update in apps_2

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

diff --git a/matita/matita/contribs/lambdadelta/apps_2/models/veq.ma b/matita/matita/contribs/lambdadelta/apps_2/models/veq.ma
index 11f07c404293f8df145f2828635c0885659af203..87a0800e75746a5481bc7e83207c9f159a64bed0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/apps_2/models/veq.ma
+++ b/matita/matita/contribs/lambdadelta/apps_2/models/veq.ma
@@ -32,24 +32,40 @@ lemma veq_repl (M): is_model M →
                     replace_2 … (veq M) (veq M) (veq M).
 /2 width=5 by mr/ qed-.
 
-(* Properties with evaluation push ******************************************)
+lemma ext_veq (M): is_model M →
+                   ∀lv1,lv2. lv1 ≐ lv2 → lv1 ≗{M} lv2.
+/2 width=1 by mq/ qed.
+
+lemma exteq_veq_trans (M): ∀lv1,lv. lv1 ≐ lv →
+                           ∀lv2. lv ≗{M} lv2 → lv1 ≗ lv2.
+// qed-.
+
+(* Properties with evaluation evaluation lift *******************************)
+
+theorem vlift_swap (M): ∀i1,i2. i1 ≤ i2 →
+                        ∀lv,d1,d2. ⫯[i1←d1] ⫯[i2←d2] lv ≐{?,dd M} ⫯[↑i2←d2] ⫯[i1←d1] lv.
+#M #i1 #i2 #Hi12 #lv #d1 #d2 #j
+elim (lt_or_eq_or_gt j i1) #Hji1 destruct
+[ >vlift_lt // >vlift_lt /2 width=3 by lt_to_le_to_lt/
+  >vlift_lt /3 width=3 by lt_S, lt_to_le_to_lt/ >vlift_lt //
+| >vlift_eq >vlift_lt /2 width=1 by monotonic_le_plus_l/ >vlift_eq //
+| >vlift_gt // elim (lt_or_eq_or_gt (↓j) i2) #Hji2 destruct
+  [ >vlift_lt // >vlift_lt /2 width=1 by lt_minus_to_plus/ >vlift_gt //
+  | >vlift_eq <(lt_succ_pred … Hji1) >vlift_eq //
+  | >vlift_gt // >vlift_gt /2 width=1 by lt_minus_to_plus_r/ >vlift_gt /2 width=3 by le_to_lt_to_lt/
+  ]
+]
+qed-.
 
-lemma push_comp (M): ∀i. compatible_3 … (push M i) (sq M) (veq M) (veq M).
+lemma vlift_comp (M): ∀i. compatible_3 … (vlift M i) (sq M) (veq M) (veq M).
 #m #i #d1 #d2 #Hd12 #lv1 #lv2 #HLv12 #j
 elim (lt_or_eq_or_gt j i) #Hij destruct
-[ >(push_lt … Hij) >(push_lt … Hij) //
-| >(push_eq …) >(push_eq …) //
-| >(push_gt … Hij) >(push_gt … Hij) //
+[ >vlift_lt // >vlift_lt //
+| >vlift_eq >vlift_eq //
+| >vlift_gt // >vlift_gt //
 ]
-qed.
+qed-.
 
-(* Inversion lemmas with evaluation push *************************************)
-
-axiom veq_inv_push_sn: ∀M,lv1,y2,d1,i. ⫯[i←d1]lv1 ≗{M} y2 →
-                       ∃∃lv2,d2. lv1 ≗ lv2 & d1 ≗ d2 & ⫯[i←d2]lv2 = y2.   
-(*
-#M #lv1 #y2 #d1 #i #H 
-*)
 (* Properies with term interpretation ***************************************) 
 
 lemma ti_comp_l (M): is_model M →
@@ -59,9 +75,14 @@ lemma ti_comp_l (M): is_model M →
 [ /4 width=3 by seq_trans, seq_sym, ms/
 | /4 width=5 by seq_sym, ml, mr/
 | /4 width=3 by seq_trans, seq_sym, mg/
-| /5 width=5 by push_comp, seq_sym, md, mr/
-| /5 width=1 by push_comp, mi, mq/
+| /5 width=5 by vlift_comp, seq_sym, md, mr/
+| /5 width=1 by vlift_comp, mi, mq/
 | /4 width=5 by seq_sym, ma, mc, mr/
 | /4 width=5 by seq_sym, me, mr/
 ]
 qed.
+
+lemma ti_ext_l (M): is_model M →
+                    ∀T,gv,lv1,lv2. lv1 ≐ lv2 →
+                    ⟦T⟧[gv, lv1] ≗{M} ⟦T⟧[gv, lv2].
+/3 width=1 by ti_comp_l, ext_veq/ qed.