(* *)
(**************************************************************************)
-include "basic_2/substitution/ldrop_ldrop.ma".
include "basic_2/static/aaa.ma".
(* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
-(* Main properties **********************************************************)
+(* Main inversion lemmas ****************************************************)
-theorem aaa_mono: ∀L,T,A1. L ⊢ T ⁝ A1 → ∀A2. L ⊢ T ⁝ A2 → A1 = A2.
-#L #T #A1 #H elim H -L -T -A1
-[ #L #k #A2 #H
- >(aaa_inv_sort … H) -H //
-| #I1 #L #K1 #V1 #B #i #HLK1 #_ #IHA1 #A2 #H
- elim (aaa_inv_lref … H) -H #I2 #K2 #V2 #HLK2 #HA2
- lapply (ldrop_mono … HLK1 … HLK2) -L #H destruct /2 width=1/
-| #a #L #V #T #B1 #A1 #_ #_ #_ #IHA1 #A2 #H
- elim (aaa_inv_abbr … H) -H /2 width=1/
-| #a #L #V1 #T1 #B1 #A1 #_ #_ #IHB1 #IHA1 #X #H
- elim (aaa_inv_abst … H) -H #B2 #A2 #HB2 #HA2 #H destruct /3 width=1/
-| #L #V1 #T1 #B1 #A1 #_ #_ #_ #IHA1 #A2 #H
+theorem aaa_mono: ∀G,L,T,A1. ⦃G, L⦄ ⊢ T ⁝ A1 → ∀A2. ⦃G, L⦄ ⊢ T ⁝ A2 → A1 = A2.
+#G #L #T #A1 #H elim H -G -L -T -A1
+[ #G #L #s #A2 #H >(aaa_inv_sort … H) -H //
+| #I1 #G #L #V1 #B #_ #IH #A2 #H
+ elim (aaa_inv_zero … H) -H #I2 #K2 #V2 #H #HA2 destruct /2 width=1 by/
+| #I1 #G #L #B #i #_ #IH #A2 #H
+ elim (aaa_inv_lref … H) -H #I2 #K2 #H #HA2 destruct /2 width=1 by/
+| #p #G #L #V #T #B1 #A1 #_ #_ #_ #IH #A2 #H
+ elim (aaa_inv_abbr … H) -H /2 width=1 by/
+| #p #G #L #V1 #T1 #B1 #A1 #_ #_ #IHB1 #IHA1 #X #H
+ elim (aaa_inv_abst … H) -H #B2 #A2 #HB2 #HA2 #H destruct /3 width=1 by eq_f2/
+| #G #L #V1 #T1 #B1 #A1 #_ #_ #_ #IHA1 #A2 #H
elim (aaa_inv_appl … H) -H #B2 #_ #HA2
lapply (IHA1 … HA2) -L #H destruct //
-| #L #V #T #A1 #_ #_ #_ #IHA1 #A2 #H
- elim (aaa_inv_cast … H) -H /2 width=1/
+| #G #L #V #T #A1 #_ #_ #_ #IHA1 #A2 #H
+ elim (aaa_inv_cast … H) -H /2 width=1 by/
]
qed-.