(* This is probably a poor choice with ssr *)
Inductive id : Type :=
  | Id : nat -> id.(* This is probably a poor choice with ssr *)
Inductive id : Type :=
  | Id : nat -> id.Instance dec_id (p q : id) : Dec (p = q).Definition beq_id (x1 x2 : id) :=
  match x1, x2 with
  | Id n1, Id n2 => beq_nat n1 n2
  end.

Theorem beq_id_refl : forall x, true = beq_id x x.