update in grond_2 and models

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

diff --git a/matita/matita/contribs/lambdadelta/apps_2/models/veq_lifts.ma b/matita/matita/contribs/lambdadelta/apps_2/models/veq_lifts.ma
index fce7d4281af06df358100efe8b446e9cf6602d79..80a103a4813faf6ca960a35f82142fbc22ee928f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/apps_2/models/veq_lifts.ma
+++ b/matita/matita/contribs/lambdadelta/apps_2/models/veq_lifts.ma
@@ -12,35 +12,50 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground_2/relocation/rtmap_basic.ma".
 include "basic_2/relocation/lifts.ma".
 include "apps_2/models/veq.ma".
 
 (* EVALUATION EQUIVALENCE  **************************************************)
 
-lemma pippo (M) (gv): is_model M → is_extensional M →
-                      ∀f,T1,T2. ⬆*[f] T1 ≘ T2 → ∀n. ⫯*[n] 𝐔❴1❵ = f →
-                      ∀lv,d. ⟦T1⟧[gv, lv] ≗{M} ⟦T2⟧[gv, ⫯[n←d]lv]. 
+(* Forward lemmas with generic relocation ***********************************)
+
+fact lifts_fwd_vlift_aux (M) (gv): is_model M → is_extensional M →
+                                   ∀f,T1,T2. ⬆*[f] T1 ≘ T2 → ∀m. 𝐁❴m,1❵ = f →
+                                   ∀lv,d. ⟦T1⟧[gv, lv] ≗{M} ⟦T2⟧[gv, ⫯[m←d]lv].
 #M #gv #H1M #H2M #f #T1 #T2 #H elim H -f -T1 -T2
 [ /4 width=3 by seq_trans, seq_sym, ms/
-| #f #i1 #i2 #Hi12 #n #Hn #lv #d
+| #f #i1 #i2 #Hi12 #m #Hm #lv #d destruct
   @(mr … H1M) [4,5: @(seq_sym … H1M) @(ml … H1M) |1,2: skip ]
+  elim (lt_or_ge i1 m) #Hi1
+  [ lapply (at_basic_inv_lt … Hi12) -Hi12 // #H destruct
+    >vlift_lt /2 width=1 by mq/
+  | lapply (at_basic_inv_ge … Hi12) -Hi12 // #H destruct
+    >vlift_gt /2 width=1 by mq, le_S_S/
+  ]
 | /4 width=3 by seq_trans, seq_sym, mg/
-| #f #p * #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #n #Hn #lv #d
+| #f #p * #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #m #Hm #lv #d destruct
   [ @(mr … H1M) [4,5: @(seq_sym … H1M) @(md … H1M) |1,2: skip ]
     @(seq_trans … H1M)
     [2: @(ti_comp_l … H1M) | skip ]
     [2: @(vlift_comp … lv lv) | skip ]
     [3: /2 width=1 by veq_refl/ ]
     [2: @(IHV … d) // | skip ]
-    @(seq_trans … H1M) [2: @(IHT … d) // | skip ]
+    @(seq_trans … H1M) [2: @(IHT (↑m) … d) // | skip ]
     /4 width=1 by seq_sym, ti_ext_l, vlift_swap/
   | @mx /2 width=1 by/ #d0 @(seq_trans … H1M)
     [3: @(seq_sym … H1M) @(ti_ext_l … H1M) | skip ]
     [2: @vlift_swap // | skip ]
     /2 width=1 by/
   ]
-| #f * #V1 #v2 #T1 #T2 #_ #_ #IHV #IHT #n #Hn #lv #d
+| #f * #V1 #v2 #T1 #T2 #_ #_ #IHV #IHT #m #Hm #lv #d
   [ /4 width=5 by seq_sym, ma, mc, mr/
   | /4 width=5 by seq_sym, me, mr/
   ]
-]  
+]
+qed-.
+
+lemma lifts_SO_fwd_vlift (M) (gv): is_model M → is_extensional M →
+                                   ∀T1,T2. ⬆*[1] T1 ≘ T2 →
+                                   ∀lv,d. ⟦T1⟧[gv, lv] ≗{M} ⟦T2⟧[gv, ⫯[d]lv].
+/2 width=3 by lifts_fwd_vlift_aux/ qed-.