(* Basic properties *********************************************************)
+lemma cpr_intro: ∀L,T1,T,T2,d,e. T1 ➡ T → L ⊢ T [d, e] ▶* T2 → L ⊢ T1 ➡ T2.
+/4 width=3/ qed-.
+
(* Basic_1: was by definition: pr2_free *)
lemma cpr_pr: ∀T1,T2. T1 ➡ T2 → ∀L. L ⊢ T1 ➡ T2.
/2 width=3/ qed.
>(tpss_inv_sort1 … H) -H //
qed-.
+(* Basic_1: was pr2_gen_abbr *)
+lemma cpr_inv_abbr1: ∀L,V1,T1,U2. L ⊢ ⓓV1. T1 ➡ U2 →
+ (∃∃V,V2,T2. V1 ➡ V & L ⊢ V [O, |L|] ▶* V2 &
+ L. ⓓV ⊢ T1 ➡ T2 &
+ U2 = ⓓV2. T2
+ ) ∨
+ ∃∃T. ⇧[0,1] T ≡ T1 & L ⊢ T ➡ U2.
+#L #V1 #T1 #Y * #X #H1 #H2
+elim (tpr_inv_abbr1 … H1) -H1 *
+[ #V #T0 #T #HV1 #HT10 #HT0 #H destruct
+ elim (tpss_inv_bind1 … H2) -H2 #V2 #T2 #HV2 #HT2 #H destruct
+ lapply (tps_lsubs_conf … HT0 (L. ⓓV) ?) -HT0 /2 width=1/ #HT0
+ lapply (tps_weak_all … HT0) -HT0 #HT0
+ lapply (tpss_lsubs_conf … HT2 (L. ⓓV) ?) -HT2 /2 width=1/ #HT2
+ lapply (tpss_weak_all … HT2) -HT2 #HT2
+ lapply (tpss_strap … HT0 HT2) -T /4 width=7/
+| /4 width=5/
+]
+qed-.
+
(* Basic_1: was: pr2_gen_cast *)
lemma cpr_inv_cast1: ∀L,V1,T1,U2. L ⊢ ⓣV1. T1 ➡ U2 → (
∃∃V2,T2. L ⊢ V1 ➡ V2 & L ⊢ T1 ➡ T2 &
elim (tpss_inv_flat1 … HU2) -HU2 #V2 #T2 #HV2 #HT2 #H destruct /4 width=5/
qed-.
-(* Basic_1: removed theorems 5:
- pr2_head_1 pr2_head_2 pr2_cflat pr2_gen_cflat clear_pr2_trans
+(* Basic_1: removed theorems 4:
+ pr2_head_2 pr2_cflat pr2_gen_cflat clear_pr2_trans
Basic_1: removed local theorems 3:
pr2_free_free pr2_free_delta pr2_delta_delta
*)