X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Flifts_lifts_bind.ma;h=e1647b35b60c9970af15ff7a71134b785599f00e;hp=10ad3cc526e35e9661231696dbf75b75cae217d9;hb=222044da28742b24584549ba86b1805a87def070;hpb=69d929da2e17a9acc74edd49c2e726c72abf42ae

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts_bind.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts_bind.ma
index 10ad3cc52..e1647b35b 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts_bind.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts_bind.ma
@@ -19,16 +19,35 @@ include "basic_2/relocation/lifts_bind.ma".
 
 (* Main properties **********************************************************)
 
-theorem liftsb_div3: ∀f2,I,I2. ⬆*[f2] I2 ≡ I → ∀f,I1. ⬆*[f] I1 ≡ I →
-                     ∀f1. f2 ⊚ f1 ≡ f → ⬆*[f1] I1 ≡ I2.
+theorem liftsb_div3: ∀f2,I,I2. ⬆*[f2] I2 ≘ I → ∀f,I1. ⬆*[f] I1 ≘ I →
+                     ∀f1. f2 ⊚ f1 ≘ f → ⬆*[f1] I1 ≘ I2.
 #f2 #I #I2 * -I -I2 #I [2: #V #V2 #HV2 ] #f #I1 #H
 [ elim (liftsb_inv_pair_dx … H) | lapply (liftsb_inv_unit_dx … H) ] -H
 /3 width=6 by lifts_div3, ext2_pair, ext2_unit/
 qed-.
 
-theorem liftsb_trans: ∀f1,I1,I. ⬆*[f1] I1 ≡ I → ∀f2,I2. ⬆*[f2] I ≡ I2 →
-                      ∀f. f2 ⊚ f1 ≡ f → ⬆*[f] I1 ≡ I2.
+theorem liftsb_trans: ∀f1,I1,I. ⬆*[f1] I1 ≘ I → ∀f2,I2. ⬆*[f2] I ≘ I2 →
+                      ∀f. f2 ⊚ f1 ≘ f → ⬆*[f] I1 ≘ I2.
 #f1 #I1 #I * -I1 -I #I1 [2: #V1 #V #HV1 ] #f2 #I2 #H
 [ elim (liftsb_inv_pair_sn … H) | lapply (liftsb_inv_unit_sn … H) ] -H
 /3 width=6 by lifts_trans, ext2_pair, ext2_unit/
 qed-.
+
+theorem liftsb_conf: ∀f1,I,I1. ⬆*[f1] I ≘ I1 → ∀f,I2. ⬆*[f] I ≘ I2 →
+                     ∀f2. f2 ⊚ f1 ≘ f → ⬆*[f2] I1 ≘ I2.
+#f1 #I #I1 * -I -I1 #I [2: #V #V1 #HV1 ] #f2 #I2 #H
+[ elim (liftsb_inv_pair_sn … H) | lapply (liftsb_inv_unit_sn … H) ] -H
+/3 width=6 by lifts_conf, ext2_pair, ext2_unit/
+qed-.
+
+(* Advanced proprerties *****************************************************)
+
+lemma liftsb_inj: ∀f. is_inj2 … (liftsb f).
+#f #T1 #U #H1 #T2 #H2 lapply (after_isid_dx 𝐈𝐝  … f)
+/3 width=6 by liftsb_div3, liftsb_fwd_isid/
+qed-.
+
+lemma liftsb_mono: ∀f,T. is_mono … (liftsb f T).
+#f #T #U1 #H1 #U2 #H2 lapply (after_isid_sn 𝐈𝐝  … f)
+/3 width=6 by liftsb_conf, liftsb_fwd_isid/
+qed-.