- we introduced the pointer_step rc in the perspective of proving

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/reducibility/tpr_tpss.ma b/matita/matita/contribs/lambda_delta/basic_2/reducibility/tpr_tpss.ma
index ebbc21330335af9d432db234133de282de12013a..e1ead4e44ff85762b7c91eac6f896f73cc54bd38 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/reducibility/tpr_tpss.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/reducibility/tpr_tpss.ma
@@ -12,8 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/unfold/ltpss_ltpss.ma".
-include "basic_2/reducibility/ltpr_ldrop.ma".
+include "basic_2/unfold/ltpss_dx_ltpss_dx.ma".
+include "basic_2/reducibility/tpr_tps.ma".
 
 (* CONTEXT-FREE PARALLEL REDUCTION ON TERMS *********************************)
 
@@ -25,37 +25,29 @@ lemma tpr_tps_ltpr: ∀T1,T2. T1 ➡ T2 →
                     ∀L2. L1 ➡ L2 →
                     ∃∃U2. U1 ➡ U2 & L2 ⊢ T2 ▶* [d, e] U2.
 #T1 #T2 #H elim H -T1 -T2
-[ #I #L1 #d #e #X #H
-  elim (tps_inv_atom1 … H) -H
-  [ #H destruct /2 width=3/
-  | * #K1 #V1 #i #Hdi #Hide #HLK1 #HVU1 #H #L2 #HL12 destruct
-    elim (ltpr_ldrop_conf … HLK1 … HL12) -L1 #X #HLK2 #H
-    elim (ltpr_inv_pair1 … H) -H #K2 #V2 #_ #HV12 #H destruct
-    elim (lift_total V2 0 (i+1)) #U2 #HVU2
-    lapply (tpr_lift … HV12 … HVU1 … HVU2) -V1 #HU12
-    @ex2_1_intro [2: @HU12 | skip | /3 width=4/ ] (**) (* /4 width=6/ is too slow *)
-  ]
+[ #I #L1 #d #e #U1 #H #L2 #HL12
+  elim (ltpr_tpr_conf … H … HL12) -L1 /3 width=3/
 | #I #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #d #e #X #H #L2 #HL12
   elim (tps_inv_flat1 … H) -H #W1 #U1 #HVW1 #HTU1 #H destruct
   elim (IHV12 … HVW1 … HL12) -V1
   elim (IHT12 … HTU1 … HL12) -T1 -HL12 /3 width=5/
-| #V1 #V2 #W #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #d #e #X #H #L2 #HL12
+| #a #V1 #V2 #W #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #d #e #X #H #L2 #HL12
   elim (tps_inv_flat1 … H) -H #VV1 #Y #HVV1 #HY #HX destruct
   elim (tps_inv_bind1 … HY) -HY #WW #TT1 #_ #HTT1 #H destruct
   elim (IHV12 … HVV1 … HL12) -V1 #VV2 #HVV12 #HVV2
   elim (IHT12 … HTT1 (L2. ⓛWW) ?) -T1 /2 width=1/ -HL12 #TT2 #HTT12 #HTT2
-  lapply (tpss_lsubs_conf … HTT2 (L2. ⓓVV2) ?) -HTT2 /3 width=5/
-| #I #V1 #V2 #T1 #T2 #U2 #HV12 #_ #HTU2 #IHV12 #IHT12 #L1 #d #e #X #H #L2 #HL12
-  elim (tps_inv_bind1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct
-  elim (IHV12 … HVV1 … HL12) -V1 #VV2 #HVV12 #HVV2
-  elim (IHT12 … HTT1 (L2. ⓑ{I} VV2) ?) -T1 /2 width=1/ -HL12 #TT2 #HTT12 #HTT2
-  elim (tpss_strip_neq … HTT2 … HTU2 ?) -T2 /2 width=1/ #T2 #HTT2 #HUT2
-  lapply (tps_lsubs_conf … HTT2 (L2. ⓑ{I} V2) ?) -HTT2 /2 width=1/ #HTT2
-  elim (ltpss_tps_conf … HTT2 (L2. ⓑ{I} VV2) (d + 1) e ?) -HTT2 /2 width=1/ #W2 #HTTW2 #HTW2
-  lapply (tps_lsubs_conf … HTTW2 (⋆. ⓑ{I} VV2) ?) -HTTW2 /2 width=1/ #HTTW2
-  lapply (tpss_lsubs_conf … HTW2 (L2. ⓑ{I} VV2) ?) -HTW2 /2 width=1/ #HTW2
-  lapply (tpss_trans_eq … HUT2 … HTW2) -T2 /3 width=5/
-| #V #V1 #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV12 #IHW12 #IHT12 #L1 #d #e #X #H #L2 #HL12
+  lapply (tpss_lsubs_trans … HTT2 (L2. ⓓVV2) ?) -HTT2 /3 width=5/
+| #a #I #V1 #V2 #T1 #T #T2 #HV12 #_ #HT2 #IHV12 #IHT1 #L1 #d #e #X #H #L2 #HL12
+  elim (tps_inv_bind1 … H) -H #W1 #U1 #HVW1 #HTU1 #H destruct
+  elim (IHV12 … HVW1 … HL12) -V1 #W2 #HW12 #HVW2
+  elim (IHT1 … HTU1 (L2. ⓑ{I} W2) ?) -T1 /2 width=1/ -HL12 #U #HU1 #HTU
+  elim (tpss_strip_neq … HTU … HT2 ?) -T /2 width=1/ #U2 #HU2 #HTU2
+  lapply (tps_lsubs_trans … HU2 (L2. ⓑ{I} V2) ?) -HU2 /2 width=1/ #HU2
+  elim (ltpss_dx_tps_conf … HU2 (L2. ⓑ{I} W2) (d + 1) e ?) -HU2 /2 width=1/ #U3 #HU3 #HU23
+  lapply (tps_lsubs_trans … HU3 (⋆. ⓑ{I} W2) ?) -HU3 /2 width=1/ #HU3
+  lapply (tpss_lsubs_trans … HU23 (L2. ⓑ{I} W2) ?) -HU23 /2 width=1/ #HU23
+  lapply (tpss_trans_eq … HTU2 … HU23) -U2 /3 width=5/
+| #a #V #V1 #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV12 #IHW12 #IHT12 #L1 #d #e #X #H #L2 #HL12
   elim (tps_inv_flat1 … H) -H #VV1 #Y #HVV1 #HY #HX destruct
   elim (tps_inv_bind1 … HY) -HY #WW1 #TT1 #HWW1 #HTT1 #H destruct
   elim (IHV12 … HVV1 … HL12) -V1 #VV2 #HVV12 #HVV2
@@ -64,10 +56,10 @@ lemma tpr_tps_ltpr: ∀T1,T2. T1 ➡ T2 →
   elim (lift_total VV2 0 1) #VV #H2VV
   lapply (tpss_lift_ge … HVV2 (L2. ⓓWW2) … HV2 … H2VV) -V2 /2 width=1/ #HVV
   @ex2_1_intro [2: @tpr_theta |1: skip |3: @tpss_bind [2: @tpss_flat ] ] /width=11/ (**) (* /4 width=11/ is too slow *)
-| #V1 #TT1 #T1 #T2 #HTT1 #_ #IHT12 #L1 #d #e #X #H #L2 #HL12
-  elim (tps_inv_bind1 … H) -H #V2 #TT2 #HV12 #HTT12 #H destruct
-  elim (tps_inv_lift1_ge … HTT12 L1 … HTT1 ?) -TT1 /2 width=1/ #T2 #HT12 #HTT2
-  elim (IHT12 … HT12 … HL12) -T1 -HL12 <minus_plus_m_m /3 width=3/
+| #V #T1 #T #T2 #_ #HT2 #IHT1 #L1 #d #e #X #H #L2 #HL12
+  elim (tps_inv_bind1 … H) -H #W #U1 #_ #HTU1 #H destruct -V
+  elim (IHT1 … HTU1 (L2.ⓓW) ?) -T1 /2 width=1/ -HL12 #U #HU1 #HTU
+  elim (tpss_inv_lift1_ge … HTU L2 … HT2 ?) -T <minus_plus_m_m /3 width=3/
 | #V1 #T1 #T2 #_ #IHT12 #L1 #d #e #X #H #L2 #HL12
   elim (tps_inv_flat1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct
   elim (IHT12 … HTT1 … HL12) -T1 -HL12 /3 width=3/
@@ -78,7 +70,8 @@ lemma tpr_tps_bind: ∀I,V1,V2,T1,T2,U1. V1 ➡ V2 → T1 ➡ T2 →
                     ⋆. ⓑ{I} V1 ⊢ T1 ▶ [0, 1] U1 →
                     ∃∃U2. U1 ➡ U2 & ⋆. ⓑ{I} V2 ⊢ T2 ▶ [0, 1] U2.
 #I #V1 #V2 #T1 #T2 #U1 #HV12 #HT12 #HTU1
-elim (tpr_tps_ltpr … HT12 … HTU1 (⋆. ⓑ{I} V2) ?) -T1 /2 width=1/ /3 width=3/
+elim (tpr_tps_ltpr … HT12 … HTU1 (⋆. ⓑ{I} V2) ?) -T1 /2 width=1/ -V1 #U2 #HU12 #HTU2
+lapply (tpss_inv_SO2 … HTU2) -HTU2 /2 width=3/
 qed.
 
 lemma tpr_tpss_ltpr: ∀L1,L2. L1 ➡ L2 → ∀T1,T2. T1 ➡ T2 →