- revision of ground_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / cpr_lift.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpr_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpr_lift.ma
index 85d034bd9942e2255d98e2812024afb2683cda2a..62418cd5d53e81a196ba9a42b4d4fe23cfc43d42 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpr_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpr_lift.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground_2/ynat/ynat_max.ma".
 include "basic_2/substitution/drop_drop.ma".
 include "basic_2/reduction/cpr.ma".
 
@@ -26,11 +27,11 @@ lemma cpr_lift: ∀G. d_liftable (cpr G).
   >(lift_mono … H1 … H2) -H1 -H2 //
 | #G #K #KV #V #V2 #W2 #i #HKV #HV2 #HVW2 #IHV2 #L #s #l #m #HLK #U1 #H #U2 #HWU2
   elim (lift_inv_lref1 … H) * #Hil #H destruct
-  [ elim (lift_trans_ge … HVW2 … HWU2) -W2 // <minus_plus #W2 #HVW2 #HWU2
-    elim (drop_trans_le … HLK … HKV) -K /2 width=2 by lt_to_le/ #X #HLK #H
-    elim (drop_inv_skip2 … H) -H /2 width=1 by lt_plus_to_minus_r/ -Hil
+  [ elim (lift_trans_ge … HVW2 … HWU2) -W2 /2 width=1 by ylt_fwd_le_succ1/ #W2 #HVW2 #HWU2
+    elim (drop_trans_le … HLK … HKV) -K /2 width=2 by ylt_fwd_le/ #X #HLK #H
+    elim (drop_inv_skip2 … H) -H /2 width=1 by ylt_to_minus/ -Hil
     #K #Y #HKV #HVY #H destruct /3 width=9 by cpr_delta/
-  | lapply (lift_trans_be … HVW2 … HWU2 ? ?) -W2 /2 width=1 by le_S/ >plus_plus_comm_23 #HVU2
+  | lapply (lift_trans_be … HVW2 … HWU2 ? ?) -W2 /2 width=1 by yle_succ_dx/ >plus_plus_comm_23 #HVU2
     lapply (drop_trans_ge_comm … HLK … HKV ?) -K // -Hil /3 width=6 by cpr_delta, drop_inv_gen/
   ]
 | #a #I #G #K #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #s #l #m #HLK #U1 #H1 #U2 #H2
@@ -70,10 +71,11 @@ lemma cpr_inv_lift1: ∀G. d_deliftable_sn (cpr G).
   elim (lift_inv_lref2 … H) -H * #Hil #H destruct
   [ elim (drop_conf_lt … HLK … HLV) -L // #L #U #HKL #HLV #HUV
     elim (IHV2 … HLV … HUV) -V #U2 #HUV2 #HU2
-    elim (lift_trans_le … HUV2 … HVW2) -V2 // >minus_plus <plus_minus_m_m /3 width=8 by cpr_delta, ex2_intro/
-  | elim (le_inv_plus_l … Hil) #Hlim #Hmi
+    elim (lift_trans_le … HUV2 … HVW2) -V2 // <yminus_succ2 <yplus_inj >yplus_SO2 >ymax_pre_sn /3 width=8 by cpr_delta, ylt_fwd_le_succ1, ex2_intro/
+  | elim (yle_inv_plus_inj2 … Hil) #Hlim #Hmi
+    lapply (yle_inv_inj … Hmi) -Hmi #Hmi
     lapply (drop_conf_ge … HLK … HLV ?) -L // #HKLV
-    elim (lift_split … HVW2 l (i - m + 1)) -HVW2 [2,3,4: /2 width=1 by le_S_S, le_S/ ] -Hil -Hlim
+    elim (lift_split … HVW2 l (i - m + 1)) -HVW2 [2,3,4: /2 width=1 by yle_succ_dx, le_S_S/ ] -Hil -Hlim
     #V1 #HV1 >plus_minus // <minus_minus /2 width=1 by le_S/ <minus_n_n <plus_n_O
     /3 width=8 by cpr_delta, ex2_intro/
   ]