(* Advanced properties ******************************************************)
(* Basic_2A1: was: aaa_lref *)
-lemma aaa_lref_drops: ∀I,G,K,V,B,i,L. ⇩*[i] L ≘ K.ⓑ[I]V → ❪G,K❫ ⊢ V ⁝ B → ❪G,L❫ ⊢ #i ⁝ B.
+lemma aaa_lref_drops: ∀I,G,K,V,B,i,L. ⇩[i] L ≘ K.ⓑ[I]V → ❪G,K❫ ⊢ V ⁝ B → ❪G,L❫ ⊢ #i ⁝ B.
#I #G #K #V #B #i elim i -i
[ #L #H lapply (drops_fwd_isid … H ?) -H //
#H destruct /2 width=1 by aaa_zero/
(* Basic_2A1: was: aaa_inv_lref *)
lemma aaa_inv_lref_drops: ∀G,A,i,L. ❪G,L❫ ⊢ #i ⁝ A →
- ∃∃I,K,V. ⇩*[i] L ≘ K.ⓑ[I]V & ❪G,K❫ ⊢ V ⁝ A.
+ ∃∃I,K,V. ⇩[i] L ≘ K.ⓑ[I]V & ❪G,K❫ ⊢ V ⁝ A.
#G #A #i elim i -i
[ #L #H elim (aaa_inv_zero … H) -H /3 width=5 by drops_refl, ex2_3_intro/
| #i #IH #L #H elim (aaa_inv_lref … H) -H
qed-.
lemma aaa_pair_inv_lref (G) (L) (i):
- ∀A. ❪G,L❫ ⊢ #i ⁝ A → ∀I,K,V. ⇩*[i] L ≘ K.ⓑ[I]V → ❪G,K❫ ⊢ V ⁝ A.
+ ∀A. ❪G,L❫ ⊢ #i ⁝ A → ∀I,K,V. ⇩[i] L ≘ K.ⓑ[I]V → ❪G,K❫ ⊢ V ⁝ A.
#G #L #i #A #H #I #K #V #HLK
elim (aaa_inv_lref_drops … H) -H #J #Y #X #HLY #HX
lapply (drops_mono … HLY … HLK) -L -i #H destruct //