ground_2 released and permanently renamed as ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_istot.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_istot.ma
deleted file mode 100644 (file)
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--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_istot.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_2/notation/relations/istotal_1.ma".
-include "ground_2/relocation/rtmap_at.ma".
-
-(* RELOCATION MAP ***********************************************************)
-
-definition istot: predicate rtmap ≝ λf. ∀i. ∃j. @❪i,f❫ ≘ j.
-
-interpretation "test for totality (rtmap)"
-   'IsTotal f = (istot f).
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma istot_inv_push: ∀g. 𝐓❪g❫ → ∀f. ⫯f = g → 𝐓❪f❫.
-#g #Hg #f #H #i elim (Hg (↑i)) -Hg
-#j #Hg elim (at_inv_npx … Hg … H) -Hg -H /2 width=3 by ex_intro/
-qed-.
-
-lemma istot_inv_next: ∀g. 𝐓❪g❫ → ∀f. ↑f = g → 𝐓❪f❫.
-#g #Hg #f #H #i elim (Hg i) -Hg
-#j #Hg elim (at_inv_xnx … Hg … H) -Hg -H /2 width=2 by ex_intro/
-qed-.
-
-(* Properties on tl *********************************************************)
-
-lemma istot_tl: ∀f. 𝐓❪f❫ → 𝐓❪⫱f❫.
-#f cases (pn_split f) *
-#g * -f /2 width=3 by istot_inv_next, istot_inv_push/
-qed.
-
-(* Properties on tls ********************************************************)
-
-lemma istot_tls: ∀n,f. 𝐓❪f❫ → 𝐓❪⫱*[n]f❫.
-#n elim n -n /3 width=1 by istot_tl/
-qed.
-
-(* Main forward lemmas on at ************************************************)
-
-corec theorem at_ext: ∀f1,f2. 𝐓❪f1❫ → 𝐓❪f2❫ →
-                      (∀i,i1,i2. @❪i,f1❫ ≘ i1 → @❪i,f2❫ ≘ i2 → i1 = i2) →
-                      f1 ≡ f2.
-#f1 cases (pn_split f1) * #g1 #H1
-#f2 cases (pn_split f2) * #g2 #H2
-#Hf1 #Hf2 #Hi
-[ @(eq_push … H1 H2) @at_ext -at_ext /2 width=3 by istot_inv_push/ -Hf1 -Hf2
-  #i #i1 #i2 #Hg1 #Hg2 lapply (Hi (↑i) (↑i1) (↑i2) ??) /2 width=7 by at_push/
-| cases (Hf2 0) -Hf1 -Hf2 -at_ext
-  #j2 #Hf2 cases (at_increasing_strict … Hf2 … H2) -H2
-  lapply (Hi 0 0 j2 … Hf2) /2 width=2 by at_refl/ -Hi -Hf2 -H1
-  #H2 #H cases (lt_le_false … H) -H //
-| cases (Hf1 0) -Hf1 -Hf2 -at_ext
-  #j1 #Hf1 cases (at_increasing_strict … Hf1 … H1) -H1
-  lapply (Hi 0 j1 0 Hf1 ?) /2 width=2 by at_refl/ -Hi -Hf1 -H2
-  #H1 #H cases (lt_le_false … H) -H //
-| @(eq_next … H1 H2) @at_ext -at_ext /2 width=3 by istot_inv_next/ -Hf1 -Hf2
-  #i #i1 #i2 #Hg1 #Hg2 lapply (Hi i (↑i1) (↑i2) ??) /2 width=5 by at_next/
-]
-qed-.
-
-(* Advanced properties on at ************************************************)
-
-lemma at_dec: ∀f,i1,i2. 𝐓❪f❫ → Decidable (@❪i1,f❫ ≘ i2).
-#f #i1 #i2 #Hf lapply (Hf i1) -Hf *
-#j2 #Hf elim (eq_nat_dec i2 j2)
-[ #H destruct /2 width=1 by or_introl/
-| /4 width=6 by at_mono, or_intror/
-]
-qed-.
-
-lemma is_at_dec_le: ∀f,i2,i. 𝐓❪f❫ → (∀i1. i1 + i ≤ i2 → @❪i1,f❫ ≘ i2 → ⊥) →
-                    Decidable (∃i1. @❪i1,f❫ ≘ i2).
-#f #i2 #i #Hf elim i -i
-[ #Ht @or_intror * /3 width=3 by at_increasing/
-| #i #IH #Ht elim (at_dec f (i2-i) i2) /3 width=2 by ex_intro, or_introl/
-  #Hi2 @IH -IH #i1 #H #Hi elim (le_to_or_lt_eq … H) -H /2 width=3 by/
-  #H destruct -Ht /2 width=1 by/
-]
-qed-.
-
-lemma is_at_dec: ∀f,i2. 𝐓❪f❫ → Decidable (∃i1. @❪i1,f❫ ≘ i2).
-#f #i2 #Hf @(is_at_dec_le ?? (↑i2)) /2 width=4 by lt_le_false/
-qed-.
-
-(* Advanced properties on isid **********************************************)
-
-lemma isid_at_total: ∀f. 𝐓❪f❫ → (∀i1,i2. @❪i1,f❫ ≘ i2 → i1 = i2) → 𝐈❪f❫.
-#f #H1f #H2f @isid_at
-#i lapply (H1f i) -H1f *
-#j #Hf >(H2f … Hf) in ⊢ (???%); -H2f //
-qed.