(* Advanced properties ******************************************************)
(* Basic_2A1: was: aaa_lref *)
-lemma aaa_lref_drops: â\88\80I,G,K,V,B,i,L. â\87©[i] L â\89\98 K.â\93\91[I]V â\86\92 â\9dªG,Kâ\9d« â\8a¢ V â\81\9d B â\86\92 â\9dªG,Lâ\9d« ⊢ #i ⁝ B.
+lemma aaa_lref_drops: â\88\80I,G,K,V,B,i,L. â\87©[i] L â\89\98 K.â\93\91[I]V â\86\92 â\9d¨G,Kâ\9d© â\8a¢ V â\81\9d B â\86\92 â\9d¨G,Lâ\9d© ⊢ #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/
(* Advanced inversion lemmas ************************************************)
(* Basic_2A1: was: aaa_inv_lref *)
-lemma aaa_inv_lref_drops: â\88\80G,A,i,L. â\9dªG,Lâ\9d« ⊢ #i ⁝ A →
- â\88\83â\88\83I,K,V. â\87©[i] L â\89\98 K.â\93\91[I]V & â\9dªG,Kâ\9d« ⊢ V ⁝ A.
+lemma aaa_inv_lref_drops: â\88\80G,A,i,L. â\9d¨G,Lâ\9d© ⊢ #i ⁝ A →
+ â\88\83â\88\83I,K,V. â\87©[i] L â\89\98 K.â\93\91[I]V & â\9d¨G,Kâ\9d© ⊢ 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):
- â\88\80A. â\9dªG,Lâ\9d« â\8a¢ #i â\81\9d A â\86\92 â\88\80I,K,V. â\87©[i] L â\89\98 K.â\93\91[I]V â\86\92 â\9dªG,Kâ\9d« ⊢ V ⁝ A.
+ â\88\80A. â\9d¨G,Lâ\9d© â\8a¢ #i â\81\9d A â\86\92 â\88\80I,K,V. â\87©[i] L â\89\98 K.â\93\91[I]V â\86\92 â\9d¨G,Kâ\9d© ⊢ 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 //
(* Basic_2A1: includes: aaa_lift *)
(* Note: it should use drops_split_trans_pair2 *)
-lemma aaa_lifts: â\88\80G,L1,T1,A. â\9dªG,L1â\9d« ⊢ T1 ⁝ A → ∀b,f,L2. ⇩*[b,f] L2 ≘ L1 →
- â\88\80T2. â\87§*[f] T1 â\89\98 T2 â\86\92 â\9dªG,L2â\9d« ⊢ T2 ⁝ A.
+lemma aaa_lifts: â\88\80G,L1,T1,A. â\9d¨G,L1â\9d© ⊢ T1 ⁝ A → ∀b,f,L2. ⇩*[b,f] L2 ≘ L1 →
+ â\88\80T2. â\87§*[f] T1 â\89\98 T2 â\86\92 â\9d¨G,L2â\9d© ⊢ T2 ⁝ A.
@(fqup_wf_ind_eq (Ⓣ)) #G0 #L0 #T0 #IH #G #L1 * *
[ #s #HG #HL #HT #A #H #b #f #L2 #HL21 #X #HX -b -IH
lapply (aaa_inv_sort … H) -H #H destruct
(* Inversion lemmas with generic slicing for local environments *************)
(* Basic_2A1: includes: aaa_inv_lift *)
-lemma aaa_inv_lifts: â\88\80G,L2,T2,A. â\9dªG,L2â\9d« ⊢ T2 ⁝ A → ∀b,f,L1. ⇩*[b,f] L2 ≘ L1 →
- â\88\80T1. â\87§*[f] T1 â\89\98 T2 â\86\92 â\9dªG,L1â\9d« ⊢ T1 ⁝ A.
+lemma aaa_inv_lifts: â\88\80G,L2,T2,A. â\9d¨G,L2â\9d© ⊢ T2 ⁝ A → ∀b,f,L1. ⇩*[b,f] L2 ≘ L1 →
+ â\88\80T1. â\87§*[f] T1 â\89\98 T2 â\86\92 â\9d¨G,L1â\9d© ⊢ T1 ⁝ A.
@(fqup_wf_ind_eq (Ⓣ)) #G0 #L0 #T0 #IH #G #L2 * *
[ #s #HG #HL #HT #A #H #b #f #L1 #HL21 #X #HX -b -IH
lapply (aaa_inv_sort … H) -H #H destruct