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From Stdlib Require Import ZArith Lia.
From Stdlib Require Import Eqdep_dec.
Local Open Scope Z_scope.
Definition t := { n: Z | n > 1 }.
Program Definition two : t := 2.
Next Obligation. lia. Qed.
Program Definition t_eq (x y: t) : {x=y} + {x<>y} :=
if Z.eq_dec (proj1_sig x) (proj1_sig y) then left _ else right _.
Next Obligation.
destruct x as [x Px], y as [y Py]. simpl in e; subst y.
f_equal. apply UIP_dec. decide equality.
Qed.
Next Obligation.
congruence.
Qed.
Definition t_list_eq: forall (x y: list t), {x=y} + {x<>y}.
Proof. decide equality. apply t_eq. Defined.
Goal match t_list_eq (two::nil) (two::nil) with left _ => True | right _ => False end.
Proof. exact I. Qed.
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