- update in Basic_2

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / reducibility / cpr_cpr.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/reducibility/cpr_cpr.ma b/matita/matita/contribs/lambda_delta/Basic_2/reducibility/cpr_cpr.ma
index 2f0e31391b21dcb27c1febb5586db477ad085d10..92db70f0f55fb527d28acea70416d9e026894166 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/reducibility/cpr_cpr.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/reducibility/cpr_cpr.ma
@@ -19,40 +19,45 @@ include "Basic_2/reducibility/cpr.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma cpr_bind_sn: â\88\80I,L,V1,V2,T1,T2. L â\8a¢ V1 â\87\92 V2 â\86\92 T1 â\87\92 T2 →
-                   L ⊢ 𝕓{I} V1. T1 ⇒ 𝕓{I} V2. T2.
-#I #L #V1 #V2 #T1 #T2 * #V #HV1 #HV2 #HT12 
-@ex2_1_intro [2: @(tpr_delta … HV1 HT12) | skip ] /2/ (* /3 width=5/ is too slow *)
+lemma cpr_bind_sn: â\88\80I,L,V1,V2,T1,T2. L â\8a¢ V1 â\9e¡ V2 â\86\92 T1 â\9e¡ T2 →
+                   L ⊢ ⓑ{I} V1. T1 ➡ ⓑ{I} V2. T2.
+#I #L #V1 #V2 #T1 #T2 * #V #HV1 #HV2 #HT12
+@ex2_1_intro [2: @(tpr_delta … HV1 HT12) | skip ] /2 width=3/ (* /3 width=5/ is too slow *)
 qed.
 
 (* Basic_1: was only: pr2_gen_cbind *)
-lemma cpr_bind_dx: â\88\80I,L,V1,V2,T1,T2. V1 â\87\92 V2 â\86\92 L. ð\9d\95\93{I} V2 â\8a¢ T1 â\87\92 T2 →
-                   L ⊢ 𝕓{I} V1. T1 ⇒ 𝕓{I} V2. T2.
+lemma cpr_bind_dx: â\88\80I,L,V1,V2,T1,T2. V1 â\9e¡ V2 â\86\92 L. â\93\91{I} V2 â\8a¢ T1 â\9e¡ T2 →
+                   L ⊢ ⓑ{I} V1. T1 ➡ ⓑ{I} V2. T2.
 #I #L #V1 #V2 #T1 #T2 #HV12 * #T #HT1 normalize #HT2
 elim (tpss_split_up … HT2 1 ? ?) -HT2 // #T0 <minus_n_O #HT0 normalize <minus_plus_m_m #HT02
-lapply (tpss_lsubs_conf … HT0 (⋆. 𝕓{I} V2) ?) -HT0 /2/ #HT0
+lapply (tpss_lsubs_conf … HT0 (⋆. ⓑ{I} V2) ?) -HT0 /2 width=1/ #HT0
 lapply (tpss_tps … HT0) -HT0 #HT0
-@ex2_1_intro [2: @(tpr_delta … HV12 HT1 HT0) | skip | /2/ ] (**) (* /3 width=5/ is too slow *)
+@ex2_1_intro [2: @(tpr_delta … HV12 HT1 HT0) | skip | /2 width=1/ ] (**) (* /3 width=5/ is too slow *)
+qed.
+
+(* Basic_1: was only: pr2_head_1 *) 
+lemma cpr_pair_sn: ∀I,L,V1,V2,T1,T2. L ⊢ V1 ➡ V2 → T1 ➡ T2 →
+                   L ⊢ ②{I} V1. T1 ➡ ②{I} V2. T2.
+* /2 width=1/ /3 width=1/
 qed.
 
 (* Advanced forward lemmas **************************************************)
 
-lemma cpr_shift_fwd: â\88\80L,T1,T2. L â\8a¢ T1 â\87\92 T2 â\86\92 L @ T1 â\87\92 L @ T2.
+lemma cpr_shift_fwd: â\88\80L,T1,T2. L â\8a¢ T1 â\9e¡ T2 â\86\92 L @ T1 â\9e¡ L @ T2.
 #L elim L -L
-[ /2/
-| normalize /3/
+[ #T1 #T2 #HT12 @(cpr_inv_atom … HT12)
+| normalize /3 width=1/
 ].
-qed.
+qed-.
 
 (* Main properties **********************************************************)
 
 (* Basic_1: was: pr2_confluence *)
-theorem cpr_conf: â\88\80L,U0,T1,T2. L â\8a¢ U0 â\87\92 T1 â\86\92 L â\8a¢ U0 â\87\92 T2 →
-                  â\88\83â\88\83T. L â\8a¢ T1 â\87\92 T & L â\8a¢ T2 â\87\92 T.
+theorem cpr_conf: â\88\80L,U0,T1,T2. L â\8a¢ U0 â\9e¡ T1 â\86\92 L â\8a¢ U0 â\9e¡ T2 →
+                  â\88\83â\88\83T. L â\8a¢ T1 â\9e¡ T & L â\8a¢ T2 â\9e¡ T.
 #L #U0 #T1 #T2 * #U1 #HU01 #HUT1 * #U2 #HU02 #HUT2
 elim (tpr_conf … HU01 HU02) -U0 #U #HU1 #HU2 
 elim (tpr_tpss_ltpr ? L … HU1 … HUT1) -U1 // #U1 #HTU1 #HU1
 elim (tpr_tpss_ltpr ? L … HU2 … HUT2) -U2 // #U2 #HTU2 #HU2
 elim (tpss_conf_eq … HU1 … HU2) -U /3 width=5/
 qed.
-