(* 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.