forall (x:A) (y:B), swap (x,y) = (y,x).Proof . reflexivity . Qed .Goal forall u:A*B, swap (swap u) = u.Proof . destruct u. reflexivity . Qed .Goal @swap A B = fun '(x,y) => (y,x).Proof . reflexivity . Qed .End TestFun.(** Tests the use of patterns in [forall] *) Section TestForall.Variables A B : Type .Goal forall '((x,y) : A*B), swap (x,y) = (y,x).Proof . intros [x y]. reflexivity . Qed .Goal forall x0:A, exists '((x,y) : A*A), swap (x,y) = (x,y).Proof .intros x0.exists (x0,x0).reflexivity .Qed .End TestForall.(** Tests the use of patterns in dependent definitions. *) Section TestDependent.Inductive Fin (n:nat) := Z : Fin n.Definition F '(n,p) : Type := (Fin n * Fin p)%type .Definition both_z '(n,p) : F (n,p) := (Z _,Z _).End TestDependent.(** Tests with a few other types just to make sure parsing is Section TestExtra.Definition proj_informative {A P} '(exist _ x _ : { x:A | P x }) : A := x.Inductive Foo := Bar : nat -> bool -> unit -> nat -> Foo.Definition foo '(Bar n b tt p) :=if b then n+p else n-p.End TestExtra.quality 100%
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