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diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csubt/ty3.ma b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csubt/ty3.ma
new file mode 100644
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+++ b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csubt/ty3.ma
@@ -0,0 +1,99 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/csubt/ty3".
+
+include "csubt/pc3.ma".
+
+include "csubt/props.ma".
+
+theorem csubt_ty3:
+ \forall (g: G).(\forall (c1: C).(\forall (t1: T).(\forall (t2: T).((ty3 g c1 
+t1 t2) \to (\forall (c2: C).((csubt g c1 c2) \to (ty3 g c2 t1 t2)))))))
+\def
+ \lambda (g: G).(\lambda (c1: C).(\lambda (t1: T).(\lambda (t2: T).(\lambda 
+(H: (ty3 g c1 t1 t2)).(ty3_ind g (\lambda (c: C).(\lambda (t: T).(\lambda 
+(t0: T).(\forall (c2: C).((csubt g c c2) \to (ty3 g c2 t t0)))))) (\lambda 
+(c: C).(\lambda (t0: T).(\lambda (t: T).(\lambda (_: (ty3 g c t0 t)).(\lambda 
+(H1: ((\forall (c2: C).((csubt g c c2) \to (ty3 g c2 t0 t))))).(\lambda (u: 
+T).(\lambda (t3: T).(\lambda (_: (ty3 g c u t3)).(\lambda (H3: ((\forall (c2: 
+C).((csubt g c c2) \to (ty3 g c2 u t3))))).(\lambda (H4: (pc3 c t3 
+t0)).(\lambda (c2: C).(\lambda (H5: (csubt g c c2)).(ty3_conv g c2 t0 t (H1 
+c2 H5) u t3 (H3 c2 H5) (csubt_pc3 g c t3 t0 H4 c2 H5)))))))))))))) (\lambda 
+(c: C).(\lambda (m: nat).(\lambda (c2: C).(\lambda (_: (csubt g c 
+c2)).(ty3_sort g c2 m))))) (\lambda (n: nat).(\lambda (c: C).(\lambda (d: 
+C).(\lambda (u: T).(\lambda (H0: (getl n c (CHead d (Bind Abbr) u))).(\lambda 
+(t: T).(\lambda (_: (ty3 g d u t)).(\lambda (H2: ((\forall (c2: C).((csubt g 
+d c2) \to (ty3 g c2 u t))))).(\lambda (c2: C).(\lambda (H3: (csubt g c 
+c2)).(let H4 \def (csubt_getl_abbr g c d u n H0 c2 H3) in (ex2_ind C (\lambda 
+(d2: C).(csubt g d d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abbr) 
+u))) (ty3 g c2 (TLRef n) (lift (S n) O t)) (\lambda (x: C).(\lambda (H5: 
+(csubt g d x)).(\lambda (H6: (getl n c2 (CHead x (Bind Abbr) u))).(ty3_abbr g 
+n c2 x u H6 t (H2 x H5))))) H4)))))))))))) (\lambda (n: nat).(\lambda (c: 
+C).(\lambda (d: C).(\lambda (u: T).(\lambda (H0: (getl n c (CHead d (Bind 
+Abst) u))).(\lambda (t: T).(\lambda (_: (ty3 g d u t)).(\lambda (H2: 
+((\forall (c2: C).((csubt g d c2) \to (ty3 g c2 u t))))).(\lambda (c2: 
+C).(\lambda (H3: (csubt g c c2)).(let H4 \def (csubt_getl_abst g c d u n H0 
+c2 H3) in (or_ind (ex2 C (\lambda (d2: C).(csubt g d d2)) (\lambda (d2: 
+C).(getl n c2 (CHead d2 (Bind Abst) u)))) (ex3_2 C T (\lambda (d2: 
+C).(\lambda (_: T).(csubt g d d2))) (\lambda (d2: C).(\lambda (u0: T).(getl n 
+c2 (CHead d2 (Bind Abbr) u0)))) (\lambda (d2: C).(\lambda (u0: T).(ty3 g d2 
+u0 u)))) (ty3 g c2 (TLRef n) (lift (S n) O u)) (\lambda (H5: (ex2 C (\lambda 
+(d2: C).(csubt g d d2)) (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abst) 
+u))))).(ex2_ind C (\lambda (d2: C).(csubt g d d2)) (\lambda (d2: C).(getl n 
+c2 (CHead d2 (Bind Abst) u))) (ty3 g c2 (TLRef n) (lift (S n) O u)) (\lambda 
+(x: C).(\lambda (H6: (csubt g d x)).(\lambda (H7: (getl n c2 (CHead x (Bind 
+Abst) u))).(ty3_abst g n c2 x u H7 t (H2 x H6))))) H5)) (\lambda (H5: (ex3_2 
+C T (\lambda (d2: C).(\lambda (_: T).(csubt g d d2))) (\lambda (d2: 
+C).(\lambda (u0: T).(getl n c2 (CHead d2 (Bind Abbr) u0)))) (\lambda (d2: 
+C).(\lambda (u0: T).(ty3 g d2 u0 u))))).(ex3_2_ind C T (\lambda (d2: 
+C).(\lambda (_: T).(csubt g d d2))) (\lambda (d2: C).(\lambda (u0: T).(getl n 
+c2 (CHead d2 (Bind Abbr) u0)))) (\lambda (d2: C).(\lambda (u0: T).(ty3 g d2 
+u0 u))) (ty3 g c2 (TLRef n) (lift (S n) O u)) (\lambda (x0: C).(\lambda (x1: 
+T).(\lambda (_: (csubt g d x0)).(\lambda (H7: (getl n c2 (CHead x0 (Bind 
+Abbr) x1))).(\lambda (H8: (ty3 g x0 x1 u)).(ty3_abbr g n c2 x0 x1 H7 u 
+H8)))))) H5)) H4)))))))))))) (\lambda (c: C).(\lambda (u: T).(\lambda (t: 
+T).(\lambda (_: (ty3 g c u t)).(\lambda (H1: ((\forall (c2: C).((csubt g c 
+c2) \to (ty3 g c2 u t))))).(\lambda (b: B).(\lambda (t0: T).(\lambda (t3: 
+T).(\lambda (_: (ty3 g (CHead c (Bind b) u) t0 t3)).(\lambda (H3: ((\forall 
+(c2: C).((csubt g (CHead c (Bind b) u) c2) \to (ty3 g c2 t0 t3))))).(\lambda 
+(t4: T).(\lambda (_: (ty3 g (CHead c (Bind b) u) t3 t4)).(\lambda (H5: 
+((\forall (c2: C).((csubt g (CHead c (Bind b) u) c2) \to (ty3 g c2 t3 
+t4))))).(\lambda (c2: C).(\lambda (H6: (csubt g c c2)).(ty3_bind g c2 u t (H1 
+c2 H6) b t0 t3 (H3 (CHead c2 (Bind b) u) (csubt_head g c c2 H6 (Bind b) u)) 
+t4 (H5 (CHead c2 (Bind b) u) (csubt_head g c c2 H6 (Bind b) 
+u)))))))))))))))))) (\lambda (c: C).(\lambda (w: T).(\lambda (u: T).(\lambda 
+(_: (ty3 g c w u)).(\lambda (H1: ((\forall (c2: C).((csubt g c c2) \to (ty3 g 
+c2 w u))))).(\lambda (v: T).(\lambda (t: T).(\lambda (_: (ty3 g c v (THead 
+(Bind Abst) u t))).(\lambda (H3: ((\forall (c2: C).((csubt g c c2) \to (ty3 g 
+c2 v (THead (Bind Abst) u t)))))).(\lambda (c2: C).(\lambda (H4: (csubt g c 
+c2)).(ty3_appl g c2 w u (H1 c2 H4) v t (H3 c2 H4))))))))))))) (\lambda (c: 
+C).(\lambda (t0: T).(\lambda (t3: T).(\lambda (_: (ty3 g c t0 t3)).(\lambda 
+(H1: ((\forall (c2: C).((csubt g c c2) \to (ty3 g c2 t0 t3))))).(\lambda (t4: 
+T).(\lambda (_: (ty3 g c t3 t4)).(\lambda (H3: ((\forall (c2: C).((csubt g c 
+c2) \to (ty3 g c2 t3 t4))))).(\lambda (c2: C).(\lambda (H4: (csubt g c 
+c2)).(ty3_cast g c2 t0 t3 (H1 c2 H4) t4 (H3 c2 H4)))))))))))) c1 t1 t2 H))))).
+
+theorem csubt_ty3_ld:
+ \forall (g: G).(\forall (c: C).(\forall (u: T).(\forall (v: T).((ty3 g c u 
+v) \to (\forall (t1: T).(\forall (t2: T).((ty3 g (CHead c (Bind Abst) v) t1 
+t2) \to (ty3 g (CHead c (Bind Abbr) u) t1 t2))))))))
+\def
+ \lambda (g: G).(\lambda (c: C).(\lambda (u: T).(\lambda (v: T).(\lambda (H: 
+(ty3 g c u v)).(\lambda (t1: T).(\lambda (t2: T).(\lambda (H0: (ty3 g (CHead 
+c (Bind Abst) v) t1 t2)).(csubt_ty3 g (CHead c (Bind Abst) v) t1 t2 H0 (CHead 
+c (Bind Abbr) u) (csubt_abst g c c (csubt_refl g c) u v H))))))))).
+