X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2Faprem%2Ffwd.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2Faprem%2Ffwd.ma;h=0000000000000000000000000000000000000000;hb=d2545ffd201b1aa49887313791386add78fa8603;hp=3f415a4c1793019c81ecc2b64711547539198ff8;hpb=57ae1762497a5f3ea75740e2908e04adb8642cc2;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_1/aprem/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1/aprem/fwd.ma deleted file mode 100644 index 3f415a4c1..000000000 --- a/matita/matita/contribs/lambdadelta/basic_1/aprem/fwd.ma +++ /dev/null @@ -1,113 +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/aprem/defs.ma". - -implied rec lemma aprem_ind (P: (nat \to (A \to (A \to Prop)))) (f: (\forall -(a1: A).(\forall (a2: A).(P O (AHead a1 a2) a1)))) (f0: (\forall (a2: -A).(\forall (a: A).(\forall (i: nat).((aprem i a2 a) \to ((P i a2 a) \to -(\forall (a1: A).(P (S i) (AHead a1 a2) a)))))))) (n: nat) (a: A) (a0: A) -(a1: aprem n a a0) on a1: P n a a0 \def match a1 with [(aprem_zero a2 a3) -\Rightarrow (f a2 a3) | (aprem_succ a2 a3 i a4 a5) \Rightarrow (f0 a2 a3 i a4 -((aprem_ind P f f0) i a2 a3 a4) a5)]. - -lemma aprem_gen_sort: - \forall (x: A).(\forall (i: nat).(\forall (h: nat).(\forall (n: nat).((aprem -i (ASort h n) x) \to False)))) -\def - \lambda (x: A).(\lambda (i: nat).(\lambda (h: nat).(\lambda (n: -nat).(\lambda (H: (aprem i (ASort h n) x)).(insert_eq A (ASort h n) (\lambda -(a: A).(aprem i a x)) (\lambda (_: A).False) (\lambda (y: A).(\lambda (H0: -(aprem i y x)).(aprem_ind (\lambda (_: nat).(\lambda (a: A).(\lambda (_: -A).((eq A a (ASort h n)) \to False)))) (\lambda (a1: A).(\lambda (a2: -A).(\lambda (H1: (eq A (AHead a1 a2) (ASort h n))).(let H2 \def (eq_ind A -(AHead a1 a2) (\lambda (ee: A).(match ee with [(ASort _ _) \Rightarrow False -| (AHead _ _) \Rightarrow True])) I (ASort h n) H1) in (False_ind False -H2))))) (\lambda (a2: A).(\lambda (a: A).(\lambda (i0: nat).(\lambda (_: -(aprem i0 a2 a)).(\lambda (_: (((eq A a2 (ASort h n)) \to False))).(\lambda -(a1: A).(\lambda (H3: (eq A (AHead a1 a2) (ASort h n))).(let H4 \def (eq_ind -A (AHead a1 a2) (\lambda (ee: A).(match ee with [(ASort _ _) \Rightarrow -False | (AHead _ _) \Rightarrow True])) I (ASort h n) H3) in (False_ind False -H4))))))))) i y x H0))) H))))). - -lemma aprem_gen_head_O: - \forall (a1: A).(\forall (a2: A).(\forall (x: A).((aprem O (AHead a1 a2) x) -\to (eq A x a1)))) -\def - \lambda (a1: A).(\lambda (a2: A).(\lambda (x: A).(\lambda (H: (aprem O -(AHead a1 a2) x)).(insert_eq A (AHead a1 a2) (\lambda (a: A).(aprem O a x)) -(\lambda (_: A).(eq A x a1)) (\lambda (y: A).(\lambda (H0: (aprem O y -x)).(insert_eq nat O (\lambda (n: nat).(aprem n y x)) (\lambda (_: nat).((eq -A y (AHead a1 a2)) \to (eq A x a1))) (\lambda (y0: nat).(\lambda (H1: (aprem -y0 y x)).(aprem_ind (\lambda (n: nat).(\lambda (a: A).(\lambda (a0: A).((eq -nat n O) \to ((eq A a (AHead a1 a2)) \to (eq A a0 a1)))))) (\lambda (a0: -A).(\lambda (a3: A).(\lambda (_: (eq nat O O)).(\lambda (H3: (eq A (AHead a0 -a3) (AHead a1 a2))).(let H4 \def (f_equal A A (\lambda (e: A).(match e with -[(ASort _ _) \Rightarrow a0 | (AHead a _) \Rightarrow a])) (AHead a0 a3) -(AHead a1 a2) H3) in ((let H5 \def (f_equal A A (\lambda (e: A).(match e with -[(ASort _ _) \Rightarrow a3 | (AHead _ a) \Rightarrow a])) (AHead a0 a3) -(AHead a1 a2) H3) in (\lambda (H6: (eq A a0 a1)).H6)) H4)))))) (\lambda (a0: -A).(\lambda (a: A).(\lambda (i: nat).(\lambda (H2: (aprem i a0 a)).(\lambda -(H3: (((eq nat i O) \to ((eq A a0 (AHead a1 a2)) \to (eq A a a1))))).(\lambda -(a3: A).(\lambda (H4: (eq nat (S i) O)).(\lambda (H5: (eq A (AHead a3 a0) -(AHead a1 a2))).(let H6 \def (f_equal A A (\lambda (e: A).(match e with -[(ASort _ _) \Rightarrow a3 | (AHead a4 _) \Rightarrow a4])) (AHead a3 a0) -(AHead a1 a2) H5) in ((let H7 \def (f_equal A A (\lambda (e: A).(match e with -[(ASort _ _) \Rightarrow a0 | (AHead _ a4) \Rightarrow a4])) (AHead a3 a0) -(AHead a1 a2) H5) in (\lambda (_: (eq A a3 a1)).(let H9 \def (eq_ind A a0 -(\lambda (a4: A).((eq nat i O) \to ((eq A a4 (AHead a1 a2)) \to (eq A a -a1)))) H3 a2 H7) in (let H10 \def (eq_ind A a0 (\lambda (a4: A).(aprem i a4 -a)) H2 a2 H7) in (let H11 \def (eq_ind nat (S i) (\lambda (ee: nat).(match ee -with [O \Rightarrow False | (S _) \Rightarrow True])) I O H4) in (False_ind -(eq A a a1) H11)))))) H6)))))))))) y0 y x H1))) H0))) H)))). - -lemma aprem_gen_head_S: - \forall (a1: A).(\forall (a2: A).(\forall (x: A).(\forall (i: nat).((aprem -(S i) (AHead a1 a2) x) \to (aprem i a2 x))))) -\def - \lambda (a1: A).(\lambda (a2: A).(\lambda (x: A).(\lambda (i: nat).(\lambda -(H: (aprem (S i) (AHead a1 a2) x)).(insert_eq A (AHead a1 a2) (\lambda (a: -A).(aprem (S i) a x)) (\lambda (_: A).(aprem i a2 x)) (\lambda (y: -A).(\lambda (H0: (aprem (S i) y x)).(insert_eq nat (S i) (\lambda (n: -nat).(aprem n y x)) (\lambda (_: nat).((eq A y (AHead a1 a2)) \to (aprem i a2 -x))) (\lambda (y0: nat).(\lambda (H1: (aprem y0 y x)).(aprem_ind (\lambda (n: -nat).(\lambda (a: A).(\lambda (a0: A).((eq nat n (S i)) \to ((eq A a (AHead -a1 a2)) \to (aprem i a2 a0)))))) (\lambda (a0: A).(\lambda (a3: A).(\lambda -(H2: (eq nat O (S i))).(\lambda (H3: (eq A (AHead a0 a3) (AHead a1 a2))).(let -H4 \def (f_equal A A (\lambda (e: A).(match e with [(ASort _ _) \Rightarrow -a0 | (AHead a _) \Rightarrow a])) (AHead a0 a3) (AHead a1 a2) H3) in ((let H5 -\def (f_equal A A (\lambda (e: A).(match e with [(ASort _ _) \Rightarrow a3 | -(AHead _ a) \Rightarrow a])) (AHead a0 a3) (AHead a1 a2) H3) in (\lambda (H6: -(eq A a0 a1)).(eq_ind_r A a1 (\lambda (a: A).(aprem i a2 a)) (let H7 \def -(eq_ind nat O (\lambda (ee: nat).(match ee with [O \Rightarrow True | (S _) -\Rightarrow False])) I (S i) H2) in (False_ind (aprem i a2 a1) H7)) a0 H6))) -H4)))))) (\lambda (a0: A).(\lambda (a: A).(\lambda (i0: nat).(\lambda (H2: -(aprem i0 a0 a)).(\lambda (H3: (((eq nat i0 (S i)) \to ((eq A a0 (AHead a1 -a2)) \to (aprem i a2 a))))).(\lambda (a3: A).(\lambda (H4: (eq nat (S i0) (S -i))).(\lambda (H5: (eq A (AHead a3 a0) (AHead a1 a2))).(let H6 \def (f_equal -A A (\lambda (e: A).(match e with [(ASort _ _) \Rightarrow a3 | (AHead a4 _) -\Rightarrow a4])) (AHead a3 a0) (AHead a1 a2) H5) in ((let H7 \def (f_equal A -A (\lambda (e: A).(match e with [(ASort _ _) \Rightarrow a0 | (AHead _ a4) -\Rightarrow a4])) (AHead a3 a0) (AHead a1 a2) H5) in (\lambda (_: (eq A a3 -a1)).(let H9 \def (eq_ind A a0 (\lambda (a4: A).((eq nat i0 (S i)) \to ((eq A -a4 (AHead a1 a2)) \to (aprem i a2 a)))) H3 a2 H7) in (let H10 \def (eq_ind A -a0 (\lambda (a4: A).(aprem i0 a4 a)) H2 a2 H7) in (let H11 \def (f_equal nat -nat (\lambda (e: nat).(match e with [O \Rightarrow i0 | (S n) \Rightarrow -n])) (S i0) (S i) H4) in (let H12 \def (eq_ind nat i0 (\lambda (n: nat).((eq -nat n (S i)) \to ((eq A a2 (AHead a1 a2)) \to (aprem i a2 a)))) H9 i H11) in -(let H13 \def (eq_ind nat i0 (\lambda (n: nat).(aprem n a2 a)) H10 i H11) in -H13))))))) H6)))))))))) y0 y x H1))) H0))) H))))). -