X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FBasic_2%2Freducibility%2Ftpr_tpss.ma;h=e043031bdba20d038dd3239d30b80f7acbd842a6;hb=04cd2181640b3828b3d193a8e819c849ef574236;hp=f640d1326c0ff491dd147664b2fc2be53c515486;hpb=f75be90562ddd964ef7ed43b956eb908f3133e3a;p=helm.git

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 f640d1326..e043031bd 100644
--- a/matita/matita/contribs/lambda_delta/Basic_2/reducibility/tpr_tpss.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/reducibility/tpr_tpss.ma
@@ -24,54 +24,54 @@ lemma tpr_tps_ltpr: ∀T1,T2. T1 ⇒ T2 →
                     ∀L1,d,e,U1. L1 ⊢ T1 [d, e] ≫ U1 →
                     ∀L2. L1 ⇒ L2 →
                     ∃∃U2. U1 ⇒ U2 & L2 ⊢ T2 [d, e] ≫* U2.
-#T1 #T2 #H elim H -H T1 T2
+#T1 #T2 #H elim H -T1 -T2
 [ #I #L1 #d #e #X #H
   elim (tps_inv_atom1 … H) -H
-  [ #H destruct -X /2/
-  | * #K1 #V1 #i #Hdi #Hide #HLK1 #HVU1 #H #L2 #HL12 destruct -I;
-    elim (ltpr_ldrop_conf … HLK1 … HL12) -HLK1 HL12 #X #HLK2 #H
-    elim (ltpr_inv_pair1 … H) -H #K2 #V2 #_ #HV12 #H destruct -X;
+  [ #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) -HV12 HVU1 #HU12
-    @ex2_1_intro [2: @HU12 | skip | /3/ ] (**) (* /4 width=6/ is too slow *)
+    lapply (tpr_lift … HV12 … HVU1 … HVU2) -V1 #HU12
+    @ex2_1_intro [2: @HU12 | skip | /3 width=4/ ] (**) (* /4 width=6/ is too slow *)
   ]
 | #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 -X;
-  elim (IHV12 … HVW1 … HL12) -IHV12 HVW1;
-  elim (IHT12 … HTU1 … HL12) -IHT12 HTU1 HL12 /3 width=5/
+  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
-  elim (tps_inv_flat1 … H) -H #VV1 #Y #HVV1 #HY #HX destruct -X;
-  elim (tps_inv_bind1 … HY) -HY #WW #TT1 #_ #HTT1 #H destruct -Y;
-  elim (IHV12 … HVV1 … HL12) -IHV12 HVV1 #VV2 #HVV12 #HVV2
-  elim (IHT12 … HTT1 (L2. 𝕓{Abst} WW) ?) -IHT12 HTT1 /2/ -HL12 #TT2 #HTT12 #HTT2
+  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. 𝕓{Abst} WW) ?) -T1 /2 width=1/ -HL12 #TT2 #HTT12 #HTT2
   lapply (tpss_lsubs_conf … HTT2 (L2. 𝕓{Abbr} 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 -X;
-  elim (IHV12 … HVV1 … HL12) -IHV12 HVV1 #VV2 #HVV12 #HVV2
-  elim (IHT12 … HTT1 (L2. 𝕓{I} VV2) ?) -IHT12 HTT1 /2/ -HL12 #TT2 #HTT12 #HTT2
-  elim (tpss_strip_neq … HTT2 … HTU2 ?) -HTT2 HTU2 T2 /2/ #T2 #HTT2 #HUT2
-  lapply (tps_lsubs_conf … HTT2 (L2. 𝕓{I} V2) ?) -HTT2 /2/ #HTT2
-  elim (ltpss_tps_conf … HTT2 (L2. 𝕓{I} VV2) (d + 1) e ?) -HTT2 /2/ #W2 #HTTW2 #HTW2 
-  lapply (tpss_lsubs_conf … HTTW2 (⋆. 𝕓{I} VV2) ?) -HTTW2 /2/ #HTTW2
+  elim (tps_inv_bind1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct
+  elim (IHV12 … HVV1 … HL12) -V1 #VV2 #HVV12 #HVV2
+  elim (IHT12 … HTT1 (L2. 𝕓{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. 𝕓{I} V2) ?) -HTT2 /2 width=1/ #HTT2
+  elim (ltpss_tps_conf … HTT2 (L2. 𝕓{I} VV2) (d + 1) e ?) -HTT2 /2 width=1/ #W2 #HTTW2 #HTW2
+  lapply (tpss_lsubs_conf … HTTW2 (⋆. 𝕓{I} VV2) ?) -HTTW2 /2 width=1/ #HTTW2
   lapply (tpss_tps … HTTW2) -HTTW2 #HTTW2
-  lapply (tpss_lsubs_conf … HTW2 (L2. 𝕓{I} VV2) ?) -HTW2 /2/ #HTW2
-  lapply (tpss_trans_eq … HUT2 … HTW2) -HUT2 HTW2 /3 width=5/
+  lapply (tpss_lsubs_conf … HTW2 (L2. 𝕓{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
-  elim (tps_inv_flat1 … H) -H #VV1 #Y #HVV1 #HY #HX destruct -X;
-  elim (tps_inv_bind1 … HY) -HY #WW1 #TT1 #HWW1 #HTT1 #H destruct -Y;
-  elim (IHV12 … HVV1 … HL12) -IHV12 HVV1 #VV2 #HVV12 #HVV2
-  elim (IHW12 … HWW1 … HL12) -IHW12 HWW1 #WW2 #HWW12 #HWW2
-  elim (IHT12 … HTT1 (L2. 𝕓{Abbr} WW2) ?) -IHT12 HTT1 /2/ -HL12 #TT2 #HTT12 #HTT2
+  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
+  elim (IHW12 … HWW1 … HL12) -W1 #WW2 #HWW12 #HWW2
+  elim (IHT12 … HTT1 (L2. 𝕓{Abbr} WW2) ?) -T1 /2 width=1/ -HL12 #TT2 #HTT12 #HTT2
   elim (lift_total VV2 0 1) #VV #H2VV
-  lapply (tpss_lift_ge … HVV2 (L2. 𝕓{Abbr} WW2) … HV2 … H2VV) -HVV2 HV2 /2/ #HVV
+  lapply (tpss_lift_ge … HVV2 (L2. 𝕓{Abbr} 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 #HT1 #_ #IHT12 #L1 #d #e #X #H #L2 #HL12
-  elim (tps_inv_bind1 … H) -H #V2 #TT2 #HV12 #HTT12 #H destruct -X;
-  elim (tps_inv_lift1_ge … HTT12 L1 … HT1 ?) -HTT12 HT1 /2/ #T2 #HT12 #HTT2
-  elim (IHT12 … HT12 … HL12) -IHT12 HT12 HL12 <minus_plus_m_m /3/
+| #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/
 | #V1 #T1 #T2 #_ #IHT12 #L1 #d #e #X #H #L2 #HL12
-  elim (tps_inv_flat1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct -X;
-  elim (IHT12 … HTT1 … HL12) -IHT12 HTT1 HL12 /3/
+  elim (tps_inv_flat1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct
+  elim (IHT12 … HTT1 … HL12) -T1 -HL12 /3 width=3/
 ]
 qed.
 
@@ -79,16 +79,16 @@ lemma tpr_tps_bind: ∀I,V1,V2,T1,T2,U1. V1 ⇒ V2 → T1 ⇒ T2 →
                     ⋆. 𝕓{I} V1 ⊢ T1 [0, 1] ≫ U1 →
                     ∃∃U2. U1 ⇒ U2 & ⋆. 𝕓{I} V2 ⊢ T2 [0, 1] ≫ U2.
 #I #V1 #V2 #T1 #T2 #U1 #HV12 #HT12 #HTU1
-elim (tpr_tps_ltpr … HT12 … HTU1 (⋆. 𝕓{I} V2) ?) -HT12 HTU1 /3/
+elim (tpr_tps_ltpr … HT12 … HTU1 (⋆. 𝕓{I} V2) ?) -T1 /2 width=1/ /3 width=3/
 qed.
 
 lemma tpr_tpss_ltpr: ∀L1,L2. L1 ⇒ L2 → ∀T1,T2. T1 ⇒ T2 →
                      ∀d,e,U1. L1 ⊢ T1 [d, e] ≫* U1 →
                      ∃∃U2. U1 ⇒ U2 & L2 ⊢ T2 [d, e] ≫* U2.
 #L1 #L2 #HL12 #T1 #T2 #HT12 #d #e #U1 #HTU1 @(tpss_ind … HTU1) -U1
-[ /2/
+[ /2 width=3/
 | -HT12 #U #U1 #_ #HU1 * #T #HUT #HT2
-  elim (tpr_tps_ltpr … HUT … HU1 … HL12) -HUT HU1 HL12 #U2 #HU12 #HTU2
-  lapply (tpss_trans_eq … HT2 … HTU2) -T /2/
+  elim (tpr_tps_ltpr … HUT … HU1 … HL12) -U -HL12 #U2 #HU12 #HTU2
+  lapply (tpss_trans_eq … HT2 … HTU2) -T /2 width=3/
 ]
 qed.