From a70ec42dd507f6800c7f871a0da45d6b9eda02ea Mon Sep 17 00:00:00 2001
From: Dan Frumin <dan@groupoid.moe>
Date: Thu, 20 May 2021 18:01:00 +0200
Subject: [PATCH] doc comment

---
 theories/typing/types.v | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/theories/typing/types.v b/theories/typing/types.v
index 678eb6c..00d84e0 100644
--- a/theories/typing/types.v
+++ b/theories/typing/types.v
@@ -250,14 +250,14 @@ Proof. destruct op; naive_solver. Qed.
 (***********************************)
 (** Closedness of typed programs   *)
 
-(* DF: It is not trivial to prove the closedness lemma for
-[is_closed_expr], because it requires a lemma like this:
+(* DF: It is not trivial to prove the closedness theorem by using the
+definition of [is_closed_expr] as it is, because it would require (for
+one of the cases) a lemma like this:
 
-    Lemma elements_insert Γ x τ :
-        elements (dom stringset (<[x:=τ]> Γ)) = x :: elements (dom stringset Γ).
+  elements (dom (<[x:=τ]> Γ)) = x :: elements (dom Γ).
 
-But this does not hold (it holds only up to multiset equality).
-So we use an auxiliary definition with sets *)
+But this does not hold (it holds only up to multiset equality). So we
+use an auxiliary definition with sets *)
 
 Definition maybe_insert_binder (x : binder) (X : stringset) : stringset :=
   match x with
-- 
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