update in groud_2 and models

[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 47d4a1b74a4238e3898c2e0ac4ff4a0469f4ab3a..e784d3b7a8148c05e71034929822171fbfb9af43 100644 (file)
--- a/matita/matita/contribs/lambdadelta/apps_2/models/veq.ma
+++ b/matita/matita/contribs/lambdadelta/apps_2/models/veq.ma
@@ -32,24 +32,51 @@ lemma veq_repl (M): is_model M →
                     replace_2 … (veq M) (veq M) (veq M).
 /2 width=5 by mr/ qed-.
 
+lemma veq_sym (M): is_model M → symmetric … (veq M).
+/3 width=5 by veq_repl, veq_refl/ qed-.
+
+lemma veq_trans (M): is_model M → Transitive … (veq M).
+/3 width=5 by veq_repl, veq_refl/ qed-.
+
+(* Properties with extebsional equivalence **********************************)
+
 lemma ext_veq (M): is_model M →
                    ∀lv1,lv2. lv1 ≐ lv2 → lv1 ≗{M} lv2.
 /2 width=1 by mq/ qed.
 
+lemma veq_repl_exteq (M): is_model M →
+                          replace_2 … (veq M) (exteq …) (exteq …).
+/2 width=5 by mr/ 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 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
-[ >(vlift_lt … Hij) >(vlift_lt … Hij) //
-| >(vlift_eq …) >(vlift_eq …) //
-| >(vlift_gt … Hij) >(vlift_gt … Hij) //
+[ >vlift_lt // >vlift_lt //
+| >vlift_eq >vlift_eq //
+| >vlift_gt // >vlift_gt //
 ]
-qed.
+qed-.
 
 (* Properies with term interpretation ***************************************) 
 
@@ -66,3 +93,8 @@ lemma ti_comp_l (M): is_model M →
 | /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.