update in static_2 and app_2

[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 905b1a33650f710a58d9f301a01e099aa5086809..dc83b79b1ac1d22edb22635bb5aafd0a14a02ee0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/apps_2/models/veq_lifts.ma
+++ b/matita/matita/contribs/lambdadelta/apps_2/models/veq_lifts.ma
@@ -20,42 +20,51 @@ include "apps_2/models/veq.ma".
 
 (* 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 #m #Hm #lv #d destruct
-  @(mr … H1M) [4,5: @(seq_sym … H1M) @(ml … H1M) |1,2: skip ]
+fact lifts_fwd_vlift_aux (M): is_model M → is_extensional M →
+                              ∀f,T1,T2. ⬆*[f] T1 ≘ T2 → ∀m. 𝐁❴m,1❵ = f →
+                              ∀gv,lv,d. ⟦T1⟧[gv, lv] ≗{M} ⟦T2⟧[gv, ⫯[m←d]lv].
+#M #H1M #H2M #f #T1 #T2 #H elim H -f -T1 -T2
+[ #f #s #m #Hf #gv #lv #d
+  @(mq … H1M) [4,5: /3 width=2 by seq_sym, ms/ |1,2: skip ]
+  /2 width=1 by mr/
+| #f #i1 #i2 #Hi12 #m #Hm #gv #lv #d destruct
+  @(mq … H1M) [4,5: /3 width=2 by seq_sym, ml/ |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/
+    >vlift_lt /2 width=1 by mr/
   | lapply (at_basic_inv_ge … Hi12) -Hi12 // #H destruct
-    >vlift_gt /2 width=1 by mq, le_S_S/
+    >vlift_gt /2 width=1 by mr, le_S_S/
   ]
-| /4 width=3 by seq_trans, seq_sym, mg/
-| #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 ]
+| #f #l #m #Hf #gv #lv #d
+  @(mq … H1M) [4,5: /3 width=2 by seq_sym, mg/ |1,2: skip ]
+  /2 width=1 by mr/
+| #f #p * #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #m #Hm #gv #lv #d destruct
+  [ @(mq … H1M) [4,5: /3 width=2 by seq_sym, md/ |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 (↑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 ]
+    [3: @ti_comp // | skip ]
+    [1,2: /2 width=2 by veq_refl/ ]
+    [2: @(vlift_comp … H1M) | skip ]
+    [1,2: /2 width=2 by/ |3,4: /2 width=2 by veq_refl/ ] -IHV
+    @(seq_trans … H1M)
+    [3: @ti_comp // | skip ]
+    [1,2: /2 width=2 by veq_refl/ ]
+    [2: @veq_sym // @vlift_swap // | skip ]
+    /2 width=1 by/
+  | @mx // [ /2 width=1 by/ ] -IHV #d0
+    @(seq_trans … H1M)
+    [3: @ti_comp // | skip ]
+    [1,2: /2 width=2 by veq_refl/ ]
+    [2: @veq_sym // @vlift_swap // | skip ]
     /2 width=1 by/
   ]
-| #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/
+| #f * #V1 #v2 #T1 #T2 #_ #_ #IHV #IHT #m #Hm #gv #lv #d
+  [ /4 width=5 by seq_sym, ma, mp, mq/
+  | /4 width=5 by seq_sym, me, mq/
   ]
 ]
 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].
+                                   ∀lv,d. ⟦T1⟧[gv, lv] ≗{M} ⟦T2⟧[gv, ⫯[0←d]lv].
 /2 width=3 by lifts_fwd_vlift_aux/ qed-.