update in static_2 and app_2

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

diff --git a/matita/matita/contribs/lambdadelta/apps_2/models/vlifts.ma b/matita/matita/contribs/lambdadelta/apps_2/models/vlifts.ma
deleted file mode 100644 (file)
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--- a/matita/matita/contribs/lambdadelta/apps_2/models/vlifts.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 "apps_2/notation/models/roplus_5.ma".
-include "static_2/syntax/lenv.ma".
-include "apps_2/models/veq.ma".
-
-(* MULTIPLE LIFT FOR MODEL EVALUATIONS **************************************)
-
-inductive vlifts (M) (gv) (lv): relation2 lenv (evaluation M) ≝
-| vlifts_atom: vlifts M gv lv (⋆) lv
-| vlifts_abbr: ∀v,d,K,V. vlifts M gv lv K v → ⟦V⟧[gv, v] = d → vlifts M gv lv (K.ⓓV) (⫯[0←d]v)
-| vlifts_abst: ∀v,d,K,V. vlifts M gv lv K v → vlifts M gv lv (K.ⓛV) (⫯[0←d]v)
-| vlifts_unit: ∀v,d,I,K. vlifts M gv lv K v → vlifts M gv lv (K.ⓤ{I}) (⫯[0←d]v)
-| vlifts_repl: ∀v1,v2,L. vlifts M gv lv L v1 → v1 ≗ v2 → vlifts M gv lv L v2
-.
-
-interpretation "multiple lift (model evaluation)"
-   'ROPlus M gv L lv v  = (vlifts M gv lv L v).
-
-(* Basic inversion lemmas ***************************************************)
-
-fact vlifts_inv_atom_aux (M) (gv) (lv): is_model M →
-                                        ∀v,L. L ⨁{M}[gv] lv ≘ v →
-                                        ⋆ = L → lv ≗ v.
-#M #gv #lv #HM #v #L #H elim H -v -L
-[ #_ /2 width=1 by veq_refl/
-| #v #d #K #V #_ #_ #_ #H destruct
-| #v #d #K #V #_ #_ #H destruct
-| #v #d #I #K #_ #_ #H destruct
-| #v1 #v2 #L #_ #Hv12 #IH #H destruct
-  /3 width=3 by veq_trans/ 
-]
-qed-.
-
-lemma vlifts_inv_atom (M) (gv) (lv): is_model M →
-                                     ∀v. ⋆ ⨁{M}[gv] lv ≘ v → lv ≗ v.
-/2 width=4 by vlifts_inv_atom_aux/ qed-.
-
-fact vlifts_inv_abbr_aux (M) (gv) (lv): is_model M →
-                                        ∀y,L. L ⨁{M}[gv] lv ≘ y →
-                                        ∀K,V. K.ⓓV = L →
-                                        ∃∃v. K ⨁[gv] lv ≘ v & ⫯[0←⟦V⟧[gv, v]]v ≗ y.
-#M #gv #lv #HM #y #L #H elim H -y -L
-[ #Y #X #H destruct
-| #v #d #K #V #Hv #Hd #_ #Y #X #H destruct
-  /3 width=3 by veq_refl, ex2_intro/
-| #v #d #K #V #_ #_ #Y #X #H destruct
-| #v #d #I #K #_ #_ #Y #X #H destruct
-| #v1 #v2 #L #_ #Hv12 #IH #Y #X #H destruct
-  elim IH -IH [|*: // ] #v #Hv #Hv1
-  /3 width=5 by veq_trans, ex2_intro/
-]
-qed-.
-
-lemma vlifts_inv_abbr (M) (gv) (lv): is_model M →
-                                     ∀y,K,V. K.ⓓV ⨁{M}[gv] lv ≘ y →
-                                     ∃∃v. K ⨁[gv] lv ≘ v & ⫯[0←⟦V⟧[gv, v]]v ≗ y.
-/2 width=3 by vlifts_inv_abbr_aux/ qed-.
-
-fact vlifts_inv_abst_aux (M) (gv) (lv): is_model M →
-                                        ∀y,L. L ⨁{M}[gv] lv ≘ y →
-                                        ∀K,W. K.ⓛW = L →
-                                        ∃∃v,d. K ⨁[gv] lv ≘ v & ⫯[0←d]v ≗ y.
-#M #gv #lv #HM #y #L #H elim H -y -L
-[ #Y #X #H destruct
-| #v #d #K #V #_ #_ #_ #Y #X #H destruct
-| #v #d #K #V #Hv #_ #Y #X #H destruct
-  /3 width=4 by veq_refl, ex2_2_intro/
-| #v #d #I #K #_ #_ #Y #X #H destruct
-| #v1 #v2 #L #_ #Hv12 #IH #Y #X #H destruct
-  elim IH -IH [|*: // ] #v #d #Hv #Hv1
-  /3 width=6 by veq_trans, ex2_2_intro/
-]
-qed-.
-
-lemma vlifts_inv_abst (M) (gv) (lv): is_model M →
-                                     ∀y,K,W. K.ⓛW ⨁{M}[gv] lv ≘ y →
-                                     ∃∃v,d. K ⨁[gv] lv ≘ v & ⫯[0←d]v ≗ y.
-/2 width=4 by vlifts_inv_abst_aux/ qed-.
-
-fact vlifts_inv_unit_aux (M) (gv) (lv): is_model M →
-                                        ∀y,L. L ⨁{M}[gv] lv ≘ y →
-                                        ∀I,K. K.ⓤ{I} = L →
-                                        ∃∃v,d. K ⨁[gv] lv ≘ v & ⫯[0←d]v ≗ y.
-#M #gv #lv #HM #y #L #H elim H -y -L
-[ #Z #Y #H destruct
-| #v #d #K #V #_ #_ #_ #Z #Y #H destruct
-| #v #d #K #V #_ #_ #Z #Y #H destruct
-| #v #d #I #K #Hv #_ #Z #Y #H destruct
-  /3 width=4 by veq_refl, ex2_2_intro/
-| #v1 #v2 #L #_ #Hv12 #IH #Z #Y #H destruct
-  elim IH -IH [|*: // ] #v #d #Hv #Hv1
-  /3 width=6 by veq_trans, ex2_2_intro/
-]
-qed-.
-
-lemma vlifts_inv_unit (M) (gv) (lv): is_model M →
-                                     ∀y,I,K. K.ⓤ{I} ⨁{M}[gv] lv ≘ y →
-                                     ∃∃v,d. K ⨁[gv] lv ≘ v & ⫯[0←d]v ≗ y.
-/2 width=4 by vlifts_inv_unit_aux/ qed-.
-
-(* Basic forward lemmas *****************************************************)
-
-lemma vlifts_fwd_bind (M) (gv) (lv): is_model M →
-                                     ∀y,I,K. K.ⓘ{I} ⨁{M}[gv] lv ≘ y →
-                                     ∃∃v,d. K ⨁[gv] lv ≘ v & ⫯[0←d]v ≗ y.
-#M #gv #lv #HM #y * [ #I | * #V ] #L #H
-[ /2 width=2 by vlifts_inv_unit/
-| elim (vlifts_inv_abbr … H) // -H #v #HL #Hv
-  /2 width=4 by ex2_2_intro/
-| /2 width=2 by vlifts_inv_abst/
-]
-qed-.