update in staic_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / apps_2 / examples / ex_rpx_fwd.ma

diff --git a/matita/matita/contribs/lambdadelta/apps_2/examples/ex_rpx_fwd.ma b/matita/matita/contribs/lambdadelta/apps_2/examples/ex_rpx_fwd.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 "static_2/static/reqx_fqup.ma".
+include "basic_2/rt_transition/lpx.ma".
+include "basic_2/rt_transition/rpx.ma".
+
+(* EXAMPLES *****************************************************************)
+
+(* Lemma "rpx_fwd_lpx_reqx" is not an inversion *****************************)
+
+definition L1 (K) (s1) (s0): lenv ≝ K.ⓛ⋆s1.ⓛⓝ#0.⋆s0.
+
+definition L (K) (s1) (s0): lenv ≝ K.ⓛ⋆s1.ⓛ⋆s0.
+
+definition L2 (K) (i1) (s0): lenv ≝ K.ⓛ#i1.ⓛ⋆s0.
+
+definition T: term ≝ #0.
+
+(* Basic properties *********************************************************)
+
+lemma ex_rpx_fwd_1 (G) (K) (s1) (s0):
+      ❪G,L1 K s1 s0❫ ⊢ ⬈ L K s1 s0.
+/3 width=1 by lpx_pair, lpx_bind_refl_dx, cpx_eps/ qed.
+
+lemma ex_rpx_fwd_2 (K) (s1) (s0) (i1) (i0):
+      L K s1 s0 ≛[T] L2 K i1 i0.
+/3 width=1 by reqx_pair, reqx_sort/ qed.
+
+lemma ex_rpx_fwd_3 (G) (K) (s1) (s0) (i1) (i0):
+      ❪G,L1 K s1 s0❫ ⊢ ⬈[T] L2 K i1 i0 → ⊥.
+#G #K #s1 #s0 #i1 #i0 #H
+elim (rpx_inv_zero_pair_sn … H) -H #Y2 #X2 #H #_ normalize #H0 destruct
+elim (rpx_inv_flat … H) -H #H #_
+elim (rpx_inv_zero_pair_sn … H) -H #Y2 #X2 #_ #H #H0 destruct
+elim (cpx_inv_sort1 … H) #s2 #H destruct
+qed-.
+
+(* Main properties **********************************************************)
+
+theorem ex_rpx_fwd (G) (K) (s1) (s0) (i1) (i0):
+        (❪G,L1 K s1 s0❫ ⊢ ⬈ L K s1 s0 → L K s1 s0 ≛[T] L2 K i1 i0 → ❪G,L1 K s1 s0❫ ⊢ ⬈[T] L2 K i1 i0) → ⊥.
+/3 width=7 by ex_rpx_fwd_3, ex_rpx_fwd_2, ex_rpx_fwd_1/ qed-.