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
-@ex2_1_intro [2: @(tpr_delta … HV1 HT12) | skip ] /2/ (* /3 width=5/ is too slow *)
+@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 *)
L ⊢ 𝕓{I} V1. T1 ⇒ 𝕓{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 (⋆. 𝕓{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.
(* Advanced forward lemmas **************************************************)
lemma cpr_shift_fwd: ∀L,T1,T2. L ⊢ T1 ⇒ T2 → L @ T1 ⇒ L @ T2.
#L elim L -L
-[ /2/
-| normalize /3/
+[ #T1 #T2 #HT12 @(cpr_inv_atom … HT12)
+| normalize /3 width=1/
].
-qed.
+qed-.
(* Main properties **********************************************************)
elim (tpr_tpss_ltpr ? L … HU2 … HUT2) -U2 // #U2 #HTU2 #HU2
elim (tpss_conf_eq … HU1 … HU2) -U /3 width=5/
qed.
-