+++ /dev/null
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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 *)
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-(**************************************************************************)
-
-include "basic_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 *)