syntactic components detached from basic_2 become static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / aaa_aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/aaa_aaa.ma b/matita/matita/contribs/lambdadelta/static_2/static/aaa_aaa.ma
new file mode 100644 (file)
index 0000000..15b4fe4
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/static_2/static/aaa_aaa.ma
@@ -0,0 +1,38 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "static_2/static/aaa.ma".
+
+(* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
+
+(* Main inversion lemmas ****************************************************)
+
+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 //
+| #G #L #V #T #A1 #_ #_ #_ #IHA1 #A2 #H
+  elim (aaa_inv_cast … H) -H /2 width=1 by/
+]
+qed-.