milestone update in ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / relocation / rtmap_isid.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/rtmap_isid.ma b/matita/matita/contribs/lambdadelta/ground/relocation/rtmap_isid.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 "ground/notation/relations/isidentity_1.ma".
-include "ground/relocation/rtmap_tls.ma".
-
-(* RELOCATION MAP ***********************************************************)
-
-coinductive isid: predicate rtmap ≝
-| isid_push: ∀f,g. isid f → ⫯f = g → isid g
-.
-
-interpretation "test for identity (rtmap)"
-   'IsIdentity f = (isid f).
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma isid_inv_gen: ∀g. 𝐈❪g❫ → ∃∃f. 𝐈❪f❫ & ⫯f = g.
-#g * -g
-#f #g #Hf * /2 width=3 by ex2_intro/
-qed-.
-
-(* Advanced inversion lemmas ************************************************)
-
-lemma isid_inv_push: ∀g. 𝐈❪g❫ → ∀f. ⫯f = g → 𝐈❪f❫.
-#g #H elim (isid_inv_gen … H) -H
-#f #Hf * -g #g #H >(injective_push … H) -H //
-qed-.
-
-lemma isid_inv_next: ∀g. 𝐈❪g❫ → ∀f. ↑f = g → ⊥.
-#g #H elim (isid_inv_gen … H) -H
-#f #Hf * -g #g #H elim (discr_next_push … H)
-qed-.
-
-(* Main inversion lemmas ****************************************************)
-
-corec theorem isid_inv_eq_repl: ∀f1,f2. 𝐈❪f1❫ → 𝐈❪f2❫ → f1 ≡ f2.
-#f1 #f2 #H1 #H2
-cases (isid_inv_gen … H1) -H1
-cases (isid_inv_gen … H2) -H2
-/3 width=5 by eq_push/
-qed-.
-
-(* Basic properties *********************************************************)
-
-corec lemma isid_eq_repl_back: eq_repl_back … isid.
-#f1 #H cases (isid_inv_gen … H) -H
-#g1 #Hg1 #H1 #f2 #Hf cases (eq_inv_px … Hf … H1) -f1
-/3 width=3 by isid_push/
-qed-.
-
-lemma isid_eq_repl_fwd: eq_repl_fwd … isid.
-/3 width=3 by isid_eq_repl_back, eq_repl_sym/ qed-.
-
-(* Alternative definition ***************************************************)
-
-corec lemma eq_push_isid: ∀f. ⫯f ≡ f → 𝐈❪f❫.
-#f #H cases (eq_inv_px … H) -H /4 width=3 by isid_push, eq_trans/
-qed.
-
-corec lemma eq_push_inv_isid: ∀f. 𝐈❪f❫ → ⫯f ≡ f.
-#f * -f
-#f #g #Hf #Hg @(eq_push … Hg) [2: @eq_push_inv_isid // | skip ]
-@eq_f //
-qed-.
-
-(* Properties with iterated push ********************************************)
-
-lemma isid_pushs: ∀n,f. 𝐈❪f❫ → 𝐈❪⫯*[n]f❫.
-#n @(nat_ind_succ … n) -n /3 width=3 by isid_push/
-qed.
-
-(* Inversion lemmas with iterated push **************************************)
-
-lemma isid_inv_pushs: ∀n,g. 𝐈❪⫯*[n]g❫ → 𝐈❪g❫.
-#n @(nat_ind_succ … n) -n /3 width=3 by isid_inv_push/
-qed.
-
-(* Properties with tail *****************************************************)
-
-lemma isid_tl: ∀f. 𝐈❪f❫ → 𝐈❪⫱f❫.
-#f cases (pn_split f) * #g * -f #H
-[ /2 width=3 by isid_inv_push/
-| elim (isid_inv_next … H) -H //
-]
-qed.
-
-(* Properties with iterated tail ********************************************)
-
-lemma isid_tls: ∀n,g. 𝐈❪g❫ → 𝐈❪⫱*[n]g❫.
-#n @(nat_ind_succ … n) -n /3 width=1 by isid_tl/
-qed.