syntactic components detached from basic_2 become static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / syntax / lveq_length.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/lveq_length.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/lveq_length.ma
deleted file mode 100644 (file)
index eca3856..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/syntax/lveq_length.ma
+++ /dev/null
@@ -1,109 +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 "basic_2/syntax/lenv_length.ma".
-include "basic_2/syntax/lveq.ma".
-
-(* EQUIVALENCE FOR LOCAL ENVIRONMENTS UP TO EXCLUSION BINDERS ***************)
-
-(* Properties with length for local environments ****************************)
-
-lemma lveq_length_eq: ∀L1,L2. |L1| = |L2| → L1 ≋ⓧ*[0, 0] L2.
-#L1 elim L1 -L1
-[ #Y2 #H >(length_inv_zero_sn … H) -Y2 /2 width=3 by lveq_atom, ex_intro/
-| #K1 #I1 #IH #Y2 #H
-  elim (length_inv_succ_sn … H) -H #I2 #K2 #HK #H destruct
-  /3 width=1 by lveq_bind/
-]
-qed.
-
-(* Forward lemmas with length for local environments ************************)
-
-lemma lveq_fwd_length_le_sn: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2 → n1 ≤ |L1|.
-#L1 #L2 #n1 #n2 #H elim H -L1 -L2 -n1 -n2 normalize
-/2 width=1 by le_S_S/
-qed-.
-
-lemma lveq_fwd_length_le_dx: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2 → n2 ≤ |L2|.
-#L1 #L2 #n1 #n2 #H elim H -L1 -L2 -n1 -n2 normalize
-/2 width=1 by le_S_S/
-qed-.
-
-lemma lveq_fwd_length: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2 →
-                       ∧∧ |L1|-|L2| = n1 & |L2|-|L1| = n2.
-#L1 #L2 #n1 #n2 #H elim H -L1 -L2 -n1 -n2 /2 width=1 by conj/
-#K1 #K2 #n #_ * #H1 #H2 >length_bind /3 width=1 by minus_Sn_m, conj/
-qed-.
-
-lemma lveq_length_fwd_sn: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2 → |L1| ≤ |L2| → 0 = n1.
-#L1 #L2 #n1 #n2 #H #HL
-elim (lveq_fwd_length … H) -H
->(eq_minus_O … HL) //
-qed-.
-
-lemma lveq_length_fwd_dx: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2 → |L2| ≤ |L1| → 0 = n2.
-#L1 #L2 #n1 #n2 #H #HL
-elim (lveq_fwd_length … H) -H
->(eq_minus_O … HL) //
-qed-.
-
-lemma lveq_inj_length: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2 →
-                       |L1| = |L2| → ∧∧ 0 = n1 & 0 = n2.
-#L1 #L2 #n1 #n2 #H #HL
-elim (lveq_fwd_length … H) -H
->HL -HL /2 width=1 by conj/ 
-qed-.
-
-lemma lveq_fwd_length_plus: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2 →
-                            |L1| + n2 = |L2| + n1.
-#L1 #L2 #n1 #n2 #H elim H -L1 -L2 -n1 -n2 normalize
-/2 width=2 by injective_plus_r/
-qed-.
-
-lemma lveq_fwd_length_eq: ∀L1,L2. L1 ≋ⓧ*[0, 0] L2 → |L1| = |L2|.
-/3 width=2 by lveq_fwd_length_plus, injective_plus_l/ qed-.
-
-lemma lveq_fwd_length_minus: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2 →
-                             |L1| - n1 = |L2| - n2.
-/3 width=3 by lveq_fwd_length_plus, lveq_fwd_length_le_dx, lveq_fwd_length_le_sn, plus_to_minus_2/ qed-.
-
-lemma lveq_fwd_abst_bind_length_le: ∀I1,I2,L1,L2,V1,n1,n2.
-                                    L1.ⓑ{I1}V1 ≋ⓧ*[n1, n2] L2.ⓘ{I2} → |L1| ≤ |L2|.
-#I1 #I2 #L1 #L2 #V1 #n1 #n2 #HL
-lapply (lveq_fwd_pair_sn … HL) #H destruct
-elim (lveq_fwd_length … HL) -HL >length_bind >length_bind //
-qed-.
-
-lemma lveq_fwd_bind_abst_length_le: ∀I1,I2,L1,L2,V2,n1,n2.
-                                    L1.ⓘ{I1} ≋ⓧ*[n1, n2] L2.ⓑ{I2}V2 → |L2| ≤ |L1|.
-/3 width=6 by lveq_fwd_abst_bind_length_le, lveq_sym/ qed-.
-
-(* Inversion lemmas with length for local environments **********************)
-
-lemma lveq_inv_void_dx_length: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2.ⓧ → |L1| ≤ |L2| →
-                               ∃∃m2. L1 ≋ ⓧ*[n1, m2] L2 & 0 = n1 & ↑m2 = n2.
-#L1 #L2 #n1 #n2 #H #HL12
-lapply (lveq_fwd_length_plus … H) normalize >plus_n_Sm #H0
-lapply (plus2_inv_le_sn … H0 HL12) -H0 -HL12 #H0
-elim (le_inv_S1 … H0) -H0 #m2 #_ #H0 destruct
-elim (lveq_inv_void_succ_dx … H) -H /2 width=3 by ex3_intro/
-qed-.
-
-lemma lveq_inv_void_sn_length: ∀L1,L2,n1,n2. L1.ⓧ ≋ⓧ*[n1, n2] L2 → |L2| ≤ |L1| →
-                               ∃∃m1. L1 ≋ ⓧ*[m1, n2] L2 & ↑m1 = n1 & 0 = n2.
-#L1 #L2 #n1 #n2 #H #HL
-lapply (lveq_sym … H) -H #H
-elim (lveq_inv_void_dx_length … H HL) -H -HL
-/3 width=4 by lveq_sym, ex3_intro/
-qed-.