X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fapps_2%2Fmodels%2Fmodel_li.ma;h=6be3c60c6cf2b49979ff13e61dfed11dd2caa3be;hp=07266f8d3f27bc34ebcdfadd7ebc980dd9bea6c0;hb=ff612dc35167ec0c145864c9aa8ae5e1ebe20a48;hpb=5a0d5df90ad4096c4d7bdc50ce69cf8673ea6e57

diff --git a/matita/matita/contribs/lambdadelta/apps_2/models/model_li.ma b/matita/matita/contribs/lambdadelta/apps_2/models/model_li.ma
index 07266f8d3..6be3c60c6 100644
--- a/matita/matita/contribs/lambdadelta/apps_2/models/model_li.ma
+++ b/matita/matita/contribs/lambdadelta/apps_2/models/model_li.ma
@@ -12,8 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/syntax/lenv.ma".
-include "apps_2/models/model_push.ma".
+include "static_2/syntax/lenv.ma".
+include "apps_2/models/model_vlift.ma".
 include "apps_2/notation/models/inwbrackets_4.ma".
 
 (* LOCAL ENVIRONMENT INTERPRETATION  ****************************************)
@@ -23,6 +23,7 @@ inductive li (M) (gv): relation2 lenv (evaluation M) ≝
 | 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)"
@@ -31,43 +32,64 @@ interpretation "local environment interpretation (model)"
 (* 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 * -v -Y
+                               ∃∃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
+| #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.
+                            ∃∃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 * -v -Y
+                               ∃∃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
+| #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.
+                            ∃∃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 * -v -Y
+                               ∃∃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 #L #V #_ #J #K #H destruct
-| #lv #d #I #L #HL #J #K #H destruct /2 width=4 by ex2_2_intro/
+| #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.
+                            ∃∃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-.