- predefined_virtuals: an addition

[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 ec95afc02fd9e29cb097295469e13ac1f38dd6e5..5bb2108769b23bc5a63df78c03d96afba73969f9 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
@@ -21,9 +21,9 @@ include "basic_2/reducibility/ltpr_ldrop.ma".
 
 (* Basic_1: was: pr0_subst1 *)
 lemma tpr_tps_ltpr: ∀T1,T2. T1 ➡ T2 →
-                    ∀L1,d,e,U1. L1 ⊢ T1 [d, e] ▶ U1 →
+                    ∀L1,d,e,U1. L1 ⊢ T1 ▶ [d, e] U1 →
                     ∀L2. L1 ➡ L2 →
-                    ∃∃U2. U1 ➡ U2 & L2 ⊢ T2 [d, e] ▶* U2.
+                    ∃∃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
@@ -44,16 +44,16 @@ lemma tpr_tps_ltpr: ∀T1,T2. T1 ➡ T2 →
   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/
+  lapply (tpss_lsubs_trans … 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
+  lapply (tps_lsubs_trans … 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 (tps_lsubs_trans … HTTW2 (⋆. ⓑ{I} VV2) ?) -HTTW2 /2 width=1/ #HTTW2
+  lapply (tpss_lsubs_trans … 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
   elim (tps_inv_flat1 … H) -H #VV1 #Y #HVV1 #HY #HX destruct
@@ -75,15 +75,15 @@ lemma tpr_tps_ltpr: ∀T1,T2. T1 ➡ T2 →
 qed.
 
 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 ⊢ 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/
 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.
+                     ∀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 width=3/
 | -HT12 #U #U1 #_ #HU1 * #T #HUT #HT2
@@ -91,3 +91,8 @@ lemma tpr_tpss_ltpr: ∀L1,L2. L1 ➡ L2 → ∀T1,T2. T1 ➡ T2 →
   lapply (tpss_trans_eq … HT2 … HTU2) -T /2 width=3/
 ]
 qed.
+
+lemma tpr_tpss_conf: ∀T1,T2. T1 ➡ T2 →
+                     ∀L,U1,d,e. L ⊢ T1 ▶* [d, e] U1 →
+                     ∃∃U2. U1 ➡ U2 & L ⊢ T2 ▶* [d, e] U2.
+/2 width=5/ qed.