X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Fstatic%2Ffdeq_fdeq.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Fstatic%2Ffdeq_fdeq.ma;h=0000000000000000000000000000000000000000;hb=adb9ba187619cea977d1d22971eba27eb437cd6a;hp=1edc17d50d5f4065d16e7cb050bf8c5c3c0b9ad2;hpb=f677b4ef7fa20f1ab36c5ee59598865d5c1b719b;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/static_2/static/fdeq_fdeq.ma b/matita/matita/contribs/lambdadelta/static_2/static/fdeq_fdeq.ma deleted file mode 100644 index 1edc17d50..000000000 --- a/matita/matita/contribs/lambdadelta/static_2/static/fdeq_fdeq.ma +++ /dev/null @@ -1,52 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||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-.