diff --git a/theories/base_logic/upred.v b/theories/base_logic/upred.v
index eec44f42d1184a029f0f7ac427ddabe77e43f49f..5beea6517bd6cecaecad9dd9344df48b22a295c8 100644
--- a/theories/base_logic/upred.v
+++ b/theories/base_logic/upred.v
@@ -18,16 +18,17 @@ Record uPred (M : ucmraT) : Type := IProp {
otherwise this condition is no longer limit preserving, and uPred
does no longer form a COFE (i.e., [uPred_compl] breaks). This is
because the distance and equivalence on this cofe ignores the
- truth valid on invalid elements. This, in turns, is required by
+ truth value on invalid elements. This, in turn, is required by
the fact that entailment has to ignore invalid elements, which is
itself essential for proving [ownM_valid].
- We could, actually, make the following condition true even for
- invalid elements: we have proved that uPred is isomorphic to a
- sub-COFE of the COFE of predicates that are monotonous both with
- respect to the step index and with respect to x. However, that
- would essentially require changing (by making more complicated)
- the model of many connectives of the logic, which we don't want. *)
+ We could, actually, remove this restriction and make this
+ condition apply even to invalid elements: we have proved that
+ uPred is isomorphic to a sub-COFE of the COFE of predicates that
+ are monotonous both with respect to the step index and with
+ respect to x. However, that would essentially require changing
+ (by making it more complicated) the model of many connectives of
+ the logic, which we don't want. *)
uPred_closed n1 n2 x : uPred_holds n1 x → n2 ≤ n1 → ✓{n2} x → uPred_holds n2 x
}.
Arguments uPred_holds {_} _ _ _ : simpl never.