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(* File reduced by coq-bug-finder from original input, then from 669 lines to 79 lines, then from 89 lines to 44 lines *)
Set Primitive Projections.
Reserved Notation "g 'o' f" (at level 40, left associativity).
Inductive paths {A : Type} (a : A) : A -> Type :=
idpath : paths a a.
Notation "x = y" := (@paths _ x y) : type_scope.
Set Implicit Arguments.
Record PreCategory :=
Build_PreCategory' {
object :> Type;
morphism : object -> object -> Type;
identity : forall x, morphism x x;
compose : forall s d d',
morphism d d'
-> morphism s d
-> morphism s d'
where "f 'o' g" := (compose f g);
left_identity : forall a b (f : morphism a b), identity b o f = f
}.
#[export] Hint Rewrite @left_identity. (* stack overflow *)
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