ground_2 released and permanently renamed as ground

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / nstream_istot.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_istot.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_istot.ma
deleted file mode 100644 (file)
index 3a19d81..0000000
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_istot.ma
+++ /dev/null
@@ -1,120 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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_2/notation/functions/apply_2.ma".
-include "ground_2/relocation/nstream_eq.ma".
-include "ground_2/relocation/rtmap_istot.ma".
-
-(* RELOCATION N-STREAM ******************************************************)
-
-rec definition apply (i: nat) on i: rtmap → nat ≝ ?.
-* #n #f cases i -i
-[ @n
-| #i lapply (apply i f) -apply -i -f
-  #i @(↑(n+i))
-]
-defined.
-
-interpretation "functional application (nstream)"
-   'Apply f i = (apply i f).
-
-(* Specific properties on at ************************************************)
-
-lemma at_O1: ∀i2,f. @❪0, i2⨮f❫ ≘ i2.
-#i2 elim i2 -i2 /2 width=5 by at_refl, at_next/
-qed.
-
-lemma at_S1: ∀n,f,i1,i2. @❪i1, f❫ ≘ i2 → @❪↑i1, n⨮f❫ ≘ ↑(n+i2).
-#n elim n -n /3 width=7 by at_push, at_next/
-qed.
-
-lemma at_total: ∀i1,f. @❪i1, f❫ ≘ f@❨i1❩.
-#i1 elim i1 -i1
-[ * // | #i #IH * /3 width=1 by at_S1/ ]
-qed.
-
-lemma at_istot: ∀f. 𝐓❪f❫.
-/2 width=2 by ex_intro/ qed.
-
-lemma at_plus2: ∀f,i1,i,n,m. @❪i1, n⨮f❫ ≘ i → @❪i1, (m+n)⨮f❫ ≘ m+i.
-#f #i1 #i #n #m #H elim m -m //
-#m <plus_S1 /2 width=5 by at_next/ (**) (* full auto fails *)
-qed.
-
-(* Specific inversion lemmas on at ******************************************)
-
-lemma at_inv_O1: ∀f,n,i2. @❪0, n⨮f❫ ≘ i2 → n = i2.
-#f #n elim n -n /2 width=6 by at_inv_ppx/
-#n #IH #i2 #H elim (at_inv_xnx … H) -H [2,3: // ]
-#j2 #Hj * -i2 /3 width=1 by eq_f/
-qed-.
-
-lemma at_inv_S1: ∀f,n,j1,i2. @❪↑j1, n⨮f❫ ≘ i2 →
-                 ∃∃j2. @❪j1, f❫ ≘ j2 & ↑(n+j2) = i2.
-#f #n elim n -n /2 width=5 by at_inv_npx/
-#n #IH #j1 #i2 #H elim (at_inv_xnx … H) -H [2,3: // ]
-#j2 #Hj * -i2 elim (IH … Hj) -IH -Hj
-#i2 #Hi * -j2 /2 width=3 by ex2_intro/
-qed-.
-
-lemma at_inv_total: ∀f,i1,i2. @❪i1, f❫ ≘ i2 → f@❨i1❩ = i2.
-/2 width=6 by at_mono/ qed-.
-
-(* Spercific forward lemmas on at *******************************************)
-
-lemma at_increasing_plus: ∀f,n,i1,i2. @❪i1, n⨮f❫ ≘ i2 → i1 + n ≤ i2.
-#f #n *
-[ #i2 #H <(at_inv_O1 … H) -i2 //
-| #i1 #i2 #H elim (at_inv_S1 … H) -H
-  #j1 #Ht * -i2 /4 width=2 by at_increasing, monotonic_le_plus_r, le_S_S/
-]
-qed-.
-
-lemma at_fwd_id: ∀f,n,i. @❪i, n⨮f❫ ≘ i → 0 = n.
-#f #n #i #H elim (at_fwd_id_ex … H) -H
-#g #H elim (push_inv_seq_dx … H) -H //
-qed-.
-
-(* Basic properties *********************************************************)
-
-lemma apply_O1: ∀n,f. (n⨮f)@❨0❩ = n.
-// qed.
-
-lemma apply_S1: ∀n,f,i. (n⨮f)@❨↑i❩ = ↑(n+f@❨i❩).
-// qed.
-
-lemma apply_eq_repl (i): eq_repl … (λf1,f2. f1@❨i❩ = f2@❨i❩).
-#i elim i -i [2: #i #IH ] * #n1 #f1 * #n2 #f2 #H
-elim (eq_inv_seq_aux … H) -H normalize //
-#Hn #Hf /4 width=1 by eq_f2, eq_f/
-qed.
-
-lemma apply_S2: ∀f,i. (↑f)@❨i❩ = ↑(f@❨i❩).
-* #n #f * //
-qed.
-
-(* Main inversion lemmas ****************************************************)
-
-theorem apply_inj: ∀f,i1,i2,j. f@❨i1❩ = j → f@❨i2❩ = j → i1 = i2.
-/2 width=4 by at_inj/ qed-.
-
-corec theorem nstream_eq_inv_ext: ∀f1,f2. (∀i. f1@❨i❩ = f2@❨i❩) → f1 ≗ f2.
-* #n1 #f1 * #n2 #f2 #Hf @eq_seq
-[ @(Hf 0)
-| @nstream_eq_inv_ext -nstream_eq_inv_ext #i
-  lapply (Hf 0) >apply_O1 >apply_O1 #H destruct
-  lapply (Hf (↑i)) >apply_S1 >apply_S1 #H
-  /3 width=2 by injective_plus_r, injective_S/
-]
-qed-.