syntactic components detached from basic_2 become static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / lifts_bind.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_bind.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_bind.ma
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--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_bind.ma
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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/syntax/ext2.ma".
-include "basic_2/relocation/lifts.ma".
-
-(* GENERIC RELOCATION FOR BINDERS *******************************************)
-
-definition liftsb: rtmap → relation bind ≝
-           λf. ext2 (lifts f).
-
-interpretation "uniform relocation (binder for local environments)"
-   'RLiftStar i I1 I2 = (liftsb (uni i) I1 I2).
-
-interpretation "generic relocation (binder for local environments)"
-   'RLiftStar f I1 I2 = (liftsb f I1 I2).
-
-(* Basic_inversion lemmas **************************************************)
-
-lemma liftsb_inv_unit_sn: ∀f,I,Z2. ⬆*[f] BUnit I ≘ Z2 → Z2 = BUnit I.
-/2 width=2 by ext2_inv_unit_sn/ qed-.
-
-lemma liftsb_inv_pair_sn: ∀f:rtmap. ∀Z2,I,V1. ⬆*[f] BPair I V1 ≘ Z2 →
-                          ∃∃V2. ⬆*[f] V1 ≘ V2 & Z2 = BPair I V2.
-/2 width=1 by ext2_inv_pair_sn/ qed-.
-
-lemma liftsb_inv_unit_dx: ∀f,I,Z1. ⬆*[f] Z1 ≘ BUnit I → Z1 = BUnit I.
-/2 width=2 by ext2_inv_unit_dx/ qed-.
-
-lemma liftsb_inv_pair_dx: ∀f:rtmap. ∀Z1,I,V2. ⬆*[f] Z1 ≘ BPair I V2 →
-                          ∃∃V1. ⬆*[f] V1 ≘ V2 & Z1 = BPair I V1.
-/2 width=1 by ext2_inv_pair_dx/ qed-.
-
-(* Basic properties *********************************************************)
-
-lemma liftsb_eq_repl_back: ∀I1,I2. eq_repl_back … (λf. ⬆*[f] I1 ≘ I2).
-#I1 #I2 #f1 * -I1 -I2 /3 width=3 by lifts_eq_repl_back, ext2_pair/
-qed-.
-
-lemma liftsb_refl: ∀f. 𝐈⦃f⦄ → reflexive … (liftsb f).
-/3 width=1 by lifts_refl, ext2_refl/ qed.
-
-lemma liftsb_total: ∀I1,f. ∃I2. ⬆*[f] I1 ≘ I2.
-* [2: #I #T1 #f elim (lifts_total T1 f) ]
-/3 width=2 by ext2_unit, ext2_pair, ex_intro/
-qed-.
-
-lemma liftsb_split_trans: ∀f,I1,I2. ⬆*[f] I1 ≘ I2 →
-                          ∀f1,f2. f2 ⊚ f1 ≘ f →
-                          ∃∃I. ⬆*[f1] I1 ≘ I & ⬆*[f2] I ≘ I2.
-#f #I1 #I2 * -I1 -I2 /2 width=3 by ext2_unit, ex2_intro/
-#I #V1 #V2 #HV12 #f1 #f2 #Hf elim (lifts_split_trans … HV12 … Hf) -f
-/3 width=3 by ext2_pair, ex2_intro/
-qed-.
-
-(* Basic forward lemmas *****************************************************)
-
-lemma liftsb_fwd_isid: ∀f,I1,I2. ⬆*[f] I1 ≘ I2 → 𝐈⦃f⦄ → I1 = I2.
-#f #I1 #I2 * -I1 -I2 /3 width=3 by lifts_fwd_isid, eq_f2/
-qed-.