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+Require Export Morphisms Setoid.
+
+Class lops := lmk_ops {
+  car: Type;
+  weq: relation car
+}.
+
+Implicit Arguments car [].
+
+Coercion car: lops >-> Sortclass.
+
+Instance weq_Equivalence `{lops}: Equivalence weq.
+Proof.
+Admitted.
+
+Module lset.
+Canonical Structure lset_ops A := lmk_ops (list A) (fun h k => True).
+End lset.
+
+Class ops := mk_ops {
+  ob: Type;
+  mor: ob -> ob -> lops;
+  dot: forall n m p, mor n m -> mor m p -> mor n p
+}.
+Coercion mor: ops >-> Funclass.
+Implicit Arguments ob [].
+
+Instance dot_weq `{ops} n m p: Proper (weq ==> weq ==> weq) (dot n m p).
+Proof.
+Admitted.
+
+Section s.
+
+Import lset.
+
+Context `{X:lops} {I: Type}.
+
+Axiom sup : forall (f: I -> X) (J : list I), X.
+
+Global Instance sup_weq: Proper (pointwise_relation _ weq ==> weq ==> weq) sup.
+Proof.
+Admitted.
+
+End s.
+
+Axiom ord : forall (n : nat), Type.
+Axiom seq : forall n, list (ord n).
+
+Infix "=="   := weq (at level 79).
+Infix "*" := (dot _ _ _)      (left associativity, at level 40).
+
+Notation "∑_ ( i ∈ l ) f" := (@sup (mor _ _) _ (fun i => f) l)
+  (at level 41, f at level 41, i, l at level 50).
+
+Axiom dotxsum : forall `{X : ops} I J n m p (f: I -> X m n) (x: X p m) y,
+  x * (∑_(i∈ J) f i) == y.
+
+Definition mx X n m := ord n -> ord m -> X.
+
+Section bsl.
+Context `{X : ops} {u: ob X}.
+Notation U := (car (@mor X u u)).
+
+Lemma toto n m p q (M : mx U n m) N (P : mx U p q) Q i j : ∑_(j0 ∈ seq m) M i j0 * (∑_(j1 ∈ seq p) N j0 j1 * P j1 j) == Q.
+Proof.
+  Fail setoid_rewrite dotxsum.
+  (* Toplevel input, characters 0-22:
+Error:
+Tactic failure:setoid rewrite failed: Unable to satisfy the rewriting constraints.
+Unable to satisfy the following constraints:
+UNDEFINED EVARS:
+ ?101==[X u n m p q M N P Q i j j0 |- U] (goal evar)
+ ?106==[X u n m p q M N P Q i j |- relation (X u u)] (internal placeholder)
+ ?107==[X u n m p q M N P Q i j |- relation (list (ord m))]
+         (internal placeholder)
+ ?108==[X u n m p q M N P Q i j (do_subrelation:=do_subrelation)
+         |- Proper (pointwise_relation (ord m) weq ==> ?107 ==> ?106) sup]
+         (internal placeholder)
+ ?109==[X u n m p q M N P Q i j |- ProperProxy ?107 (seq m)]
+         (internal placeholder)
+ ?110==[X u n m p q M N P Q i j |- relation (X u u)] (internal placeholder)
+ ?111==[X u n m p q M N P Q i j (do_subrelation:=do_subrelation)
+         |- Proper (?106 ==> ?110 ==> Basics.flip Basics.impl) weq]
+         (internal placeholder)
+ ?112==[X u n m p q M N P Q i j |- ProperProxy ?110 Q] (internal placeholder)UNIVERSES:
+ {} |= Top.14 <= Top.37
+        Top.25 <= Top.24
+        Top.25 <= Top.32
+
+ALGEBRAIC UNIVERSES:{}
+UNDEFINED UNIVERSES:METAS:
+ 470[y] := ?101 : car (?99 ?467 ?465)
+ 469[x] := M i _UNBOUND_REL_1 : car (?99 ?467 ?466)  [type is checked]
+ 468[f] := fun i : ?463 => N _UNBOUND_REL_2 i * P i j :
+ ?463 -> ?99 ?466 ?465  [type is checked]
+ 467[p] := u : ob ?99  [type is checked]
+ 466[m] := u : ob ?99  [type is checked]
+ 465[n] := u : ob ?99  [type is checked]
+ 464[J] := seq p : list ?463  [type is checked]
+ 463[I] := ord p : Type  [type is checked]
+ *)
+Abort.
+
+End bsl.