X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=inline;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Flifts_lifts.ma;h=3822e2dd0ab1146121c1125fc8c691e716ac54f5;hb=42705ef31dd3513a998533e02b5f20fb38dd4fb2;hp=f679a756da0fc4524bb4cbd1254f8c5ebb0f2c4a;hpb=9be6753b7f120a4222df17d1116fe91e871f9367;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts.ma
index f679a756d..3822e2dd0 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts.ma
@@ -106,13 +106,25 @@ qed-.
 (* Advanced proprerties *****************************************************)
 
 (* Basic_2A1: includes: lift_inj *)
-lemma lifts_inj: ∀f,T1,U. ⬆*[f] T1 ≡ U → ∀T2. ⬆*[f] T2 ≡ U → T1 = T2.
+lemma lifts_inj: ∀f. is_inj2 … (lifts f).
 #f #T1 #U #H1 #T2 #H2 lapply (after_isid_dx 𝐈𝐝  … f)
 /3 width=6 by lifts_div3, lifts_fwd_isid/
 qed-.
 
 (* Basic_2A1: includes: lift_mono *)
-lemma lifts_mono: ∀f,T,U1. ⬆*[f] T ≡ U1 → ∀U2. ⬆*[f] T ≡ U2 → U1 = U2.
+lemma lifts_mono: ∀f,T. is_mono … (lifts f T).
 #f #T #U1 #H1 #U2 #H2 lapply (after_isid_sn 𝐈𝐝  … f)
 /3 width=6 by lifts_conf, lifts_fwd_isid/
 qed-.
+
+lemma liftable2_sn_bi: ∀R. liftable2_sn R → liftable2_bi R.
+#R #HR #T1 #T2 #HT12 #f #U1 #HTU1 #U2 #HTU2
+elim (HR … HT12 … HTU1) -HR -T1 #X #HTX #HUX
+<(lifts_mono … HTX … HTU2) -T2 -U2 -f //
+qed-.
+
+lemma deliftable2_sn_bi: ∀R. deliftable2_sn R → deliftable2_bi R.
+#R #HR #U1 #U2 #HU12 #f #T1 #HTU1 #T2 #HTU2
+elim (HR … HU12 … HTU1) -HR -U1 #X #HUX #HTX
+<(lifts_inj … HUX … HTU2) -U2 -T2 -f //
+qed-.