update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_1/s/props.ma b/matita/matita/contribs/lambdadelta/basic_1/s/props.ma
index 3cb4fbd741a230babdff2138ceabd076ed404d68..75318f07a90a2c624953e48ce9d9d4ed415948ed 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/s/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/s/props.ma
@@ -14,20 +14,17 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/s/defs.ma".
+include "basic_1/s/defs.ma".
 
-theorem s_S:
+lemma s_S:
  \forall (k: K).(\forall (i: nat).(eq nat (s k (S i)) (S (s k i))))
 \def
  \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(eq nat (s k0 (S 
 i)) (S (s k0 i))))) (\lambda (b: B).(\lambda (i: nat).(refl_equal nat (S (s 
 (Bind b) i))))) (\lambda (f: F).(\lambda (i: nat).(refl_equal nat (S (s (Flat 
 f) i))))) k).
-(* COMMENTS
-Initial nodes: 65
-END *)
 
-theorem s_plus:
+lemma s_plus:
  \forall (k: K).(\forall (i: nat).(\forall (j: nat).(eq nat (s k (plus i j)) 
 (plus (s k i) j))))
 \def
@@ -36,11 +33,8 @@ nat).(eq nat (s k0 (plus i j)) (plus (s k0 i) j))))) (\lambda (b: B).(\lambda
 (i: nat).(\lambda (j: nat).(refl_equal nat (plus (s (Bind b) i) j))))) 
 (\lambda (f: F).(\lambda (i: nat).(\lambda (j: nat).(refl_equal nat (plus (s 
 (Flat f) i) j))))) k).
-(* COMMENTS
-Initial nodes: 79
-END *)
 
-theorem s_plus_sym:
+lemma s_plus_sym:
  \forall (k: K).(\forall (i: nat).(\forall (j: nat).(eq nat (s k (plus i j)) 
 (plus i (s k j)))))
 \def
@@ -50,11 +44,8 @@ nat).(eq nat (s k0 (plus i j)) (plus i (s k0 j)))))) (\lambda (_: B).(\lambda
 nat n (plus i (S j)))) (refl_equal nat (plus i (S j))) (S (plus i j)) 
 (plus_n_Sm i j))))) (\lambda (f: F).(\lambda (i: nat).(\lambda (j: 
 nat).(refl_equal nat (plus i (s (Flat f) j)))))) k).
-(* COMMENTS
-Initial nodes: 117
-END *)
 
-theorem s_minus:
+lemma s_minus:
  \forall (k: K).(\forall (i: nat).(\forall (j: nat).((le j i) \to (eq nat (s 
 k (minus i j)) (minus (s k i) j)))))
 \def
@@ -65,11 +56,8 @@ i)).(eq_ind_r nat (minus (S i) j) (\lambda (n: nat).(eq nat n (minus (S i)
 j))) (refl_equal nat (minus (S i) j)) (S (minus i j)) (minus_Sn_m i j H)))))) 
 (\lambda (f: F).(\lambda (i: nat).(\lambda (j: nat).(\lambda (_: (le j 
 i)).(refl_equal nat (minus (s (Flat f) i) j)))))) k).
-(* COMMENTS
-Initial nodes: 137
-END *)
 
-theorem minus_s_s:
+lemma minus_s_s:
  \forall (k: K).(\forall (i: nat).(\forall (j: nat).(eq nat (minus (s k i) (s 
 k j)) (minus i j))))
 \def
@@ -78,11 +66,8 @@ nat).(eq nat (minus (s k0 i) (s k0 j)) (minus i j))))) (\lambda (_:
 B).(\lambda (i: nat).(\lambda (j: nat).(refl_equal nat (minus i j))))) 
 (\lambda (_: F).(\lambda (i: nat).(\lambda (j: nat).(refl_equal nat (minus i 
 j))))) k).
-(* COMMENTS
-Initial nodes: 67
-END *)
 
-theorem s_le:
+lemma s_le:
  \forall (k: K).(\forall (i: nat).(\forall (j: nat).((le i j) \to (le (s k i) 
 (s k j)))))
 \def
@@ -90,62 +75,35 @@ theorem s_le:
 nat).((le i j) \to (le (s k0 i) (s k0 j)))))) (\lambda (_: B).(\lambda (i: 
 nat).(\lambda (j: nat).(\lambda (H: (le i j)).(le_n_S i j H))))) (\lambda (_: 
 F).(\lambda (i: nat).(\lambda (j: nat).(\lambda (H: (le i j)).H)))) k).
-(* COMMENTS
-Initial nodes: 65
-END *)
 
-theorem s_lt:
+lemma s_lt:
  \forall (k: K).(\forall (i: nat).(\forall (j: nat).((lt i j) \to (lt (s k i) 
 (s k j)))))
 \def
  \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(\forall (j: 
 nat).((lt i j) \to (lt (s k0 i) (s k0 j)))))) (\lambda (_: B).(\lambda (i: 
-nat).(\lambda (j: nat).(\lambda (H: (lt i j)).(le_n_S (S i) j H))))) (\lambda 
-(_: F).(\lambda (i: nat).(\lambda (j: nat).(\lambda (H: (lt i j)).H)))) k).
-(* COMMENTS
-Initial nodes: 67
-END *)
+nat).(\lambda (j: nat).(\lambda (H: (lt i j)).(lt_n_S i j H))))) (\lambda (_: 
+F).(\lambda (i: nat).(\lambda (j: nat).(\lambda (H: (lt i j)).H)))) k).
 
-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).(K_ind (\lambda (k0: K).(\forall (i: nat).(\forall (j: 
-nat).((eq nat (s k0 i) (s k0 j)) \to (eq nat i j))))) (\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))))) (\lambda (f: F).(\lambda (i: nat).(\lambda 
-(j: nat).(\lambda (H: (eq nat (s (Flat f) i) (s (Flat f) j))).H)))) k).
-(* COMMENTS
-Initial nodes: 97
-END *)
-
-theorem s_inc:
+lemma s_inc:
  \forall (k: K).(\forall (i: nat).(le i (s k i)))
 \def
  \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(le i (s k0 i)))) 
-(\lambda (b: B).(\lambda (i: nat).(le_S_n i (s (Bind b) i) (le_S (S i) (s 
-(Bind b) i) (le_n (s (Bind b) i)))))) (\lambda (f: F).(\lambda (i: nat).(le_n 
-(s (Flat f) i)))) k).
-(* COMMENTS
-Initial nodes: 73
-END *)
+(\lambda (b: B).(\lambda (i: nat).(le_S_n i (s (Bind b) i) (le_S_n (S i) (S 
+(s (Bind b) i)) (le_S_n (S (S i)) (S (S (s (Bind b) i))) (le_S (S (S (S i))) 
+(S (S (s (Bind b) i))) (le_n (S (S (s (Bind b) i)))))))))) (\lambda (f: 
+F).(\lambda (i: nat).(le_n (s (Flat f) i)))) k).
 
-theorem s_arith0:
+lemma s_arith0:
  \forall (k: K).(\forall (i: nat).(eq nat (minus (s k i) (s k O)) i))
 \def
  \lambda (k: K).(\lambda (i: nat).(eq_ind_r nat (minus i O) (\lambda (n: 
 nat).(eq nat n i)) (eq_ind nat i (\lambda (n: nat).(eq nat n i)) (refl_equal 
 nat i) (minus i O) (minus_n_O i)) (minus (s k i) (s k O)) (minus_s_s k i O))).
-(* COMMENTS
-Initial nodes: 77
-END *)
 
-theorem s_arith1:
+lemma s_arith1:
  \forall (b: B).(\forall (i: nat).(eq nat (minus (s (Bind b) i) (S O)) i))
 \def
  \lambda (_: B).(\lambda (i: nat).(eq_ind nat i (\lambda (n: nat).(eq nat n 
 i)) (refl_equal nat i) (minus i O) (minus_n_O i))).
-(* COMMENTS
-Initial nodes: 35
-END *)