renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / fdeq_fdeq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/fdeq_fdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/static/fdeq_fdeq.ma
new file mode 100644 (file)
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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/static/rdeq_rdeq.ma".
+include "basic_2/static/fdeq.ma".
+
+(* DEGREE-BASED EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES ****************)
+
+(* Advanced properties ******************************************************)
+
+lemma fdeq_sym: ∀h,o. tri_symmetric … (fdeq h o).
+#h #o #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: ∀h,o. tri_transitive … (fdeq h o).
+#h #o #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: ∀h,o,G,G1,G2,L,L1,L2,T,T1,T2.
+                      ⦃G, L, T⦄ ≛[h, o] ⦃G1, L1, T1⦄→ ⦃G, L, T⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄.
+/3 width=5 by fdeq_trans, fdeq_sym/ qed-.
+
+theorem fdeq_canc_dx: ∀h,o,G1,G2,G,L1,L2,L,T1,T2,T.
+                      ⦃G1, L1, T1⦄ ≛[h, o] ⦃G, L, T⦄ → ⦃G2, L2, T2⦄ ≛[h, o] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ ≛[h, o] ⦃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: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ →
+                            ∀U1,U2. ⦃G1, L1, U1⦄ ≛[h, o] ⦃G2, L2, U2⦄ →
+                            (T2 ≛[h, o] U2 → ⊥) → (T1 ≛[h, o] U1 → ⊥).
+#h #o #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-.