- ldrop is now drop as in basic_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lift.ma
index e0029e15dc487698f539c973fafc3c8a3a7431b3..e3ac0af1990cc4a1af9b14960082d238ab69d427 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lift.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/substitution/ldrop_ldrop.ma".
+include "basic_2/substitution/drop_drop.ma".
 include "basic_2/multiple/fqus_alt.ma".
 include "basic_2/static/sta.ma".
 include "basic_2/static/da.ma".
@@ -28,10 +28,10 @@ lemma sta_cpx: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 •[h] T2 →
 [ /3 width=4 by cpx_st, da_inv_sort/
 | #G #L #K #V1 #V2 #W2 #i #HLK #_ #HVW2 #IHV12 #H
   elim (da_inv_lref … H) -H * #K0 #V0 [| #l0 ] #HLK0
-  lapply (ldrop_mono … HLK0 … HLK) -HLK0 #H destruct /3 width=7 by cpx_delta/
+  lapply (drop_mono … HLK0 … HLK) -HLK0 #H destruct /3 width=7 by cpx_delta/
 | #G #L #K #W1 #W2 #V1 #i #HLK #_ #HWV1 #IHW12 #H
   elim (da_inv_lref … H) -H * #K0 #W0 [| #l1 ] #HLK0
-  lapply (ldrop_mono … HLK0 … HLK) -HLK0 #H destruct /3 width=7 by cpx_delta/
+  lapply (drop_mono … HLK0 … HLK) -HLK0 #H destruct /3 width=7 by cpx_delta/
 | /4 width=2 by cpx_bind, da_inv_bind/
 | /4 width=3 by cpx_flat, da_inv_flat/
 | /4 width=3 by cpx_eps, da_inv_flat/
@@ -50,21 +50,21 @@ lemma cpx_lift: ∀h,g,G. l_liftable (cpx h g G).
 | #I #G #K #KV #V #V2 #W2 #i #HKV #HV2 #HVW2 #IHV2 #L #s #d #e #HLK #U1 #H #U2 #HWU2
   elim (lift_inv_lref1 … H) * #Hid #H destruct
   [ elim (lift_trans_ge … HVW2 … HWU2) -W2 // <minus_plus #W2 #HVW2 #HWU2
-    elim (ldrop_trans_le … HLK … HKV) -K /2 width=2 by lt_to_le/ #X #HLK #H
-    elim (ldrop_inv_skip2 … H) -H /2 width=1 by lt_plus_to_minus_r/ -Hid
+    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/ -Hid
     #K #Y #HKV #HVY #H destruct /3 width=10 by cpx_delta/
   | lapply (lift_trans_be … HVW2 … HWU2 ? ?) -W2 /2 width=1 by le_S/ >plus_plus_comm_23 #HVU2
-    lapply (ldrop_trans_ge_comm … HLK … HKV ?) -K /3 width=7 by cpx_delta, ldrop_inv_gen/
+    lapply (drop_trans_ge_comm … HLK … HKV ?) -K /3 width=7 by cpx_delta, drop_inv_gen/
   ]
 | #a #I #G #K #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #s #d #e #HLK #U1 #H1 #U2 #H2
   elim (lift_inv_bind1 … H1) -H1 #VV1 #TT1 #HVV1 #HTT1 #H1 destruct
-  elim (lift_inv_bind1 … H2) -H2 #VV2 #TT2 #HVV2 #HTT2 #H2 destruct /4 width=6 by cpx_bind, ldrop_skip/
+  elim (lift_inv_bind1 … H2) -H2 #VV2 #TT2 #HVV2 #HTT2 #H2 destruct /4 width=6 by cpx_bind, drop_skip/
 | #I #G #K #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #s #d #e #HLK #U1 #H1 #U2 #H2
   elim (lift_inv_flat1 … H1) -H1 #VV1 #TT1 #HVV1 #HTT1 #H1 destruct
   elim (lift_inv_flat1 … H2) -H2 #VV2 #TT2 #HVV2 #HTT2 #H2 destruct /3 width=6 by cpx_flat/
 | #G #K #V #T1 #T #T2 #_ #HT2 #IHT1 #L #s #d #e #HLK #U1 #H #U2 #HTU2
   elim (lift_inv_bind1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct
-  elim (lift_conf_O1 … HTU2 … HT2) -T2 /4 width=6 by cpx_zeta, ldrop_skip/
+  elim (lift_conf_O1 … HTU2 … HT2) -T2 /4 width=6 by cpx_zeta, drop_skip/
 | #G #K #V #T1 #T2 #_ #IHT12 #L #s #d #e #HLK #U1 #H #U2 #HTU2
   elim (lift_inv_flat1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct /3 width=6 by cpx_eps/
 | #G #K #V1 #V2 #T #_ #IHV12 #L #s #d #e #HLK #U1 #H #U2 #HVU2
@@ -73,13 +73,13 @@ lemma cpx_lift: ∀h,g,G. l_liftable (cpx h g G).
   elim (lift_inv_flat1 … HX1) -HX1 #V0 #X #HV10 #HX #HX1 destruct
   elim (lift_inv_bind1 … HX) -HX #W0 #T0 #HW0 #HT10 #HX destruct
   elim (lift_inv_bind1 … HX2) -HX2 #X #T3 #HX #HT23 #HX2 destruct
-  elim (lift_inv_flat1 … HX) -HX #W3 #V3 #HW23 #HV23 #HX destruct /4 width=6 by cpx_beta, ldrop_skip/
+  elim (lift_inv_flat1 … HX) -HX #W3 #V3 #HW23 #HV23 #HX destruct /4 width=6 by cpx_beta, drop_skip/
 | #a #G #K #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L #s #d #e #HLK #X1 #HX1 #X2 #HX2
   elim (lift_inv_flat1 … HX1) -HX1 #V0 #X #HV10 #HX #HX1 destruct
   elim (lift_inv_bind1 … HX) -HX #W0 #T0 #HW0 #HT10 #HX destruct
   elim (lift_inv_bind1 … HX2) -HX2 #W3 #X #HW23 #HX #HX2 destruct
   elim (lift_inv_flat1 … HX) -HX #V3 #T3 #HV3 #HT23 #HX destruct
-  elim (lift_trans_ge … HV2 … HV3) -V2 /4 width=6 by cpx_theta, ldrop_skip/
+  elim (lift_trans_ge … HV2 … HV3) -V2 /4 width=6 by cpx_theta, drop_skip/
 ]
 qed.
 
@@ -94,18 +94,18 @@ lemma cpx_inv_lift1: ∀h,g,G. l_deliftable_sn (cpx h g G).
   lapply (lift_inv_sort2 … H) -H #H destruct /3 width=3 by cpx_st, lift_sort, ex2_intro/
 | #I #G #L #LV #V #V2 #W2 #i #HLV #HV2 #HVW2 #IHV2 #K #s #d #e #HLK #T1 #H
   elim (lift_inv_lref2 … H) -H * #Hid #H destruct
-  [ elim (ldrop_conf_lt … HLK … HLV) -L // #L #U #HKL #HLV #HUV
+  [ 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=9 by cpx_delta, ex2_intro/
   | elim (le_inv_plus_l … Hid) #Hdie #Hei
-    lapply (ldrop_conf_ge … HLK … HLV ?) -L // #HKLV
+    lapply (drop_conf_ge … HLK … HLV ?) -L // #HKLV
     elim (lift_split … HVW2 d (i - e + 1)) -HVW2 /3 width=1 by le_S, le_S_S/ -Hid -Hdie
     #V1 #HV1 >plus_minus // <minus_minus /2 width=1 by le_S/ <minus_n_n <plus_n_O /3 width=9 by cpx_delta, ex2_intro/
   ]
 | #a #I #G #L #V1 #V2 #U1 #U2 #_ #_ #IHV12 #IHU12 #K #s #d #e #HLK #X #H
   elim (lift_inv_bind2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct
   elim (IHV12 … HLK … HWV1) -IHV12 #W2 #HW12 #HWV2
-  elim (IHU12 … HTU1) -IHU12 -HTU1 /3 width=6 by cpx_bind, ldrop_skip, lift_bind, ex2_intro/
+  elim (IHU12 … HTU1) -IHU12 -HTU1 /3 width=6 by cpx_bind, drop_skip, lift_bind, ex2_intro/
 | #I #G #L #V1 #V2 #U1 #U2 #_ #_ #IHV12 #IHU12 #K #s #d #e #HLK #X #H
   elim (lift_inv_flat2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct
   elim (IHV12 … HLK … HWV1) -V1
@@ -124,14 +124,14 @@ lemma cpx_inv_lift1: ∀h,g,G. l_deliftable_sn (cpx h g G).
   elim (lift_inv_flat2 … HX) -HX #V0 #Y #HV01 #HY #HX destruct
   elim (lift_inv_bind2 … HY) -HY #W0 #T0 #HW01 #HT01 #HY destruct
   elim (IHV12 … HLK … HV01) -V1 #V3 #HV32 #HV03
-  elim (IHT12 (K.ⓛW0) s … HT01) -T1 /2 width=1 by ldrop_skip/ #T3 #HT32 #HT03
+  elim (IHT12 (K.ⓛW0) s … HT01) -T1 /2 width=1 by drop_skip/ #T3 #HT32 #HT03
   elim (IHW12 … HLK … HW01) -W1
   /4 width=7 by cpx_beta, lift_bind, lift_flat, ex2_intro/
 | #a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #K #s #d #e #HLK #X #HX
   elim (lift_inv_flat2 … HX) -HX #V0 #Y #HV01 #HY #HX destruct
   elim (lift_inv_bind2 … HY) -HY #W0 #T0 #HW01 #HT01 #HY destruct
   elim (IHV1 … HLK … HV01) -V1 #V3 #HV3 #HV03
-  elim (IHT12 (K.ⓓW0) s … HT01) -T1 /2 width=1 by ldrop_skip/ #T3 #HT32 #HT03
+  elim (IHT12 (K.ⓓW0) s … HT01) -T1 /2 width=1 by drop_skip/ #T3 #HT32 #HT03
   elim (IHW12 … HLK … HW01) -W1 #W3 #HW32 #HW03
   elim (lift_trans_le … HV3 … HV2) -V
   /4 width=9 by cpx_theta, lift_bind, lift_flat, ex2_intro/
@@ -147,7 +147,7 @@ lemma fqu_cpx_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T
 /3 width=3 by fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, cpx_pair_sn, cpx_bind, cpx_flat, ex2_intro/
 [ #I #G #L #V2 #U2 #HVU2
   elim (lift_total U2 0 1)
-  /4 width=7 by fqu_drop, cpx_delta, ldrop_pair, ldrop_drop, ex2_intro/
+  /4 width=7 by fqu_drop, cpx_delta, drop_pair, drop_drop, ex2_intro/
 | #G #L #K #T1 #U1 #e #HLK1 #HTU1 #T2 #HTU2
   elim (lift_total T2 0 (e+1))
   /3 width=11 by cpx_lift, fqu_drop, ex2_intro/
@@ -202,7 +202,7 @@ lemma fqu_cpx_trans_neq: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 [ #I #G #L #V1 #V2 #HV12 #_ elim (lift_total V2 0 1)
   #U2 #HVU2 @(ex3_intro … U2)
-  [1,3: /3 width=7 by fqu_drop, cpx_delta, ldrop_pair, ldrop_drop/
+  [1,3: /3 width=7 by fqu_drop, cpx_delta, drop_pair, drop_drop/
   | #H destruct /2 width=7 by lift_inv_lref2_be/
   ]
 | #I #G #L #V1 #T #V2 #HV12 #H @(ex3_intro … (②{I}V2.T))