@or_intror @(ex4_3_intro … HLK … HT12) // /3 width=3/ (**) (* explicit constructors *)
| * #K #V1 #T1 #HLK #HVT1 #HT1 #Hi
lapply (ldrop_fwd_ldrop2 … HLK) #H0LK
- elim (cpr_inv_lift … H0LK … HT1 … HT2) -H0LK -T /4 width=6/
+ elim (cpr_inv_lift1 … H0LK … HT1 … HT2) -H0LK -T /4 width=6/
]
qed-.
(* Basic_1: was: pr3_gen_abst *)
-lemma cprs_inv_abst1: ∀I,W,L,V1,T1,U2. L ⊢ ⓛV1. T1 ➡* U2 →
+lemma cprs_inv_abst1: ∀I,W,a,L,V1,T1,U2. L ⊢ ⓛ{a}V1. T1 ➡* U2 →
∃∃V2,T2. L ⊢ V1 ➡* V2 & L. ⓑ{I} W ⊢ T1 ➡* T2 &
- U2 = ⓛV2. T2.
-#I #W #L #V1 #T1 #U2 #H @(cprs_ind … H) -U2 /2 width=5/
+ U2 = ⓛ{a}V2. T2.
+#I #W #a #L #V1 #T1 #U2 #H @(cprs_ind … H) -U2 /2 width=5/
#U #U2 #_ #HU2 * #V #T #HV1 #HT1 #H destruct
elim (cpr_inv_abst1 … HU2 I W) -HU2 #V2 #T2 #HV2 #HT2 #H destruct /3 width=5/
qed-.
-lemma cprs_inv_abst: ∀L,V1,V2,T1,T2. L ⊢ ⓛV1. T1 ➡* ⓛV2. T2 → ∀I,W.
+lemma cprs_inv_abst: ∀a,L,V1,V2,T1,T2. L ⊢ ⓛ{a}V1. T1 ➡* ⓛ{a}V2. T2 → ∀I,W.
L ⊢ V1 ➡* V2 ∧ L. ⓑ{I} W ⊢ T1 ➡* T2.
-#L #V1 #V2 #T1 #T2 #H #I #W
+#a #L #V1 #V2 #T1 #T2 #H #I #W
elim (cprs_inv_abst1 I W … H) -H #V #T #HV1 #HT1 #H destruct /2 width=1/
qed-.
qed.
(* Basic_1: was: pr3_gen_lift *)
-lemma cprs_inv_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K →
- ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀U2. L ⊢ U1 ➡* U2 →
- ∃∃T2. ⇧[d, e] T2 ≡ U2 & K ⊢ T1 ➡* T2.
+lemma cprs_inv_lift1: ∀L,K,d,e. ⇩[d, e] L ≡ K →
+ ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀U2. L ⊢ U1 ➡* U2 →
+ ∃∃T2. ⇧[d, e] T2 ≡ U2 & K ⊢ T1 ➡* T2.
#L #K #d #e #HLK #T1 #U1 #HTU1 #U2 #HU12 @(cprs_ind … HU12) -U2 /2 width=3/
-HTU1 #U #U2 #_ #HU2 * #T #HTU #HT1
-elim (cpr_inv_lift … HLK … HTU … HU2) -U -HLK /3 width=5/
+elim (cpr_inv_lift1 … HLK … HTU … HU2) -U -HLK /3 width=5/
qed.