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[helm.git] / matita / contribs / LAMBDA-TYPES / LambdaDelta-1 / getl / dec.ma

diff --git a/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/getl/dec.ma b/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/getl/dec.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 *********************)
+
+include "LambdaDelta-1/getl/props.ma".
+
+theorem getl_dec:
+ \forall (c: C).(\forall (i: nat).(or (ex_3 C B T (\lambda (e: C).(\lambda 
+(b: B).(\lambda (v: T).(getl i c (CHead e (Bind b) v)))))) (\forall (d: 
+C).((getl i c d) \to (\forall (P: Prop).P)))))
+\def
+ \lambda (c: C).(C_ind (\lambda (c0: C).(\forall (i: nat).(or (ex_3 C B T 
+(\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl i c0 (CHead e (Bind b) 
+v)))))) (\forall (d: C).((getl i c0 d) \to (\forall (P: Prop).P)))))) 
+(\lambda (n: nat).(\lambda (i: nat).(or_intror (ex_3 C B T (\lambda (e: 
+C).(\lambda (b: B).(\lambda (v: T).(getl i (CSort n) (CHead e (Bind b) 
+v)))))) (\forall (d: C).((getl i (CSort n) d) \to (\forall (P: Prop).P))) 
+(\lambda (d: C).(\lambda (H: (getl i (CSort n) d)).(\lambda (P: 
+Prop).(getl_gen_sort n i d H P))))))) (\lambda (c0: C).(\lambda (H: ((\forall 
+(i: nat).(or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: 
+T).(getl i c0 (CHead e (Bind b) v)))))) (\forall (d: C).((getl i c0 d) \to 
+(\forall (P: Prop).P))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (i: 
+nat).(nat_ind (\lambda (n: nat).(or (ex_3 C B T (\lambda (e: C).(\lambda (b: 
+B).(\lambda (v: T).(getl n (CHead c0 k t) (CHead e (Bind b) v)))))) (\forall 
+(d: C).((getl n (CHead c0 k t) d) \to (\forall (P: Prop).P))))) (K_ind 
+(\lambda (k0: K).(or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: 
+T).(getl O (CHead c0 k0 t) (CHead e (Bind b) v)))))) (\forall (d: C).((getl O 
+(CHead c0 k0 t) d) \to (\forall (P: Prop).P))))) (\lambda (b: B).(or_introl 
+(ex_3 C B T (\lambda (e: C).(\lambda (b0: B).(\lambda (v: T).(getl O (CHead 
+c0 (Bind b) t) (CHead e (Bind b0) v)))))) (\forall (d: C).((getl O (CHead c0 
+(Bind b) t) d) \to (\forall (P: Prop).P))) (ex_3_intro C B T (\lambda (e: 
+C).(\lambda (b0: B).(\lambda (v: T).(getl O (CHead c0 (Bind b) t) (CHead e 
+(Bind b0) v))))) c0 b t (getl_refl b c0 t)))) (\lambda (f: F).(let H_x \def 
+(H O) in (let H0 \def H_x in (or_ind (ex_3 C B T (\lambda (e: C).(\lambda (b: 
+B).(\lambda (v: T).(getl O c0 (CHead e (Bind b) v)))))) (\forall (d: 
+C).((getl O c0 d) \to (\forall (P: Prop).P))) (or (ex_3 C B T (\lambda (e: 
+C).(\lambda (b: B).(\lambda (v: T).(getl O (CHead c0 (Flat f) t) (CHead e 
+(Bind b) v)))))) (\forall (d: C).((getl O (CHead c0 (Flat f) t) d) \to 
+(\forall (P: Prop).P)))) (\lambda (H1: (ex_3 C B T (\lambda (e: C).(\lambda 
+(b: B).(\lambda (v: T).(getl O c0 (CHead e (Bind b) v))))))).(ex_3_ind C B T 
+(\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl O c0 (CHead e (Bind b) 
+v))))) (or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl 
+O (CHead c0 (Flat f) t) (CHead e (Bind b) v)))))) (\forall (d: C).((getl O 
+(CHead c0 (Flat f) t) d) \to (\forall (P: Prop).P)))) (\lambda (x0: 
+C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H2: (getl O c0 (CHead x0 (Bind 
+x1) x2))).(or_introl (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: 
+T).(getl O (CHead c0 (Flat f) t) (CHead e (Bind b) v)))))) (\forall (d: 
+C).((getl O (CHead c0 (Flat f) t) d) \to (\forall (P: Prop).P))) (ex_3_intro 
+C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl O (CHead c0 (Flat 
+f) t) (CHead e (Bind b) v))))) x0 x1 x2 (getl_flat c0 (CHead x0 (Bind x1) x2) 
+O H2 f t))))))) H1)) (\lambda (H1: ((\forall (d: C).((getl O c0 d) \to 
+(\forall (P: Prop).P))))).(or_intror (ex_3 C B T (\lambda (e: C).(\lambda (b: 
+B).(\lambda (v: T).(getl O (CHead c0 (Flat f) t) (CHead e (Bind b) v)))))) 
+(\forall (d: C).((getl O (CHead c0 (Flat f) t) d) \to (\forall (P: Prop).P))) 
+(\lambda (d: C).(\lambda (H2: (getl O (CHead c0 (Flat f) t) d)).(\lambda (P: 
+Prop).(H1 d (getl_intro O c0 d c0 (drop_refl c0) (clear_gen_flat f c0 d t 
+(getl_gen_O (CHead c0 (Flat f) t) d H2))) P)))))) H0)))) k) (\lambda (n: 
+nat).(\lambda (_: (or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda 
+(v: T).(getl n (CHead c0 k t) (CHead e (Bind b) v)))))) (\forall (d: 
+C).((getl n (CHead c0 k t) d) \to (\forall (P: Prop).P))))).(let H_x \def (H 
+(r k n)) in (let H1 \def H_x in (or_ind (ex_3 C B T (\lambda (e: C).(\lambda 
+(b: B).(\lambda (v: T).(getl (r k n) c0 (CHead e (Bind b) v)))))) (\forall 
+(d: C).((getl (r k n) c0 d) \to (\forall (P: Prop).P))) (or (ex_3 C B T 
+(\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl (S n) (CHead c0 k t) 
+(CHead e (Bind b) v)))))) (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to 
+(\forall (P: Prop).P)))) (\lambda (H2: (ex_3 C B T (\lambda (e: C).(\lambda 
+(b: B).(\lambda (v: T).(getl (r k n) c0 (CHead e (Bind b) v))))))).(ex_3_ind 
+C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl (r k n) c0 (CHead 
+e (Bind b) v))))) (or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda 
+(v: T).(getl (S n) (CHead c0 k t) (CHead e (Bind b) v)))))) (\forall (d: 
+C).((getl (S n) (CHead c0 k t) d) \to (\forall (P: Prop).P)))) (\lambda (x0: 
+C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H3: (getl (r k n) c0 (CHead x0 
+(Bind x1) x2))).(or_introl (ex_3 C B T (\lambda (e: C).(\lambda (b: 
+B).(\lambda (v: T).(getl (S n) (CHead c0 k t) (CHead e (Bind b) v)))))) 
+(\forall (d: C).((getl (S n) (CHead c0 k t) d) \to (\forall (P: Prop).P))) 
+(ex_3_intro C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl (S n) 
+(CHead c0 k t) (CHead e (Bind b) v))))) x0 x1 x2 (getl_head k n c0 (CHead x0 
+(Bind x1) x2) H3 t))))))) H2)) (\lambda (H2: ((\forall (d: C).((getl (r k n) 
+c0 d) \to (\forall (P: Prop).P))))).(or_intror (ex_3 C B T (\lambda (e: 
+C).(\lambda (b: B).(\lambda (v: T).(getl (S n) (CHead c0 k t) (CHead e (Bind 
+b) v)))))) (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to (\forall (P: 
+Prop).P))) (\lambda (d: C).(\lambda (H3: (getl (S n) (CHead c0 k t) 
+d)).(\lambda (P: Prop).(H2 d (getl_gen_S k c0 d t n H3) P)))))) H1))))) 
+i)))))) c).
+