X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2Fr%2Fprops.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2Fr%2Fprops.ma;h=0000000000000000000000000000000000000000;hb=d2545ffd201b1aa49887313791386add78fa8603;hp=6dc07a0e181260407f027d8dfc1164f51b1f0a9c;hpb=57ae1762497a5f3ea75740e2908e04adb8642cc2;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_1/r/props.ma b/matita/matita/contribs/lambdadelta/basic_1/r/props.ma deleted file mode 100644 index 6dc07a0e1..000000000 --- a/matita/matita/contribs/lambdadelta/basic_1/r/props.ma +++ /dev/null @@ -1,153 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||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". - -lemma 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). - -lemma 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). - -lemma 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). - -lemma 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)))). - -lemma 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). - -lemma 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). - -lemma 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))). - -lemma 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)))). - -lemma r_arith2: - \forall (k: K).(\forall (i: nat).(\forall (j: nat).((le (S i) (s k j)) \to -(le (r k i) j)))) -\def - \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(\forall (j: -nat).((le (S i) (s k0 j)) \to (le (r k0 i) j))))) (\lambda (_: B).(\lambda -(i: nat).(\lambda (j: nat).(\lambda (H: (le (S i) (S j))).(let H_y \def -(le_S_n i j H) in H_y))))) (\lambda (_: F).(\lambda (i: nat).(\lambda (j: -nat).(\lambda (H: (le (S i) j)).H)))) k). - -lemma r_arith3: - \forall (k: K).(\forall (i: nat).(\forall (j: nat).((le (s k j) (S i)) \to -(le j (r k i))))) -\def - \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(\forall (j: -nat).((le (s k0 j) (S i)) \to (le j (r k0 i)))))) (\lambda (_: B).(\lambda -(i: nat).(\lambda (j: nat).(\lambda (H: (le (S j) (S i))).(let H_y \def -(le_S_n j i H) in H_y))))) (\lambda (_: F).(\lambda (i: nat).(\lambda (j: -nat).(\lambda (H: (le j (S i))).H)))) k). - -lemma r_arith4: - \forall (k: K).(\forall (i: nat).(\forall (j: nat).(eq nat (minus (S i) (s k -j)) (minus (r k i) j)))) -\def - \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(\forall (j: -nat).(eq nat (minus (S i) (s k0 j)) (minus (r k0 i) j))))) (\lambda (b: -B).(\lambda (i: nat).(\lambda (j: nat).(refl_equal nat (minus (r (Bind b) i) -j))))) (\lambda (f: F).(\lambda (i: nat).(\lambda (j: nat).(refl_equal nat -(minus (r (Flat f) i) j))))) k). - -lemma r_arith5: - \forall (k: K).(\forall (i: nat).(\forall (j: nat).((lt (s k j) (S i)) \to -(lt j (r k i))))) -\def - \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(\forall (j: -nat).((lt (s k0 j) (S i)) \to (lt j (r k0 i)))))) (\lambda (_: B).(\lambda -(i: nat).(\lambda (j: nat).(\lambda (H: (lt (S j) (S i))).(lt_S_n j i H))))) -(\lambda (_: F).(\lambda (i: nat).(\lambda (j: nat).(\lambda (H: (lt j (S -i))).H)))) k). - -lemma r_arith6: - \forall (k: K).(\forall (i: nat).(\forall (j: nat).(eq nat (minus (r k i) (S -j)) (minus i (s k j))))) -\def - \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(\forall (j: -nat).(eq nat (minus (r k0 i) (S j)) (minus i (s k0 j)))))) (\lambda (b: -B).(\lambda (i: nat).(\lambda (j: nat).(refl_equal nat (minus i (s (Bind b) -j)))))) (\lambda (f: F).(\lambda (i: nat).(\lambda (j: nat).(refl_equal nat -(minus i (s (Flat f) j)))))) k). - -lemma r_arith7: - \forall (k: K).(\forall (i: nat).(\forall (j: nat).((eq nat (S i) (s k j)) -\to (eq nat (r k i) j)))) -\def - \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (i: nat).(\forall (j: -nat).((eq nat (S i) (s k0 j)) \to (eq nat (r k0 i) j))))) (\lambda (_: -B).(\lambda (i: nat).(\lambda (j: nat).(\lambda (H: (eq nat (S i) (S -j))).(eq_add_S i j H))))) (\lambda (_: F).(\lambda (i: nat).(\lambda (j: -nat).(\lambda (H: (eq nat (S i) j)).H)))) k). -