update for the article

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

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/fdeq_fdeq.ma b/matita/matita/contribs/lambdadelta/static_2/static/fdeq_fdeq.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/rdeq_rdeq.ma".
-include "static_2/static/fdeq.ma".
-
-(* SORT-IRRELEVANT EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES *************)
-
-(* Advanced properties ******************************************************)
-
-lemma fdeq_sym: tri_symmetric … fdeq.
-#G1 #G2 #L1 #L2 #T1 #T2 * -G1 -L1 -T1
-/3 width=1 by fdeq_intro_dx, rdeq_sym, tdeq_sym/
-qed-.
-
-(* Main properties **********************************************************)
-
-theorem fdeq_trans: tri_transitive … fdeq.
-#G1 #G #L1 #L #T1 #T * -G -L -T
-#L #T #HL1 #HT1 #G2 #L2 #T2 * -G2 -L2 -T2
-/4 width=5 by fdeq_intro_sn, rdeq_trans, tdeq_rdeq_div, tdeq_trans/
-qed-.
-
-theorem fdeq_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 fdeq_trans, fdeq_sym/ qed-.
-
-theorem fdeq_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 fdeq_trans, fdeq_sym/ qed-.
-
-(* Main inversion lemmas with degree-based equivalence on terms *************)
-
-theorem fdeq_tdneq_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 (fdeq_inv_gen_sn … HT) -HT #_ #_ #HT
-elim (fdeq_inv_gen_sn … HU) -HU #_ #_ #HU
-/3 width=5 by tdeq_repl/
-qed-.