update in ground_2 and models

[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
index 07266f8d3f27bc34ebcdfadd7ebc980dd9bea6c0..8d59fe006d913b5c34454e5aaa71c494a9d2216a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/apps_2/models/model_li.ma
+++ b/matita/matita/contribs/lambdadelta/apps_2/models/model_li.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/syntax/lenv.ma".
-include "apps_2/models/model_push.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 +32,52 @@ 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-.