- some additions and corrections

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / conversion / cpc.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/conversion/cpc.ma b/matita/matita/contribs/lambda_delta/basic_2/conversion/cpc.ma
index ed64873efc75b09641fdb12122c95e3c2423806c..5fb614a8c0af7aa29e469fd628a933fc5c37f430 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/conversion/cpc.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/conversion/cpc.ma
@@ -25,13 +25,15 @@ interpretation
 
 (* Basic properties *********************************************************)
 
-lemma cpc_refl: ∀L,T. L ⊢ T ⬌ T.
+lemma cpc_refl: ∀L. reflexive … (cpc L).
 /2 width=1/ qed.
 
-lemma cpc_sym: ∀L,T1,T2. L ⊢ T1 ⬌ T2 → L ⊢ T2 ⬌ T1.
+lemma cpc_sym: ∀L. symmetric … (cpc L).
 #L #T1 #T2 * /2 width=1/
 qed.
 
-lemma cpc_cpr: ∀L,T1,T2. L ⊢ T1 ⬌ T2 → ∃∃T. L ⊢ T1 ➡ T & L ⊢ T2 ➡ T.
+(* Basic forward lemmas *****************************************************)
+
+lemma cpc_fwd_cpr: ∀L,T1,T2. L ⊢ T1 ⬌ T2 → ∃∃T. L ⊢ T1 ➡ T & L ⊢ T2 ➡ T.
 #L #T1 #T2 * /2 width=3/
 qed.