syntactic components detached from basic_2 become static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / syntax / lveq_lveq.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/lveq_lveq.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/lveq_lveq.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 "static_2/syntax/lveq_length.ma".
+
+(* EQUIVALENCE FOR LOCAL ENVIRONMENTS UP TO EXCLUSION BINDERS ***************)
+
+(* Main inversion lemmas ****************************************************)
+
+theorem lveq_inv_bind: ∀K1,K2. K1 ≋ⓧ*[0, 0] K2 →
+                       ∀I1,I2,m1,m2. K1.ⓘ{I1} ≋ⓧ*[m1, m2] K2.ⓘ{I2} →
+                       ∧∧ 0 = m1 & 0 = m2.
+#K1 #K2 #HK #I1 #I2 #m1 #m2 #H
+lapply (lveq_fwd_length_eq … HK) -HK #HK
+elim (lveq_inj_length … H) -H normalize /3 width=1 by conj, eq_f/
+qed-.
+
+theorem lveq_inj: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2 →
+                  ∀m1,m2. L1 ≋ⓧ*[m1, m2] L2 →
+                  ∧∧ n1 = m1 & n2 = m2.
+#L1 #L2 #n1 #n2 #Hn #m1 #m2 #Hm
+elim (lveq_fwd_length … Hn) -Hn #H1 #H2 destruct
+elim (lveq_fwd_length … Hm) -Hm #H1 #H2 destruct
+/2 width=1 by conj/
+qed-.
+
+theorem lveq_inj_void_sn_ge: ∀K1,K2. |K2| ≤ |K1| →
+                             ∀n1,n2. K1 ≋ⓧ*[n1, n2] K2 →
+                             ∀m1,m2. K1.ⓧ ≋ⓧ*[m1, m2] K2 →
+                             ∧∧ ↑n1 = m1 & 0 = m2 & 0 = n2.
+#L1 #L2 #HL #n1 #n2 #Hn #m1 #m2 #Hm
+elim (lveq_fwd_length … Hn) -Hn #H1 #H2 destruct
+elim (lveq_fwd_length … Hm) -Hm #H1 #H2 destruct
+>length_bind >eq_minus_S_pred >(eq_minus_O … HL)
+/3 width=4 by plus_minus, and3_intro/
+qed-.
+
+theorem lveq_inj_void_dx_le: ∀K1,K2. |K1| ≤ |K2| →
+                             ∀n1,n2. K1 ≋ⓧ*[n1, n2] K2 →
+                             ∀m1,m2. K1 ≋ⓧ*[m1, m2] K2.ⓧ →
+                             ∧∧ ↑n2 = m2 & 0 = m1 & 0 = n1.
+/3 width=5 by lveq_inj_void_sn_ge, lveq_sym/ qed-. (* auto: 2x lveq_sym *)