- lambda_delta: programmed renaming to lambdadelta

[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
new file mode 100644 (file)
index 0000000..9d9017c
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+++ b/matita/matita/contribs/lambdadelta/basic_2/static/aaa_aaa.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "basic_2/substitution/ldrop_ldrop.ma".
+include "basic_2/static/aaa.ma".
+
+(* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
+
+(* Main properties **********************************************************)
+
+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
+  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/
+]
+qed-.