+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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_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:
- \forall (k: K).(\forall (i: nat).(\forall (j: nat).(eq nat (s k (plus i j))
-(plus (s k i) j))))
-\def
- \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(\forall (j:
-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:
- \forall (k: K).(\forall (i: nat).(\forall (j: nat).(eq nat (s k (plus i j))
-(plus i (s k j)))))
-\def
- \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(\forall (j:
-nat).(eq nat (s k0 (plus i j)) (plus i (s k0 j)))))) (\lambda (_: B).(\lambda
-(i: nat).(\lambda (j: nat).(eq_ind_r nat (plus i (S j)) (\lambda (n: nat).(eq
-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:
- \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
- \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(\forall (j:
-nat).((le j i) \to (eq nat (s k0 (minus i j)) (minus (s k0 i) j))))))
-(\lambda (_: B).(\lambda (i: nat).(\lambda (j: nat).(\lambda (H: (le j
-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:
- \forall (k: K).(\forall (i: nat).(\forall (j: nat).(eq nat (minus (s k i) (s
-k j)) (minus i j))))
-\def
- \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(\forall (j:
-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:
- \forall (k: K).(\forall (i: nat).(\forall (j: nat).((le i j) \to (le (s k i)
-(s k j)))))
-\def
- \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(\forall (j:
-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:
- \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 *)
-
-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:
- \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 *)
-
-theorem 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:
- \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 *)
-
projects / helm.git / blobdiff