- 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 553cde83a7407b2252b9a5bc5a8bdc44bb6d68a0..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
@@ -20,21 +20,27 @@ include "Basic_2/reducibility/cpr.ma".
 (* Advanced properties ******************************************************)
 
 lemma cpr_bind_sn: ∀I,L,V1,V2,T1,T2. L ⊢ V1 ➡ V2 → T1 ➡ T2 →
-                   L ⊢ 𝕓{I} V1. T1 ➡ 𝕓{I} V2. T2.
-#I #L #V1 #V2 #T1 #T2 * #V #HV1 #HV2 #HT12 
+                   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: ∀I,L,V1,V2,T1,T2. V1 ➡ V2 → L. 𝕓{I} V2 ⊢ T1 ➡ T2 →
-                   L ⊢ 𝕓{I} V1. T1 ➡ 𝕓{I} V2. T2.
+lemma cpr_bind_dx: ∀I,L,V1,V2,T1,T2. V1 ➡ V2 → L. ⓑ{I} V2 ⊢ T1 ➡ 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 width=1/ #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 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: ∀L,T1,T2. L ⊢ T1 ➡ T2 → L @ T1 ➡ L @ T2.