update in static_2 and app_2

[helm.git] / matita / matita / contribs / lambdadelta / apps_2 / models / model_li.ma

diff --git a/matita/matita/contribs/lambdadelta/apps_2/models/model_li.ma b/matita/matita/contribs/lambdadelta/apps_2/models/model_li.ma
deleted file mode 100644 (file)
index 6be3c60..0000000
--- a/matita/matita/contribs/lambdadelta/apps_2/models/model_li.ma
+++ /dev/null
@@ -1,95 +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/syntax/lenv.ma".
-include "apps_2/models/model_vlift.ma".
-include "apps_2/notation/models/inwbrackets_4.ma".
-
-(* LOCAL ENVIRONMENT INTERPRETATION  ****************************************)
-
-inductive li (M) (gv): relation2 lenv (evaluation M) ≝
-| li_atom: ∀lv. li M gv (⋆) lv
-| li_abbr: ∀lv,d,L,V. li M gv L lv → ⟦V⟧[gv, lv] ≗ d → li M gv (L.ⓓV) (⫯[d]lv)
-| li_abst: ∀lv,d,L,W. li M gv L lv → li M gv (L.ⓛW) (⫯[d]lv)
-| li_unit: ∀lv,d,I,L. li M gv L lv → li M gv (L.ⓤ{I}) (⫯[d]lv)
-| li_repl: ∀lv1,lv2,L. li M gv L lv1 → lv1 ≐ lv2 → li M gv L lv2
-.
-
-interpretation "local environment interpretation (model)"
-   'InWBrackets M gv L lv  = (li M gv L lv).
-
-(* Basic inversion lemmas ***************************************************)
-
-fact li_inv_abbr_aux (M) (gv): ∀v,Y. v ϵ ⟦Y⟧{M}[gv] → ∀L,V. Y = L.ⓓV →
-                               ∃∃lv,d. lv ϵ ⟦L⟧{M}[gv] & ⟦V⟧{M}[gv, lv] ≗ d & ⫯{M}[d]lv ≐ v.
-#M #gv #v #Y #H elim H -v -Y
-[ #lv #K #W #H destruct
-| #lv #d #L #V #HL #HV #_ #K #W #H destruct /2 width=5 by ex3_2_intro/
-| #lv #d #L #V #_ #_ #K #W #H destruct
-| #lv #d #I #L #_ #_ #K #W #H destruct
-| #lv1 #lv2 #L #_ #Hlv12 #IH #K #W #H destruct
-  elim IH -IH [|*: // ] #lv #d #HK #HW #Hlv
-  /3 width=5 by exteq_trans, ex3_2_intro/
-]
-qed-.
-
-lemma li_inv_abbr (M) (gv): ∀v,L,V. v ϵ ⟦L.ⓓV⟧{M}[gv] →
-                            ∃∃lv,d. lv ϵ ⟦L⟧{M}[gv] & ⟦V⟧{M}[gv, lv] ≗ d & ⫯{M}[d]lv ≐ v.
-/2 width=3 by li_inv_abbr_aux/ qed-.
-
-fact li_inv_abst_aux (M) (gv): ∀v,Y. v ϵ ⟦Y⟧{M}[gv] → ∀L,W. Y = L.ⓛW →
-                               ∃∃lv,d. lv ϵ ⟦L⟧{M}[gv] & ⫯{M}[d]lv ≐ v.
-#M #gv #v #Y #H elim H -v -Y
-[ #lv #K #U #H destruct
-| #lv #d #L #V #_ #_ #_ #K #U #H destruct
-| #lv #d #L #V #HL #_ #K #U #H destruct /2 width=4 by ex2_2_intro/
-| #lv #d #I #L #_ #_ #K #U #H destruct
-| #lv1 #lv2 #L #_ #Hlv12 #IH #K #U #H destruct
-  elim IH -IH [|*: // ] #lv #d #HK #Hlv
-  /3 width=4 by exteq_trans, ex2_2_intro/
-]
-qed-.
-
-lemma li_inv_abst (M) (gv): ∀v,L,W. v ϵ ⟦L.ⓛW⟧{M}[gv] →
-                            ∃∃lv,d. lv ϵ ⟦L⟧{M}[gv] & ⫯{M}[d]lv ≐ v.
-/2 width=4 by li_inv_abst_aux/ qed-.
-
-fact li_inv_unit_aux (M) (gv): ∀v,Y. v ϵ ⟦Y⟧{M}[gv] → ∀I,L. Y = L.ⓤ{I} →
-                               ∃∃lv,d. lv ϵ ⟦L⟧{M}[gv] & ⫯{M}[d]lv ≐ v.
-#M #gv #v #Y #H elim H -v -Y
-[ #lv #J #K #H destruct
-| #lv #d #L #V #_ #_ #_ #J #K #H destruct
-| #lv #d #L #V #_ #_ #J #K #H destruct
-| #lv #d #I #L #HL #_ #J #K #H destruct /2 width=4 by ex2_2_intro/
-| #lv1 #lv2 #L #_ #Hlv12 #IH #J #K #H destruct
-  elim IH -IH [|*: // ] #lv #d #HK #Hlv
-  /3 width=4 by exteq_trans, ex2_2_intro/
-]
-qed-.
-
-lemma li_inv_unit (M) (gv): ∀v,I,L. v ϵ ⟦L.ⓤ{I}⟧{M}[gv] →
-                            ∃∃lv,d. lv ϵ ⟦L⟧{M}[gv] & ⫯{M}[d]lv ≐ v.
-/2 width=4 by li_inv_unit_aux/ qed-.
-
-(* Advanced forward lemmas **************************************************)
-
-lemma li_fwd_bind (M) (gv): ∀v,I,L. v ϵ ⟦L.ⓘ{I}⟧{M}[gv] →
-                            ∃∃lv,d. lv ϵ ⟦L⟧{M}[gv] & ⫯{M}[d]lv ≐ v.
-#m #gv #v * [ #I | * #V ] #L #H
-[ @(li_inv_unit … H)
-| elim (li_inv_abbr … H) -H #lv #d #Hl #_ #Hv
-  /2 width=4 by ex2_2_intro/
-| @(li_inv_abst … H)
-]
-qed-.