milestone in basic_2, λδ-2A reconstructed

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / tdpos / tdpos.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/tdpos/tdpos.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/tdpos/tdpos.etc
deleted file mode 100644 (file)
index 1b6b119..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc/tdpos/tdpos.etc
+++ /dev/null
@@ -1,63 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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 "static_2/notation/relations/positive_3.ma".
-include "static_2/syntax/item_sd.ma".
-include "static_2/syntax/term.ma".
-
-(* DEGREE POSITIVITY ON TERMS ***********************************************)
-
-inductive tdpos (h) (o): predicate term ≝
-| tdpos_sort: ∀s,d. deg h o s (↑d) → tdpos h o (⋆s)
-| tdpos_lref: ∀i. tdpos h o (#i)
-| tdpos_gref: ∀l. tdpos h o (§l)
-| tdpos_pair: ∀I,V,T. tdpos h o V → tdpos h o T → tdpos h o (②{I}V.T)
-.
-
-interpretation
-   "context-free degree positivity (term)"
-   'Positive h o T = (tdpos h o T).
-
-(* Basic inversion lemmas ***************************************************)
-
-fact tdpos_inv_sort_aux (h) (o): 
-                        ∀X. 𝐏[h,o]⦃X⦄ → ∀s. X = ⋆s → ∃d. deg h o s (↑d).
-#h #o #H *
-[ #s #d #Hsd #x #H destruct /2 width=2 by ex_intro/
-| #i #x #H destruct
-| #l #x #H destruct
-| #I #V #T #_ #_ #x #H destruct
-]
-qed-.
-
-lemma tdpos_inv_sort (h) (o): ∀s. 𝐏[h,o]⦃⋆s⦄ → ∃d. deg h o s (↑d).
-/2 width=3 by tdpos_inv_sort_aux/ qed-.
-
-fact tdpos_inv_pair_aux (h) (o): ∀X. 𝐏[h,o]⦃X⦄ → ∀I,V,T. X = ②{I}V.T →
-                                 ∧∧ 𝐏[h,o]⦃V⦄ & 𝐏[h,o]⦃T⦄.
-#h #o #H *
-[ #s #d #_ #Z #X1 #X2 #H destruct
-| #i #Z #X1 #X2 #H destruct
-| #l #Z #X1 #X2 #H destruct
-| #I #V #T #HV #HT #Z #X1 #X2 #H destruct /2 width=1 by conj/
-]
-qed-.
-
-lemma tdpos_inv_pair (h) (o): ∀I,V,T. 𝐏[h,o]⦃②{I}V.T⦄ →
-                              ∧∧ 𝐏[h,o]⦃V⦄ & 𝐏[h,o]⦃T⦄.
-/2 width=4 by tdpos_inv_pair_aux/ qed-.
-
-(* Basic properties *********************************************************)
-
-axiom tdpos_total (h): ∀T. ∃o. 𝐏[h,o]⦃T⦄.