- support for pointwise extensions of a term relation started ...

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / reducibility / tpr_lift.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/reducibility/tpr_lift.ma b/matita/matita/contribs/lambda_delta/basic_2/reducibility/tpr_lift.ma
index a161723abde32a7dc0e92f6dab185df2fd189a1f..b4d76066affbb8af45839e6fa16b90455c4474a1 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/reducibility/tpr_lift.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/reducibility/tpr_lift.ma
@@ -20,68 +20,65 @@ include "basic_2/reducibility/tpr.ma".
 (* Relocation properties ****************************************************)
 
 (* Basic_1: was: pr0_lift *)
-lemma tpr_lift: ∀T1,T2. T1 ➡ T2 →
-                ∀d,e,U1. ⇧[d, e] T1 ≡ U1 → ∀U2. ⇧[d, e] T2 ≡ U2 → U1 ➡ U2.
+lemma tpr_lift: t_liftable tpr.
 #T1 #T2 #H elim H -T1 -T2
-[ * #i #d #e #U1 #HU1 #U2 #HU2
+[ * #i #U1 #d #e #HU1 #U2 #HU2
   lapply (lift_mono … HU1 … HU2) -HU1 #H destruct
   [ lapply (lift_inv_sort1 … HU2) -HU2 #H destruct //
   | lapply (lift_inv_lref1 … HU2) * * #Hid #H destruct //
   | lapply (lift_inv_gref1 … HU2) -HU2 #H destruct //
   ]
-| #I #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #d #e #X1 #HX1 #X2 #HX2
+| #I #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #X1 #d #e #HX1 #X2 #HX2
   elim (lift_inv_flat1 … HX1) -HX1 #W1 #U1 #HVW1 #HTU1 #HX1 destruct
   elim (lift_inv_flat1 … HX2) -HX2 #W2 #U2 #HVW2 #HTU2 #HX2 destruct /3 width=4/
-| #a #V1 #V2 #W #T1 #T2 #_ #_ #IHV12 #IHT12 #d #e #X1 #HX1 #X2 #HX2
+| #a #V1 #V2 #W #T1 #T2 #_ #_ #IHV12 #IHT12 #X1 #d #e #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 #V3 #T3 #HV23 #HT23 #HX2 destruct /3 width=4/
-| #a #I #V1 #V2 #T1 #T #T2 #_ #_ #HT2 #IHV12 #IHT1 #d #e #X1 #HX1 #X2 #HX2
+| #a #I #V1 #V2 #T1 #T #T2 #_ #_ #HT2 #IHV12 #IHT1 #X1 #d #e #HX1 #X2 #HX2
   elim (lift_inv_bind1 … HX1) -HX1 #W1 #U1 #HVW1 #HTU1 #HX1 destruct
   elim (lift_inv_bind1 … HX2) -HX2 #W2 #U0 #HVW2 #HTU0 #HX2 destruct
   elim (lift_total T (d + 1) e) #U #HTU
   @tpr_delta
   [4: @(tps_lift_le … HT2 … HTU HTU0 ?) /2 width=1/ |1: skip |2: /2 width=4/ |3: /2 width=4/ ] (**) (*/3. is too slow *)
-| #a #V #V1 #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV12 #IHW12 #IHT12 #d #e #X1 #HX1 #X2 #HX2
+| #a #V #V1 #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV12 #IHW12 #IHT12 #X1 #d #e #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 ?) -V // /3 width=4/
-| #V #T1 #T #T2 #_ #HT2 #IHT1 #d #e #X #H #U2 #HTU2
+| #V #T1 #T #T2 #_ #HT2 #IHT1 #X #d #e #H #U2 #HTU2
   elim (lift_inv_bind1 … H) -H #V3 #T3 #_ #HT13 #H destruct -V
   elim (lift_conf_O1 … HTU2 … HT2) -T2 /3 width=4/
-| #V #T1 #T2 #_ #IHT12 #d #e #X #HX #T #HT2
+| #V #T1 #T2 #_ #IHT12 #X #d #e #HX #T #HT2
   elim (lift_inv_flat1 … HX) -HX #V0 #T0 #_ #HT0 #HX destruct /3 width=4/
 ]
 qed.
 
 (* Basic_1: was: pr0_gen_lift *)
-lemma tpr_inv_lift1: ∀T1,T2. T1 ➡ T2 →
-                     ∀d,e,U1. ⇧[d, e] U1 ≡ T1 →
-                     ∃∃U2. ⇧[d, e] U2 ≡ T2 & U1 ➡ U2.
+lemma tpr_inv_lift1: t_deliftable_sn tpr.
 #T1 #T2 #H elim H -T1 -T2
-[ * #i #d #e #U1 #HU1
-  [ lapply (lift_inv_sort2 … HU1) -HU1 #H destruct /2 width=3/
-  | lapply (lift_inv_lref2 … HU1) -HU1 * * #Hid #H destruct /3 width=3/
-  | lapply (lift_inv_gref2 … HU1) -HU1 #H destruct /2 width=3/
+[ * #i #X #d #e #HX
+  [ lapply (lift_inv_sort2 … HX) -HX #H destruct /2 width=3/
+  | lapply (lift_inv_lref2 … HX) -HX * * #Hid #H destruct /3 width=3/
+  | lapply (lift_inv_gref2 … HX) -HX #H destruct /2 width=3/
   ]
-| #I #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #d #e #X #HX
+| #I #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #X #d #e #HX
   elim (lift_inv_flat2 … HX) -HX #V0 #T0 #HV01 #HT01 #HX destruct
   elim (IHV12 … HV01) -V1
   elim (IHT12 … HT01) -T1 /3 width=5/
-| #a #V1 #V2 #W1 #T1 #T2 #_ #_ #IHV12 #IHT12 #d #e #X #HX
+| #a #V1 #V2 #W1 #T1 #T2 #_ #_ #IHV12 #IHT12 #X #d #e #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 … HV01) -V1
   elim (IHT12 … HT01) -T1 /3 width=5/
-| #a #I #V1 #V2 #T1 #T #T2 #_ #_ #HT2 #IHV12 #IHT1 #d #e #X #HX
+| #a #I #V1 #V2 #T1 #T #T2 #_ #_ #HT2 #IHV12 #IHT1 #X #d #e #HX
   elim (lift_inv_bind2 … HX) -HX #W1 #U1 #HWV1 #HUT1 #HX destruct
   elim (IHV12 … HWV1) -V1 #W2 #HWV2 #HW12
   elim (IHT1 … HUT1) -T1 #U #HUT #HU1
   elim (tps_inv_lift1_le … HT2 … HUT ?) -T // [3: /2 width=5/ |2: skip ] #U2 #HU2 #HUT2
   @ex2_1_intro  [2: /2 width=2/ |1: skip |3: /2 width=3/ ] (**) (* /3 width=5/ is slow *)
-| #a #V #V1 #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV12 #IHW12 #IHT12 #d #e #X #HX
+| #a #V #V1 #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV12 #IHW12 #IHT12 #X #d #e #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 … HV01) -V1 #V3 #HV32 #HV03
@@ -89,11 +86,11 @@ lemma tpr_inv_lift1: ∀T1,T2. T1 ➡ T2 →
   elim (IHT12 … HT01) -T1 #T3 #HT32 #HT03
   elim (lift_trans_le … HV32 … HV2 ?) -V2 // #V2 #HV32 #HV2
   @ex2_1_intro [2: /3 width=2/ |1: skip |3: /2 width=3/ ] (**) (* /4 width=5/ is slow *)
-| #V #T1 #T #T2 #_ #HT2 #IHT1 #d #e #X #HX
+| #V #T1 #T #T2 #_ #HT2 #IHT1 #X #d #e #HX
   elim (lift_inv_bind2 … HX) -HX #V3 #T3 #_ #HT31 #H destruct
   elim (IHT1 … HT31) -T1 #T1 #HT1 #HT31
   elim (lift_div_le … HT2 … HT1 ?) -T // /3 width=5/
-| #V #T1 #T2 #_ #IHT12 #d #e #X #HX
+| #V #T1 #T2 #_ #IHT12 #X #d #e #HX
   elim (lift_inv_flat2 … HX) -HX #V0 #T0 #_ #HT01 #H destruct
   elim (IHT12 … HT01) -T1 /3 width=3/
 ]