- some improvements in the generation of terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / s / fwd.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/s/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1/s/fwd.ma
new file mode 100644 (file)
index 0000000..c9ab5db
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_1/s/fwd.ma
@@ -0,0 +1,51 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/s/defs.ma".
+
+theorem s_inj:
+ \forall (k: K).(\forall (i: nat).(\forall (j: nat).((eq nat (s k i) (s k j)) 
+\to (eq nat i j))))
+\def
+ \lambda (k: K).(let TMP_1 \def (\lambda (k0: K).(\forall (i: nat).(\forall 
+(j: nat).((eq nat (s k0 i) (s k0 j)) \to (eq nat i j))))) in (let TMP_2 \def 
+(\lambda (b: B).(\lambda (i: nat).(\lambda (j: nat).(\lambda (H: (eq nat (s 
+(Bind b) i) (s (Bind b) j))).(eq_add_S i j H))))) in (let TMP_3 \def (\lambda 
+(f: F).(\lambda (i: nat).(\lambda (j: nat).(\lambda (H: (eq nat (s (Flat f) 
+i) (s (Flat f) j))).H)))) in (K_ind TMP_1 TMP_2 TMP_3 k)))).
+
+theorem s_le_gen:
+ \forall (k: K).(\forall (i: nat).(\forall (j: nat).((le (s k i) (s k j)) \to 
+(le i j))))
+\def
+ \lambda (k: K).(let TMP_1 \def (\lambda (k0: K).(\forall (i: nat).(\forall 
+(j: nat).((le (s k0 i) (s k0 j)) \to (le i j))))) in (let TMP_2 \def (\lambda 
+(b: B).(\lambda (i: nat).(\lambda (j: nat).(\lambda (H: (le (s (Bind b) i) (s 
+(Bind b) j))).(le_S_n i j H))))) in (let TMP_3 \def (\lambda (f: F).(\lambda 
+(i: nat).(\lambda (j: nat).(\lambda (H: (le (s (Flat f) i) (s (Flat f) 
+j))).H)))) in (K_ind TMP_1 TMP_2 TMP_3 k)))).
+
+theorem s_lt_gen:
+ \forall (k: K).(\forall (i: nat).(\forall (j: nat).((lt (s k i) (s k j)) \to 
+(lt i j))))
+\def
+ \lambda (k: K).(let TMP_1 \def (\lambda (k0: K).(\forall (i: nat).(\forall 
+(j: nat).((lt (s k0 i) (s k0 j)) \to (lt i j))))) in (let TMP_3 \def (\lambda 
+(b: B).(\lambda (i: nat).(\lambda (j: nat).(\lambda (H: (lt (s (Bind b) i) (s 
+(Bind b) j))).(let TMP_2 \def (S i) in (le_S_n TMP_2 j H)))))) in (let TMP_4 
+\def (\lambda (f: F).(\lambda (i: nat).(\lambda (j: nat).(\lambda (H: (lt (s 
+(Flat f) i) (s (Flat f) j))).H)))) in (K_ind TMP_1 TMP_3 TMP_4 k)))).
+