X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matitaB%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FBasic-1%2Fr%2Fprops.ma;fp=matitaB%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FBasic-1%2Fr%2Fprops.ma;h=0000000000000000000000000000000000000000;hb=88a68a9c334646bc17314d5327cd3b790202acd6;hp=0815aaf5e8f042a0c78610639874b09323c36dc9;hpb=4904accd80118cb8126e308ae098d87f8651c9f4;p=helm.git

diff --git a/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/r/props.ma b/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/r/props.ma
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--- a/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/r/props.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 "Basic-1/r/defs.ma".
-
-include "Basic-1/s/defs.ma".
-
-theorem r_S:
- \forall (k: K).(\forall (i: nat).(eq nat (r k (S i)) (S (r k i))))
-\def
- \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(eq nat (r k0 (S 
-i)) (S (r k0 i))))) (\lambda (b: B).(\lambda (i: nat).(refl_equal nat (S (r 
-(Bind b) i))))) (\lambda (f: F).(\lambda (i: nat).(refl_equal nat (S (r (Flat 
-f) i))))) k).
-(* COMMENTS
-Initial nodes: 65
-END *)
-
-theorem r_plus:
- \forall (k: K).(\forall (i: nat).(\forall (j: nat).(eq nat (r k (plus i j)) 
-(plus (r k i) j))))
-\def
- \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(\forall (j: 
-nat).(eq nat (r k0 (plus i j)) (plus (r k0 i) j))))) (\lambda (b: B).(\lambda 
-(i: nat).(\lambda (j: nat).(refl_equal nat (plus (r (Bind b) i) j))))) 
-(\lambda (f: F).(\lambda (i: nat).(\lambda (j: nat).(refl_equal nat (plus (r 
-(Flat f) i) j))))) k).
-(* COMMENTS
-Initial nodes: 79
-END *)
-
-theorem r_plus_sym:
- \forall (k: K).(\forall (i: nat).(\forall (j: nat).(eq nat (r k (plus i j)) 
-(plus i (r k j)))))
-\def
- \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(\forall (j: 
-nat).(eq nat (r k0 (plus i j)) (plus i (r k0 j)))))) (\lambda (_: B).(\lambda 
-(i: nat).(\lambda (j: nat).(refl_equal nat (plus i j))))) (\lambda (_: 
-F).(\lambda (i: nat).(\lambda (j: nat).(plus_n_Sm i j)))) k).
-(* COMMENTS
-Initial nodes: 63
-END *)
-
-theorem r_minus:
- \forall (i: nat).(\forall (n: nat).((lt n i) \to (\forall (k: K).(eq nat 
-(minus (r k i) (S n)) (r k (minus i (S n)))))))
-\def
- \lambda (i: nat).(\lambda (n: nat).(\lambda (H: (lt n i)).(\lambda (k: 
-K).(K_ind (\lambda (k0: K).(eq nat (minus (r k0 i) (S n)) (r k0 (minus i (S 
-n))))) (\lambda (_: B).(refl_equal nat (minus i (S n)))) (\lambda (_: 
-F).(minus_x_Sy i n H)) k)))).
-(* COMMENTS
-Initial nodes: 69
-END *)
-
-theorem r_dis:
- \forall (k: K).(\forall (P: Prop).(((((\forall (i: nat).(eq nat (r k i) i))) 
-\to P)) \to (((((\forall (i: nat).(eq nat (r k i) (S i)))) \to P)) \to P)))
-\def
- \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (P: Prop).(((((\forall (i: 
-nat).(eq nat (r k0 i) i))) \to P)) \to (((((\forall (i: nat).(eq nat (r k0 i) 
-(S i)))) \to P)) \to P)))) (\lambda (b: B).(\lambda (P: Prop).(\lambda (H: 
-((((\forall (i: nat).(eq nat (r (Bind b) i) i))) \to P))).(\lambda (_: 
-((((\forall (i: nat).(eq nat (r (Bind b) i) (S i)))) \to P))).(H (\lambda (i: 
-nat).(refl_equal nat i))))))) (\lambda (f: F).(\lambda (P: Prop).(\lambda (_: 
-((((\forall (i: nat).(eq nat (r (Flat f) i) i))) \to P))).(\lambda (H0: 
-((((\forall (i: nat).(eq nat (r (Flat f) i) (S i)))) \to P))).(H0 (\lambda 
-(i: nat).(refl_equal nat (S i)))))))) k).
-(* COMMENTS
-Initial nodes: 151
-END *)
-
-theorem s_r:
- \forall (k: K).(\forall (i: nat).(eq nat (s k (r k i)) (S i)))
-\def
- \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(eq nat (s k0 (r k0 
-i)) (S i)))) (\lambda (_: B).(\lambda (i: nat).(refl_equal nat (S i)))) 
-(\lambda (_: F).(\lambda (i: nat).(refl_equal nat (S i)))) k).
-(* COMMENTS
-Initial nodes: 51
-END *)
-
-theorem r_arith0:
- \forall (k: K).(\forall (i: nat).(eq nat (minus (r k (S i)) (S O)) (r k i)))
-\def
- \lambda (k: K).(\lambda (i: nat).(eq_ind_r nat (S (r k i)) (\lambda (n: 
-nat).(eq nat (minus n (S O)) (r k i))) (eq_ind_r nat (r k i) (\lambda (n: 
-nat).(eq nat n (r k i))) (refl_equal nat (r k i)) (minus (S (r k i)) (S O)) 
-(minus_Sx_SO (r k i))) (r k (S i)) (r_S k i))).
-(* COMMENTS
-Initial nodes: 105
-END *)
-
-theorem r_arith1:
- \forall (k: K).(\forall (i: nat).(\forall (j: nat).(eq nat (minus (r k (S 
-i)) (S j)) (minus (r k i) j))))
-\def
- \lambda (k: K).(\lambda (i: nat).(\lambda (j: nat).(eq_ind_r nat (S (r k i)) 
-(\lambda (n: nat).(eq nat (minus n (S j)) (minus (r k i) j))) (refl_equal nat 
-(minus (r k i) j)) (r k (S i)) (r_S k i)))).
-(* COMMENTS
-Initial nodes: 69
-END *)
-