some renaming and reordering of variables

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_lift.ma
index a482c5f84cb6b7e278975a23006ea3676c13a71d..98f4a46be9afb02ff557975fba78c33a23ce1d0c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_lift.ma
@@ -50,12 +50,12 @@ lemma sta_cpx: ∀h,o,G,L,T1,T2,d. ⦃G, L⦄ ⊢ T1 •*[h, 1] T2 →
 
 lemma cpx_lift: ∀h,o,G. d_liftable (cpx h o G).
 #h #o #G #K #T1 #T2 #H elim H -G -K -T1 -T2
-[ #I #G #K #L #c #l #k #_ #U1 #H1 #U2 #H2
+[ #I #G #K #L #b #l #k #_ #U1 #H1 #U2 #H2
   >(lift_mono … H1 … H2) -H1 -H2 //
-| #G #K #s #d #Hkd #L #c #l #k #_ #U1 #H1 #U2 #H2
+| #G #K #s #d #Hkd #L #b #l #k #_ #U1 #H1 #U2 #H2
   >(lift_inv_sort1 … H1) -U1
   >(lift_inv_sort1 … H2) -U2 /2 width=2 by cpx_st/
-| #I #G #K #KV #V #V2 #W2 #i #HKV #HV2 #HVW2 #IHV2 #L #c #l #k #HLK #U1 #H #U2 #HWU2
+| #I #G #K #KV #V #V2 #W2 #i #HKV #HV2 #HVW2 #IHV2 #L #b #l #k #HLK #U1 #H #U2 #HWU2
   elim (lift_inv_lref1 … H) * #Hil #H destruct
   [ 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
@@ -64,25 +64,25 @@ lemma cpx_lift: ∀h,o,G. d_liftable (cpx h o G).
   | 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 /3 width=7 by cpx_delta, drop_inv_gen/
   ]
-| #a #I #G #K #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #c #l #k #HLK #U1 #H1 #U2 #H2
+| #a #I #G #K #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #b #l #k #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, drop_skip/
-| #I #G #K #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #c #l #k #HLK #U1 #H1 #U2 #H2
+| #I #G #K #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #b #l #k #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 #c #l #k #HLK #U1 #H #U2 #HTU2
+| #G #K #V #T1 #T #T2 #_ #HT2 #IHT1 #L #b #l #k #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, drop_skip/
-| #G #K #V #T1 #T2 #_ #IHT12 #L #c #l #k #HLK #U1 #H #U2 #HTU2
+| #G #K #V #T1 #T2 #_ #IHT12 #L #b #l #k #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 #c #l #k #HLK #U1 #H #U2 #HVU2
+| #G #K #V1 #V2 #T #_ #IHV12 #L #b #l #k #HLK #U1 #H #U2 #HVU2
   elim (lift_inv_flat1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct /3 width=6 by cpx_ct/
-| #a #G #K #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L #c #l #k #HLK #X1 #HX1 #X2 #HX2
+| #a #G #K #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L #b #l #k #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 #X #T3 #HX #HT23 #HX2 destruct
   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 #c #l #k #HLK #X1 #HX1 #X2 #HX2
+| #a #G #K #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L #b #l #k #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
@@ -93,14 +93,14 @@ qed.
 
 lemma cpx_inv_lift1: ∀h,o,G. d_deliftable_sn (cpx h o G).
 #h #o #G #L #U1 #U2 #H elim H -G -L -U1 -U2
-[ * #i #G #L #K #c #l #k #_ #T1 #H
+[ * #i #G #L #K #b #l #k #_ #T1 #H
   [ lapply (lift_inv_sort2 … H) -H #H destruct /2 width=3 by cpx_atom, lift_sort, ex2_intro/
   | elim (lift_inv_lref2 … H) -H * #Hil #H destruct /3 width=3 by cpx_atom, lift_lref_ge_minus, lift_lref_lt, ex2_intro/
   | lapply (lift_inv_gref2 … H) -H #H destruct /2 width=3 by cpx_atom, lift_gref, ex2_intro/
   ]
-| #G #L #s #d #Hkd #K #c #l #k #_ #T1 #H
+| #G #L #s #d #Hkd #K #b #l #k #_ #T1 #H
   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 #c #l #k #HLK #T1 #H
+| #I #G #L #LV #V #V2 #W2 #i #HLV #HV2 #HVW2 #IHV2 #K #b #l #k #HLK #T1 #H
   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
@@ -111,36 +111,36 @@ lemma cpx_inv_lift1: ∀h,o,G. d_deliftable_sn (cpx h o G).
     elim (lift_split … HVW2 l (i - k + 1)) -HVW2 /3 width=1 by yle_succ, yle_pred_sn, 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=9 by cpx_delta, ex2_intro/
   ]
-| #a #I #G #L #V1 #V2 #U1 #U2 #_ #_ #IHV12 #IHU12 #K #c #l #k #HLK #X #H
+| #a #I #G #L #V1 #V2 #U1 #U2 #_ #_ #IHV12 #IHU12 #K #b #l #k #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, drop_skip, lift_bind, ex2_intro/
-| #I #G #L #V1 #V2 #U1 #U2 #_ #_ #IHV12 #IHU12 #K #c #l #k #HLK #X #H
+| #I #G #L #V1 #V2 #U1 #U2 #_ #_ #IHV12 #IHU12 #K #b #l #k #HLK #X #H
   elim (lift_inv_flat2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct
   elim (IHV12 … HLK … HWV1) -V1
   elim (IHU12 … HLK … HTU1) -U1 -HLK /3 width=5 by cpx_flat, lift_flat, ex2_intro/
-| #G #L #V #U1 #U #U2 #_ #HU2 #IHU1 #K #c #l #k #HLK #X #H
+| #G #L #V #U1 #U #U2 #_ #HU2 #IHU1 #K #b #l #k #HLK #X #H
   elim (lift_inv_bind2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct
-  elim (IHU1 (K.ⓓW1) c … HTU1) /2 width=1 by drop_skip/ -L -U1 #T #HTU #HT1
+  elim (IHU1 (K.ⓓW1) b … HTU1) /2 width=1 by drop_skip/ -L -U1 #T #HTU #HT1
   elim (lift_div_le … HU2 … HTU) -U /3 width=5 by cpx_zeta, ex2_intro/
-| #G #L #V #U1 #U2 #_ #IHU12 #K #c #l #k #HLK #X #H
+| #G #L #V #U1 #U2 #_ #IHU12 #K #b #l #k #HLK #X #H
   elim (lift_inv_flat2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct
   elim (IHU12 … HLK … HTU1) -L -U1 /3 width=3 by cpx_eps, ex2_intro/
-| #G #L #V1 #V2 #U1 #_ #IHV12 #K #c #l #k #HLK #X #H
+| #G #L #V1 #V2 #U1 #_ #IHV12 #K #b #l #k #HLK #X #H
   elim (lift_inv_flat2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct
   elim (IHV12 … HLK … HWV1) -L -V1 /3 width=3 by cpx_ct, ex2_intro/
-| #a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #K #c #l #k #HLK #X #HX
+| #a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #K #b #l #k #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 (IHV12 … HLK … HV01) -V1 #V3 #HV32 #HV03
-  elim (IHT12 (K.ⓛW0) c … HT01) -T1 /2 width=1 by drop_skip/ #T3 #HT32 #HT03
+  elim (IHT12 (K.ⓛW0) b … 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 #c #l #k #HLK #X #HX
+| #a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #K #b #l #k #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) c … HT01) -T1 /2 width=1 by drop_skip/ #T3 #HT32 #HT03
+  elim (IHT12 (K.ⓓW0) b … 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/