partial commit: "reduction" component

[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 41c77dc3f80c347e0ef209a7e3e0431f1674bae0..6d626e91d9df88c773e2f0ce2d1100803048b4a0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpr_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpr_lift.ma
@@ -20,11 +20,11 @@ include "basic_2/reduction/cpr.ma".
 (* Relocation properties ****************************************************)
 
 (* Basic_1: includes: pr0_lift pr2_lift *)
-lemma cpr_lift: l_liftable cpr.
-#K #T1 #T2 #H elim H -K -T1 -T2
-[ #I #K #L #d #e #_ #U1 #H1 #U2 #H2
+lemma cpr_lift: ∀G. l_liftable (cpr G).
+#G #K #T1 #T2 #H elim H -G -K -T1 -T2
+[ #I #G #K #L #d #e #_ #U1 #H1 #U2 #H2
   >(lift_mono … H1 … H2) -H1 -H2 //
-| #K #KV #V #V2 #W2 #i #HKV #HV2 #HVW2 #IHV2 #L #d #e #HLK #U1 #H #U2 #HWU2
+| #G #K #KV #V #V2 #W2 #i #HKV #HV2 #HVW2 #IHV2 #L #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/ #X #HLK #H
@@ -32,23 +32,23 @@ lemma cpr_lift: l_liftable cpr.
   | lapply (lift_trans_be … HVW2 … HWU2 ? ?) -W2 // /2 width=1/ >plus_plus_comm_23 #HVU2
     lapply (ldrop_trans_ge_comm … HLK … HKV ?) -K // -Hid /3 width=6/
   ]
-| #a #I #K #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #d #e #HLK #U1 #H1 #U2 #H2
+| #a #I #G #K #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #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=5/
-| #I #K #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #d #e #HLK #U1 #H1 #U2 #H2
+| #I #G #K #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #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/
-| #K #V #T1 #T #T2 #_ #HT2 #IHT1 #L #d #e #HLK #U1 #H #U2 #HTU2
+| #G #K #V #T1 #T #T2 #_ #HT2 #IHT1 #L #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=5/
-| #K #V #T1 #T2 #_ #IHT12 #L #d #e #HLK #U1 #H #U2 #HTU2
+| #G #K #V #T1 #T2 #_ #IHT12 #L #d #e #HLK #U1 #H #U2 #HTU2
   elim (lift_inv_flat1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct /3 width=5/
-| #a #K #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L #d #e #HLK #X1 #HX1 #X2 #HX2
+| #a #G #K #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L #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 #X #T3 #HX #HT23 #HX2 destruct
   elim (lift_inv_flat1 … HX) -HX #W3 #V3 #HW23 #HV23 #HX destruct /4 width=5/
-| #a #K #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L #d #e #HLK #X1 #HX1 #X2 #HX2
+| #a #G #K #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L #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
@@ -58,14 +58,14 @@ lemma cpr_lift: l_liftable cpr.
 qed.
 
 (* Basic_1: includes: pr0_gen_lift pr2_gen_lift *)
-lemma cpr_inv_lift1: l_deliftable_sn cpr.
-#L #U1 #U2 #H elim H -L -U1 -U2
-[ * #L #i #K #d #e #_ #T1 #H
+lemma cpr_inv_lift1: ∀G. l_deliftable_sn (cpr G).
+#G #L #U1 #U2 #H elim H -G -L -U1 -U2
+[ * #G #L #i #K #d #e #_ #T1 #H
   [ lapply (lift_inv_sort2 … H) -H #H destruct /2 width=3/
   | elim (lift_inv_lref2 … H) -H * #Hid #H destruct /3 width=3/
   | lapply (lift_inv_gref2 … H) -H #H destruct /2 width=3/
   ]
-| #L #LV #V #V2 #W2 #i #HLV #HV2 #HVW2 #IHV2 #K #d #e #HLK #T1 #H
+| #G #L #LV #V #V2 #W2 #i #HLV #HV2 #HVW2 #IHV2 #K #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 (IHV2 … HLV … HUV) -V #U2 #HUV2 #HU2
@@ -75,29 +75,29 @@ lemma cpr_inv_lift1: l_deliftable_sn cpr.
     elim (lift_split … HVW2 d (i - e + 1)) -HVW2 [4: // |3: /2 width=1/ |2: /3 width=1/ ] -Hid -Hdie
     #V1 #HV1 >plus_minus // <minus_minus // /2 width=1/ <minus_n_n <plus_n_O /3 width=8/
   ]
-| #a #I #L #V1 #V2 #U1 #U2 #_ #_ #IHV12 #IHU12 #K #d #e #HLK #X #H
+| #a #I #G #L #V1 #V2 #U1 #U2 #_ #_ #IHV12 #IHU12 #K #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=5/
-| #I #L #V1 #V2 #U1 #U2 #_ #_ #IHV12 #IHU12 #K #d #e #HLK #X #H
+| #I #G #L #V1 #V2 #U1 #U2 #_ #_ #IHV12 #IHU12 #K #d #e #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/
-| #L #V #U1 #U #U2 #_ #HU2 #IHU1 #K #d #e #HLK #X #H
+| #G #L #V #U1 #U #U2 #_ #HU2 #IHU1 #K #d #e #HLK #X #H
   elim (lift_inv_bind2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct
   elim (IHU1 (K.ⓓW1) … HTU1) /2 width=1/ -L -U1 #T #HTU #HT1
   elim (lift_div_le … HU2 … HTU) -U // /3 width=5/
-| #L #V #U1 #U2 #_ #IHU12 #K #d #e #HLK #X #H
+| #G #L #V #U1 #U2 #_ #IHU12 #K #d #e #HLK #X #H
   elim (lift_inv_flat2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct
   elim (IHU12 … HLK … HTU1) -L -U1 /3 width=3/
-| #a #L #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #K #d #e #HLK #X #HX
+| #a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #K #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 (IHV12 … HLK … HV01) -V1 #V3 #HV32 #HV03
   elim (IHT12 (K.ⓛW0) … HT01) -T1 /2 width=1/ #T3 #HT32 #HT03
   elim (IHW12 … HLK … HW01) -W1 #W3 #HW32 #HW03
   @ex2_intro [2: /3 width=2/ | skip |3: /2 width=1/ ] (**) (* /4 width=6/ is slow *) 
-| #a #L #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #K #d #e #HLK #X #HX
+| #a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #K #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