update for the article

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

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/feqx_feqx.ma b/matita/matita/contribs/lambdadelta/static_2/static/feqx_feqx.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_reqx.ma".
+include "static_2/static/feqx.ma".
+
+(* SORT-IRRELEVANT EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES *************)
+
+(* Advanced properties ******************************************************)
+
+lemma feqx_sym: tri_symmetric … feqx.
+#G1 #G2 #L1 #L2 #T1 #T2 * -G1 -L1 -T1
+/3 width=1 by feqx_intro_dx, reqx_sym, teqx_sym/
+qed-.
+
+(* Main properties **********************************************************)
+
+theorem feqx_trans: tri_transitive … feqx.
+#G1 #G #L1 #L #T1 #T * -G -L -T
+#L #T #HL1 #HT1 #G2 #L2 #T2 * -G2 -L2 -T2
+/4 width=5 by feqx_intro_sn, reqx_trans, teqx_reqx_div, teqx_trans/
+qed-.
+
+theorem feqx_canc_sn: ∀G,G1,L,L1,T,T1. ⦃G,L,T⦄ ≛ ⦃G1,L1,T1⦄→
+                      ∀G2,L2,T2. ⦃G,L,T⦄ ≛ ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ≛ ⦃G2,L2,T2⦄.
+/3 width=5 by feqx_trans, feqx_sym/ qed-.
+
+theorem feqx_canc_dx: ∀G1,G,L1,L,T1,T. ⦃G1,L1,T1⦄ ≛ ⦃G,L,T⦄ →
+                      ∀G2,L2,T2. ⦃G2,L2,T2⦄ ≛ ⦃G,L,T⦄ → ⦃G1,L1,T1⦄ ≛ ⦃G2,L2,T2⦄.
+/3 width=5 by feqx_trans, feqx_sym/ qed-.
+
+(* Main inversion lemmas with degree-based equivalence on terms *************)
+
+theorem feqx_tneqx_repl_dx: ∀G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ≛ ⦃G2,L2,T2⦄ →
+                            ∀U1,U2. ⦃G1,L1,U1⦄ ≛ ⦃G2,L2,U2⦄ →
+                            (T2 ≛ U2 → ⊥) → (T1 ≛ U1 → ⊥).
+#G1 #G2 #L1 #L2 #T1 #T2 #HT #U1 #U2 #HU #HnTU2 #HTU1
+elim (feqx_inv_gen_sn … HT) -HT #_ #_ #HT
+elim (feqx_inv_gen_sn … HU) -HU #_ #_ #HU
+/3 width=5 by teqx_repl/
+qed-.