milestone update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/pstream_eq.ma b/matita/matita/contribs/lambdadelta/ground/relocation/pstream_eq.ma
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--- a/matita/matita/contribs/lambdadelta/ground/relocation/pstream_eq.ma
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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.tcs.unibo.it                            *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "ground/lib/stream_eq.ma".
-include "ground/relocation/rtmap_eq.ma".
-
-(* RELOCATION N-STREAM ******************************************************)
-
-(* Specific properties ******************************************************)
-
-fact eq_inv_seq_aux: ∀f1,f2,p1,p2. p1⨮f1 ≡ p2⨮f2 → p1 = p2 ∧ f1 ≡ f2.
-#f1 #f2 #p1 #p2 @(pnat_ind_2 … p1 p2) -p1 -p2
-[ #p2 #H elim (eq_inv_px … H) -H [2,3: // ]
-  #g1 #H1 #H elim (push_inv_seq_dx … H) -H /2 width=1 by conj/
-| #p1 #_ #H elim (eq_inv_np … H) -H //
-| #p1 #p2 #IH #H lapply (eq_inv_nn … H ????) -H [5:|*: // ]
-  #H elim (IH H) -IH -H /2 width=1 by conj/
-]
-qed-.
-
-lemma eq_inv_seq: ∀g1,g2. g1 ≡ g2 → ∀f1,f2,p1,p2. p1⨮f1 = g1 → p2⨮f2 = g2 →
-                  p1 = p2 ∧ f1 ≡ f2.
-/2 width=1 by eq_inv_seq_aux/ qed-.
-
-corec lemma nstream_eq: ∀f1,f2. f1 ≡ f2 → f1 ≗ f2.
-* #p1 #f1 * #p2 #f2 #Hf cases (eq_inv_gen … Hf) -Hf *
-#g1 #g2 #Hg #H1 #H2
-[ cases (push_inv_seq_dx … H1) -H1 * -p1 #H1
-  cases (push_inv_seq_dx … H2) -H2 * -p2 #H2
-  @stream_eq_cons /2 width=1 by/
-| cases (next_inv_seq_dx … H1) -H1 #m1 #H1 * -p1
-  cases (next_inv_seq_dx … H2) -H2 #m2 #H2 * -p2
-  cases (eq_inv_seq … Hg … H1 H2) -g1 -g2 #Hm #Hf
-  @stream_eq_cons /2 width=1 by/
-]
-qed-.
-
-corec lemma nstream_inv_eq: ∀f1,f2. f1 ≗ f2 → f1 ≡ f2.
-* #p1 #f1 * #p2 #f2 #H cases (stream_eq_inv_cons ??? H) -H [|*: // ]
-#Hf * -p2 cases p1 -p1 /3 width=5 by eq_push/
-#n @eq_next /3 width=5 by stream_eq_cons/
-qed.
-
-lemma eq_seq_id: ∀f1,f2. f1 ≡ f2 → ∀n. n⨮f1 ≡ n⨮f2.
-/4 width=1 by nstream_inv_eq, nstream_eq, stream_eq_cons/ qed.