some added lemmas removed from auto

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / relocation / lifts_lifts.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_lifts.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_lifts.ma
index 41c641716a280339f1c67ae399d534dead1e23aa..971d23ac978dbc1f392b2644d17d5a9323caeebc 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_lifts.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_lifts.ma
@@ -20,9 +20,9 @@ include "static_2/relocation/lifts.ma".
 
 (* Basic_1: includes: lift_gen_lift *)
 (* Basic_2A1: includes: lift_div_le lift_div_be *)
-theorem lifts_div4: â\88\80f2,Tf,T. â¬\86*[f2] Tf â\89\98 T â\86\92 â\88\80g2,Tg. â¬\86*[g2] Tg ≘ T →
+theorem lifts_div4: â\88\80f2,Tf,T. â\87§*[f2] Tf â\89\98 T â\86\92 â\88\80g2,Tg. â\87§*[g2] Tg ≘ T →
                     ∀f1,g1. H_at_div f2 g2 f1 g1 →
-                    â\88\83â\88\83T0. â¬\86*[f1] T0 â\89\98 Tf & â¬\86*[g1] T0 ≘ Tg.
+                    â\88\83â\88\83T0. â\87§*[f1] T0 â\89\98 Tf & â\87§*[g1] T0 ≘ Tg.
 #f2 #Tf #T #H elim H -f2 -Tf -T
 [ #f2 #s #g2 #Tg #H #f1 #g1 #_
   lapply (lifts_inv_sort2 … H) -H #H destruct
@@ -46,13 +46,13 @@ theorem lifts_div4: ∀f2,Tf,T. ⬆*[f2] Tf ≘ T → ∀g2,Tg. ⬆*[g2] Tg ≘
 ]
 qed-.
 
-lemma lifts_div4_one: â\88\80f,Tf,T. â¬\86*[⫯f] Tf ≘ T →
-                      â\88\80T1. â¬\86*[1] T1 ≘ T →
-                      â\88\83â\88\83T0. â¬\86*[1] T0 â\89\98 Tf & â¬\86*[f] T0 ≘ T1.
+lemma lifts_div4_one: â\88\80f,Tf,T. â\87§*[⫯f] Tf ≘ T →
+                      â\88\80T1. â\87§*[1] T1 ≘ T →
+                      â\88\83â\88\83T0. â\87§*[1] T0 â\89\98 Tf & â\87§*[f] T0 ≘ T1.
 /4 width=6 by lifts_div4, at_div_id_dx, at_div_pn/ qed-.
 
-theorem lifts_div3: â\88\80f2,T,T2. â¬\86*[f2] T2 â\89\98 T â\86\92 â\88\80f,T1. â¬\86*[f] T1 ≘ T →
-                    â\88\80f1. f2 â\8a\9a f1 â\89\98 f â\86\92 â¬\86*[f1] T1 ≘ T2.
+theorem lifts_div3: â\88\80f2,T,T2. â\87§*[f2] T2 â\89\98 T â\86\92 â\88\80f,T1. â\87§*[f] T1 ≘ T →
+                    â\88\80f1. f2 â\8a\9a f1 â\89\98 f â\86\92 â\87§*[f1] T1 ≘ T2.
 #f2 #T #T2 #H elim H -f2 -T -T2
 [ #f2 #s #f #T1 #H >(lifts_inv_sort2 … H) -T1 //
 | #f2 #i2 #i #Hi2 #f #T1 #H #f1 #Ht21 elim (lifts_inv_lref2 … H) -H
@@ -70,8 +70,8 @@ qed-.
 (* Basic_1: was: lift1_lift1 (left to right) *)
 (* Basic_1: includes: lift_free (left to right) lift_d lift1_xhg (right to left) lift1_free (right to left) *)
 (* Basic_2A1: includes: lift_trans_be lift_trans_le lift_trans_ge lifts_lift_trans_le lifts_lift_trans *)
-theorem lifts_trans: â\88\80f1,T1,T. â¬\86*[f1] T1 â\89\98 T â\86\92 â\88\80f2,T2. â¬\86*[f2] T ≘ T2 →
-                     â\88\80f. f2 â\8a\9a f1 â\89\98 f â\86\92 â¬\86*[f] T1 ≘ T2.
+theorem lifts_trans: â\88\80f1,T1,T. â\87§*[f1] T1 â\89\98 T â\86\92 â\88\80f2,T2. â\87§*[f2] T ≘ T2 →
+                     â\88\80f. f2 â\8a\9a f1 â\89\98 f â\86\92 â\87§*[f] T1 ≘ T2.
 #f1 #T1 #T #H elim H -f1 -T1 -T
 [ #f1 #s #f2 #T2 #H >(lifts_inv_sort1 … H) -T2 //
 | #f1 #i1 #i #Hi1 #f2 #T2 #H #f #Ht21 elim (lifts_inv_lref1 … H) -H
@@ -86,9 +86,14 @@ theorem lifts_trans: ∀f1,T1,T. ⬆*[f1] T1 ≘ T → ∀f2,T2. ⬆*[f2] T ≘
 ]
 qed-.
 
+lemma lifts_trans4_one (f) (T1) (T2):
+                       ∀T. ⇧*[1]T1 ≘ T → ⇧*[⫯f]T ≘ T2 →
+                       ∃∃T0. ⇧*[f]T1 ≘ T0 & ⇧*[1]T0 ≘ T2.
+/4 width=6 by lifts_trans, lifts_split_trans, after_uni_one_dx/ qed-.
+
 (* Basic_2A1: includes: lift_conf_O1 lift_conf_be *)
-theorem lifts_conf: â\88\80f1,T,T1. â¬\86*[f1] T â\89\98 T1 â\86\92 â\88\80f,T2. â¬\86*[f] T ≘ T2 →
-                    â\88\80f2. f2 â\8a\9a f1 â\89\98 f â\86\92 â¬\86*[f2] T1 ≘ T2.
+theorem lifts_conf: â\88\80f1,T,T1. â\87§*[f1] T â\89\98 T1 â\86\92 â\88\80f,T2. â\87§*[f] T ≘ T2 →
+                    â\88\80f2. f2 â\8a\9a f1 â\89\98 f â\86\92 â\87§*[f2] T1 ≘ T2.
 #f1 #T #T1 #H elim H -f1 -T -T1
 [ #f1 #s #f #T2 #H >(lifts_inv_sort1 … H) -T2 //
 | #f1 #i #i1 #Hi1 #f #T2 #H #f2 #Ht21 elim (lifts_inv_lref1 … H) -H
@@ -128,3 +133,10 @@ lemma deliftable2_sn_bi: ∀R. deliftable2_sn R → deliftable2_bi R.
 elim (HR … HU12 … HTU1) -HR -U1 #X #HUX #HTX
 <(lifts_inj … HUX … HTU2) -U2 -T2 -f //
 qed-.
+
+lemma lifts_trans_uni (T):
+      ∀l1,T1. ⇧*[l1] T1 ≘ T →
+      ∀l2,T2. ⇧*[l2] T ≘ T2 → ⇧*[l1+l2] T1 ≘ T2.
+#T #l1 #T1 #HT1 #l2 #T2 #HT2
+@(lifts_trans … HT1 … HT2) //
+qed-.