renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / aaa_aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/aaa_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/static/aaa_aaa.ma
index 4bf7888c093d531c0cfcc7a3f80b41cbcb4bd6fa..f6224a96ef8efe7702283ad9757e0a4ec52604bf 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/aaa_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/aaa_aaa.ma
@@ -12,28 +12,27 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/relocation/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. ⦃G, L⦄ ⊢ T ⁝ A1 → ∀A2. ⦃G, 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-.