From d6d612f97dba1555eed622e33e4106dcf5a9ffbd Mon Sep 17 00:00:00 2001 From: Ferruccio Guidi Date: Fri, 8 Sep 2006 09:42:26 +0000 Subject: [PATCH] removing unnecessary files --- .../Level-1/LambdaDelta/aplus/props.ma~ | 259 ------------------ .../LAMBDA-TYPES/Level-1/problems-1.ma~ | 107 -------- .../LAMBDA-TYPES/Level-1/problems-2.ma~ | 158 ----------- .../LAMBDA-TYPES/Level-1/problems.ma~ | 32 --- 4 files changed, 556 deletions(-) delete mode 100644 matita/contribs/LAMBDA-TYPES/Level-1/LambdaDelta/aplus/props.ma~ delete mode 100644 matita/contribs/LAMBDA-TYPES/Level-1/problems-1.ma~ delete mode 100644 matita/contribs/LAMBDA-TYPES/Level-1/problems-2.ma~ delete mode 100644 matita/contribs/LAMBDA-TYPES/Level-1/problems.ma~ diff --git a/matita/contribs/LAMBDA-TYPES/Level-1/LambdaDelta/aplus/props.ma~ b/matita/contribs/LAMBDA-TYPES/Level-1/LambdaDelta/aplus/props.ma~ deleted file mode 100644 index 9f259df79..000000000 --- a/matita/contribs/LAMBDA-TYPES/Level-1/LambdaDelta/aplus/props.ma~ +++ /dev/null @@ -1,259 +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 *********************) - -set "baseuri" "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/aplus/props". - -include "aplus/defs.ma". - -theorem aplus_reg_r: - \forall (g: G).(\forall (a1: A).(\forall (a2: A).(\forall (h1: nat).(\forall -(h2: nat).((eq A (aplus g a1 h1) (aplus g a2 h2)) \to (\forall (h: nat).(eq A -(aplus g a1 (plus h h1)) (aplus g a2 (plus h h2))))))))) -\def - \lambda (g: G).(\lambda (a1: A).(\lambda (a2: A).(\lambda (h1: nat).(\lambda -(h2: nat).(\lambda (H: (eq A (aplus g a1 h1) (aplus g a2 h2))).(\lambda (h: -nat).(nat_ind (\lambda (n: nat).(eq A (aplus g a1 (plus n h1)) (aplus g a2 -(plus n h2)))) H (\lambda (n: nat).(\lambda (H0: (eq A (aplus g a1 (plus n -h1)) (aplus g a2 (plus n h2)))).(sym_equal A (asucc g (aplus g a2 (plus n -h2))) (asucc g (aplus g a1 (plus n h1))) (sym_equal A (asucc g (aplus g a1 -(plus n h1))) (asucc g (aplus g a2 (plus n h2))) (sym_equal A (asucc g (aplus -g a2 (plus n h2))) (asucc g (aplus g a1 (plus n h1))) (f_equal2 G A A asucc g -g (aplus g a2 (plus n h2)) (aplus g a1 (plus n h1)) (refl_equal G g) (sym_eq -A (aplus g a1 (plus n h1)) (aplus g a2 (plus n h2)) H0))))))) h))))))). - -theorem aplus_assoc: - \forall (g: G).(\forall (a: A).(\forall (h1: nat).(\forall (h2: nat).(eq A -(aplus g (aplus g a h1) h2) (aplus g a (plus h1 h2)))))) -\def - \lambda (g: G).(\lambda (a: A).(\lambda (h1: nat).(nat_ind (\lambda (n: -nat).(\forall (h2: nat).(eq A (aplus g (aplus g a n) h2) (aplus g a (plus n -h2))))) (\lambda (h2: nat).(refl_equal A (aplus g a h2))) (\lambda (n: -nat).(\lambda (_: ((\forall (h2: nat).(eq A (aplus g (aplus g a n) h2) (aplus -g a (plus n h2)))))).(\lambda (h2: nat).(nat_ind (\lambda (n0: nat).(eq A -(aplus g (asucc g (aplus g a n)) n0) (asucc g (aplus g a (plus n n0))))) -(eq_ind nat n (\lambda (n0: nat).(eq A (asucc g (aplus g a n)) (asucc g -(aplus g a n0)))) (refl_equal A (asucc g (aplus g a n))) (plus n O) (plus_n_O -n)) (\lambda (n0: nat).(\lambda (H0: (eq A (aplus g (asucc g (aplus g a n)) -n0) (asucc g (aplus g a (plus n n0))))).(eq_ind nat (S (plus n n0)) (\lambda -(n1: nat).(eq A (asucc g (aplus g (asucc g (aplus g a n)) n0)) (asucc g -(aplus g a n1)))) (sym_equal A (asucc g (asucc g (aplus g a (plus n n0)))) -(asucc g (aplus g (asucc g (aplus g a n)) n0)) (sym_equal A (asucc g (aplus g -(asucc g (aplus g a n)) n0)) (asucc g (asucc g (aplus g a (plus n n0)))) -(sym_equal A (asucc g (asucc g (aplus g a (plus n n0)))) (asucc g (aplus g -(asucc g (aplus g a n)) n0)) (f_equal2 G A A asucc g g (asucc g (aplus g a -(plus n n0))) (aplus g (asucc g (aplus g a n)) n0) (refl_equal G g) (sym_eq A -(aplus g (asucc g (aplus g a n)) n0) (asucc g (aplus g a (plus n n0))) -H0))))) (plus n (S n0)) (plus_n_Sm n n0)))) h2)))) h1))). - -theorem aplus_asucc: - \forall (g: G).(\forall (h: nat).(\forall (a: A).(eq A (aplus g (asucc g a) -h) (asucc g (aplus g a h))))) -\def - \lambda (g: G).(\lambda (h: nat).(\lambda (a: A).(eq_ind_r A (aplus g a -(plus (S O) h)) (\lambda (a0: A).(eq A a0 (asucc g (aplus g a h)))) -(refl_equal A (asucc g (aplus g a h))) (aplus g (aplus g a (S O)) h) -(aplus_assoc g a (S O) h)))). - -theorem aplus_sort_O_S_simpl: - \forall (g: G).(\forall (n: nat).(\forall (k: nat).(eq A (aplus g (ASort O -n) (S k)) (aplus g (ASort O (next g n)) k)))) -\def - \lambda (g: G).(\lambda (n: nat).(\lambda (k: nat).(eq_ind A (aplus g (asucc -g (ASort O n)) k) (\lambda (a: A).(eq A a (aplus g (ASort O (next g n)) k))) -(refl_equal A (aplus g (ASort O (next g n)) k)) (asucc g (aplus g (ASort O n) -k)) (aplus_asucc g k (ASort O n))))). - -theorem aplus_sort_S_S_simpl: - \forall (g: G).(\forall (n: nat).(\forall (h: nat).(\forall (k: nat).(eq A -(aplus g (ASort (S h) n) (S k)) (aplus g (ASort h n) k))))) -\def - \lambda (g: G).(\lambda (n: nat).(\lambda (h: nat).(\lambda (k: nat).(eq_ind -A (aplus g (asucc g (ASort (S h) n)) k) (\lambda (a: A).(eq A a (aplus g -(ASort h n) k))) (refl_equal A (aplus g (ASort h n) k)) (asucc g (aplus g -(ASort (S h) n) k)) (aplus_asucc g k (ASort (S h) n)))))). - -alias id "next_plus_next" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/next_plus/props/next_plus_next.con". -alias id "next_plus" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/next_plus/defs/next_plus.con". -theorem aplus_asort_O_simpl: - \forall (g: G).(\forall (h: nat).(\forall (n: nat).(eq A (aplus g (ASort O -n) h) (ASort O (next_plus g n h))))) -\def - \lambda (g: G).(\lambda (h: nat).(nat_ind (\lambda (n: nat).(\forall (n0: -nat).(eq A (aplus g (ASort O n0) n) (ASort O (next_plus g n0 n))))) (\lambda -(n: nat).(refl_equal A (ASort O n))) (\lambda (n: nat).(\lambda (H: ((\forall -(n0: nat).(eq A (aplus g (ASort O n0) n) (ASort O (next_plus g n0 -n)))))).(\lambda (n0: nat).(eq_ind A (aplus g (asucc g (ASort O n0)) n) -(\lambda (a: A).(eq A a (ASort O (next g (next_plus g n0 n))))) (eq_ind nat -(next_plus g (next g n0) n) (\lambda (n1: nat).(eq A (aplus g (ASort O (next -g n0)) n) (ASort O n1))) (H (next g n0)) (next g (next_plus g n0 n)) -(next_plus_next g n0 n)) (asucc g (aplus g (ASort O n0) n)) (aplus_asucc g n -(ASort O n0)))))) h)). - -theorem aplus_asort_le_simpl: - \forall (g: G).(\forall (h: nat).(\forall (k: nat).(\forall (n: nat).((le h -k) \to (eq A (aplus g (ASort k n) h) (ASort (minus k h) n)))))) -\def - \lambda (g: G).(\lambda (h: nat).(nat_ind (\lambda (n: nat).(\forall (k: -nat).(\forall (n0: nat).((le n k) \to (eq A (aplus g (ASort k n0) n) (ASort -(minus k n) n0)))))) (\lambda (k: nat).(\lambda (n: nat).(\lambda (_: (le O -k)).(eq_ind nat k (\lambda (n0: nat).(eq A (ASort k n) (ASort n0 n))) -(refl_equal A (ASort k n)) (minus k O) (minus_n_O k))))) (\lambda (h0: -nat).(\lambda (H: ((\forall (k: nat).(\forall (n: nat).((le h0 k) \to (eq A -(aplus g (ASort k n) h0) (ASort (minus k h0) n))))))).(\lambda (k: -nat).(nat_ind (\lambda (n: nat).(\forall (n0: nat).((le (S h0) n) \to (eq A -(asucc g (aplus g (ASort n n0) h0)) (ASort (minus n (S h0)) n0))))) (\lambda -(n: nat).(\lambda (H0: (le (S h0) O)).(ex2_ind nat (\lambda (n0: nat).(eq nat -O (S n0))) (\lambda (n0: nat).(le h0 n0)) (eq A (asucc g (aplus g (ASort O n) -h0)) (ASort (minus O (S h0)) n)) (\lambda (x: nat).(\lambda (H1: (eq nat O (S -x))).(\lambda (_: (le h0 x)).(let H3 \def (eq_ind nat O (\lambda (ee: -nat).(match ee in nat return (\lambda (_: nat).Prop) with [O \Rightarrow True -| (S _) \Rightarrow False])) I (S x) H1) in (False_ind (eq A (asucc g (aplus -g (ASort O n) h0)) (ASort (minus O (S h0)) n)) H3))))) (le_gen_S h0 O H0)))) -(\lambda (n: nat).(\lambda (_: ((\forall (n0: nat).((le (S h0) n) \to (eq A -(asucc g (aplus g (ASort n n0) h0)) (ASort (minus n (S h0)) n0)))))).(\lambda -(n0: nat).(\lambda (H1: (le (S h0) (S n))).(eq_ind A (aplus g (asucc g (ASort -(S n) n0)) h0) (\lambda (a: A).(eq A a (ASort (minus (S n) (S h0)) n0))) (H n -n0 (le_S_n h0 n H1)) (asucc g (aplus g (ASort (S n) n0) h0)) (aplus_asucc g -h0 (ASort (S n) n0))))))) k)))) h)). - -alias id "minus_n_n" = "cic:/Coq/Arith/Minus/minus_n_n.con". -theorem aplus_asort_simpl: - \forall (g: G).(\forall (h: nat).(\forall (k: nat).(\forall (n: nat).(eq A -(aplus g (ASort k n) h) (ASort (minus k h) (next_plus g n (minus h k))))))) -\def - \lambda (g: G).(\lambda (h: nat).(\lambda (k: nat).(\lambda (n: -nat).(lt_le_e k h (eq A (aplus g (ASort k n) h) (ASort (minus k h) (next_plus -g n (minus h k)))) (\lambda (H: (lt k h)).(eq_ind_r nat (plus k (minus h k)) -(\lambda (n0: nat).(eq A (aplus g (ASort k n) n0) (ASort (minus k h) -(next_plus g n (minus h k))))) (eq_ind A (aplus g (aplus g (ASort k n) k) -(minus h k)) (\lambda (a: A).(eq A a (ASort (minus k h) (next_plus g n (minus -h k))))) (eq_ind_r A (ASort (minus k k) n) (\lambda (a: A).(eq A (aplus g a -(minus h k)) (ASort (minus k h) (next_plus g n (minus h k))))) (eq_ind nat O -(\lambda (n0: nat).(eq A (aplus g (ASort n0 n) (minus h k)) (ASort (minus k -h) (next_plus g n (minus h k))))) (eq_ind_r nat O (\lambda (n0: nat).(eq A -(aplus g (ASort O n) (minus h k)) (ASort n0 (next_plus g n (minus h k))))) -(aplus_asort_O_simpl g (minus h k) n) (minus k h) (O_minus k h (le_S_n k h -(le_S (S k) h H)))) (minus k k) (minus_n_n k)) (aplus g (ASort k n) k) -(aplus_asort_le_simpl g k k n (le_n k))) (aplus g (ASort k n) (plus k (minus -h k))) (aplus_assoc g (ASort k n) k (minus h k))) h (le_plus_minus k h -(le_S_n k h (le_S (S k) h H))))) (\lambda (H: (le h k)).(eq_ind_r A (ASort -(minus k h) n) (\lambda (a: A).(eq A a (ASort (minus k h) (next_plus g n -(minus h k))))) (eq_ind_r nat O (\lambda (n0: nat).(eq A (ASort (minus k h) -n) (ASort (minus k h) (next_plus g n n0)))) (refl_equal A (ASort (minus k h) -(next_plus g n O))) (minus h k) (O_minus h k H)) (aplus g (ASort k n) h) -(aplus_asort_le_simpl g h k n H))))))). - -theorem aplus_ahead_simpl: - \forall (g: G).(\forall (h: nat).(\forall (a1: A).(\forall (a2: A).(eq A -(aplus g (AHead a1 a2) h) (AHead a1 (aplus g a2 h)))))) -\def - \lambda (g: G).(\lambda (h: nat).(nat_ind (\lambda (n: nat).(\forall (a1: -A).(\forall (a2: A).(eq A (aplus g (AHead a1 a2) n) (AHead a1 (aplus g a2 -n)))))) (\lambda (a1: A).(\lambda (a2: A).(refl_equal A (AHead a1 a2)))) -(\lambda (n: nat).(\lambda (H: ((\forall (a1: A).(\forall (a2: A).(eq A -(aplus g (AHead a1 a2) n) (AHead a1 (aplus g a2 n))))))).(\lambda (a1: -A).(\lambda (a2: A).(eq_ind A (aplus g (asucc g (AHead a1 a2)) n) (\lambda -(a: A).(eq A a (AHead a1 (asucc g (aplus g a2 n))))) (eq_ind A (aplus g -(asucc g a2) n) (\lambda (a: A).(eq A (aplus g (asucc g (AHead a1 a2)) n) -(AHead a1 a))) (H a1 (asucc g a2)) (asucc g (aplus g a2 n)) (aplus_asucc g n -a2)) (asucc g (aplus g (AHead a1 a2) n)) (aplus_asucc g n (AHead a1 a2))))))) -h)). - -alias id "next_plus_lt" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/next_plus/props/next_plus_lt.con". -theorem aplus_asucc_false: - \forall (g: G).(\forall (a: A).(\forall (h: nat).((eq A (aplus g (asucc g a) -h) a) \to (\forall (P: Prop).P)))) -\def - \lambda (g: G).(\lambda (a: A).(A_ind (\lambda (a0: A).(\forall (h: -nat).((eq A (aplus g (asucc g a0) h) a0) \to (\forall (P: Prop).P)))) -(\lambda (n: nat).(\lambda (n0: nat).(\lambda (h: nat).(\lambda (H: (eq A -(aplus g (match n with [O \Rightarrow (ASort O (next g n0)) | (S h) -\Rightarrow (ASort h n0)]) h) (ASort n n0))).(\lambda (P: Prop).((match n in -nat return (\lambda (n1: nat).((eq A (aplus g (match n1 with [O \Rightarrow -(ASort O (next g n0)) | (S h) \Rightarrow (ASort h n0)]) h) (ASort n1 n0)) -\to P)) with [O \Rightarrow (\lambda (H0: (eq A (aplus g (ASort O (next g -n0)) h) (ASort O n0))).(let H1 \def (eq_ind A (aplus g (ASort O (next g n0)) -h) (\lambda (a: A).(eq A a (ASort O n0))) H0 (ASort (minus O h) (next_plus g -(next g n0) (minus h O))) (aplus_asort_simpl g h O (next g n0))) in (let H2 -\def (f_equal A nat (\lambda (e: A).(match e in A return (\lambda (_: A).nat) -with [(ASort _ n) \Rightarrow n | (AHead _ _) \Rightarrow ((let rec next_plus -(g: G) (n: nat) (i: nat) on i: nat \def (match i with [O \Rightarrow n | (S -i0) \Rightarrow (next g (next_plus g n i0))]) in next_plus) g (next g n0) -(minus h O))])) (ASort (minus O h) (next_plus g (next g n0) (minus h O))) -(ASort O n0) H1) in (let H3 \def (eq_ind_r nat (minus h O) (\lambda (n: -nat).(eq nat (next_plus g (next g n0) n) n0)) H2 h (minus_n_O h)) in -(le_lt_false (next_plus g (next g n0) h) n0 (eq_ind nat (next_plus g (next g -n0) h) (\lambda (n1: nat).(le (next_plus g (next g n0) h) n1)) (le_n -(next_plus g (next g n0) h)) n0 H3) (next_plus_lt g h n0) P))))) | (S n1) -\Rightarrow (\lambda (H0: (eq A (aplus g (ASort n1 n0) h) (ASort (S n1) -n0))).(let H1 \def (eq_ind A (aplus g (ASort n1 n0) h) (\lambda (a: A).(eq A -a (ASort (S n1) n0))) H0 (ASort (minus n1 h) (next_plus g n0 (minus h n1))) -(aplus_asort_simpl g h n1 n0)) in (let H2 \def (f_equal A nat (\lambda (e: -A).(match e in A return (\lambda (_: A).nat) with [(ASort n _) \Rightarrow n -| (AHead _ _) \Rightarrow ((let rec minus (n: nat) on n: (nat \to nat) \def -(\lambda (m: nat).(match n with [O \Rightarrow O | (S k) \Rightarrow (match m -with [O \Rightarrow (S k) | (S l) \Rightarrow (minus k l)])])) in minus) n1 -h)])) (ASort (minus n1 h) (next_plus g n0 (minus h n1))) (ASort (S n1) n0) -H1) in ((let H3 \def (f_equal A nat (\lambda (e: A).(match e in A return -(\lambda (_: A).nat) with [(ASort _ n) \Rightarrow n | (AHead _ _) -\Rightarrow ((let rec next_plus (g: G) (n: nat) (i: nat) on i: nat \def -(match i with [O \Rightarrow n | (S i0) \Rightarrow (next g (next_plus g n -i0))]) in next_plus) g n0 (minus h n1))])) (ASort (minus n1 h) (next_plus g -n0 (minus h n1))) (ASort (S n1) n0) H1) in (\lambda (H4: (eq nat (minus n1 h) -(S n1))).(le_Sx_x n1 (eq_ind nat (minus n1 h) (\lambda (n2: nat).(le n2 n1)) -(minus_le n1 h) (S n1) H4) P))) H2))))]) H)))))) (\lambda (a0: A).(\lambda -(_: ((\forall (h: nat).((eq A (aplus g (asucc g a0) h) a0) \to (\forall (P: -Prop).P))))).(\lambda (a1: A).(\lambda (H0: ((\forall (h: nat).((eq A (aplus -g (asucc g a1) h) a1) \to (\forall (P: Prop).P))))).(\lambda (h: -nat).(\lambda (H1: (eq A (aplus g (AHead a0 (asucc g a1)) h) (AHead a0 -a1))).(\lambda (P: Prop).(let H2 \def (eq_ind A (aplus g (AHead a0 (asucc g -a1)) h) (\lambda (a: A).(eq A a (AHead a0 a1))) H1 (AHead a0 (aplus g (asucc -g a1) h)) (aplus_ahead_simpl g h a0 (asucc g a1))) in (let H3 \def (f_equal A -A (\lambda (e: A).(match e in A return (\lambda (_: A).A) with [(ASort _ _) -\Rightarrow ((let rec aplus (g: G) (a: A) (n: nat) on n: A \def (match n with -[O \Rightarrow a | (S n0) \Rightarrow (asucc g (aplus g a n0))]) in aplus) g -(asucc g a1) h) | (AHead _ a) \Rightarrow a])) (AHead a0 (aplus g (asucc g -a1) h)) (AHead a0 a1) H2) in (H0 h H3 P)))))))))) a)). - -theorem aplus_inj: - \forall (g: G).(\forall (h1: nat).(\forall (h2: nat).(\forall (a: A).((eq A -(aplus g a h1) (aplus g a h2)) \to (eq nat h1 h2))))) -\def - \lambda (g: G).(\lambda (h1: nat).(nat_ind (\lambda (n: nat).(\forall (h2: -nat).(\forall (a: A).((eq A (aplus g a n) (aplus g a h2)) \to (eq nat n -h2))))) (\lambda (h2: nat).(nat_ind (\lambda (n: nat).(\forall (a: A).((eq A -(aplus g a O) (aplus g a n)) \to (eq nat O n)))) (\lambda (a: A).(\lambda (_: -(eq A a a)).(refl_equal nat O))) (\lambda (n: nat).(\lambda (_: ((\forall (a: -A).((eq A a (aplus g a n)) \to (eq nat O n))))).(\lambda (a: A).(\lambda (H0: -(eq A a (asucc g (aplus g a n)))).(let H1 \def (eq_ind_r A (asucc g (aplus g -a n)) (\lambda (a0: A).(eq A a a0)) H0 (aplus g (asucc g a) n) (aplus_asucc g -n a)) in (aplus_asucc_false g a n (sym_eq A a (aplus g (asucc g a) n) H1) (eq -nat O (S n)))))))) h2)) (\lambda (n: nat).(\lambda (H: ((\forall (h2: -nat).(\forall (a: A).((eq A (aplus g a n) (aplus g a h2)) \to (eq nat n -h2)))))).(\lambda (h2: nat).(nat_ind (\lambda (n0: nat).(\forall (a: A).((eq -A (aplus g a (S n)) (aplus g a n0)) \to (eq nat (S n) n0)))) (\lambda (a: -A).(\lambda (H0: (eq A (asucc g (aplus g a n)) a)).(let H1 \def (eq_ind_r A -(asucc g (aplus g a n)) (\lambda (a0: A).(eq A a0 a)) H0 (aplus g (asucc g a) -n) (aplus_asucc g n a)) in (aplus_asucc_false g a n H1 (eq nat (S n) O))))) -(\lambda (n0: nat).(\lambda (_: ((\forall (a: A).((eq A (asucc g (aplus g a -n)) (aplus g a n0)) \to (eq nat (S n) n0))))).(\lambda (a: A).(\lambda (H1: -(eq A (asucc g (aplus g a n)) (asucc g (aplus g a n0)))).(let H2 \def -(eq_ind_r A (asucc g (aplus g a n)) (\lambda (a0: A).(eq A a0 (asucc g (aplus -g a n0)))) H1 (aplus g (asucc g a) n) (aplus_asucc g n a)) in (let H3 \def -(eq_ind_r A (asucc g (aplus g a n0)) (\lambda (a0: A).(eq A (aplus g (asucc g -a) n) a0)) H2 (aplus g (asucc g a) n0) (aplus_asucc g n0 a)) in (f_equal nat -nat S n n0 (H n0 (asucc g a) H3)))))))) h2)))) h1)). - diff --git a/matita/contribs/LAMBDA-TYPES/Level-1/problems-1.ma~ b/matita/contribs/LAMBDA-TYPES/Level-1/problems-1.ma~ deleted file mode 100644 index f3b166546..000000000 --- a/matita/contribs/LAMBDA-TYPES/Level-1/problems-1.ma~ +++ /dev/null @@ -1,107 +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 *) -(* *) -(**************************************************************************) - -(* Problematic objects for disambiguation/typechecking ********************) -(* FG: PLEASE COMMENT THE NON WORKING OBJECTS *****************************) - -set "baseuri" "cic:/matita/LAMBDA-TYPES/Level-1/problems". - -include "LambdaDelta/theory.ma". - -theorem iso_trans: - \forall (t1: T).(\forall (t2: T).((iso t1 t2) \to (\forall (t3: T).((iso t2 -t3) \to (iso t1 t3))))) -\def - \lambda (t1: T).(\lambda (t2: T).(\lambda (H: (iso t1 t2)).(iso_ind (\lambda -(t: T).(\lambda (t0: T).(\forall (t3: T).((iso t0 t3) \to (iso t t3))))) -(\lambda (n1: nat).(\lambda (n2: nat).(\lambda (t3: T).(\lambda (H0: (iso -(TSort n2) t3)).(let H1 \def (match H0 in iso return (\lambda (t: T).(\lambda -(t0: T).(\lambda (_: (iso t t0)).((eq T t (TSort n2)) \to ((eq T t0 t3) \to -(iso (TSort n1) t3)))))) with [(iso_sort n0 n3) \Rightarrow (\lambda (H0: (eq -T (TSort n0) (TSort n2))).(\lambda (H1: (eq T (TSort n3) t3)).((let H2 \def -(f_equal T nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat) with -[(TSort n) \Rightarrow n | (TLRef _) \Rightarrow n0 | (THead _ _ _) -\Rightarrow n0])) (TSort n0) (TSort n2) H0) in (eq_ind nat n2 (\lambda (_: -nat).((eq T (TSort n3) t3) \to (iso (TSort n1) t3))) (\lambda (H3: (eq T -(TSort n3) t3)).(eq_ind T (TSort n3) (\lambda (t: T).(iso (TSort n1) t)) -(iso_sort n1 n3) t3 H3)) n0 (sym_eq nat n0 n2 H2))) H1))) | (iso_lref i1 i2) -\Rightarrow (\lambda (H0: (eq T (TLRef i1) (TSort n2))).(\lambda (H1: (eq T -(TLRef i2) t3)).((let H2 \def (eq_ind T (TLRef i1) (\lambda (e: T).(match e -in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef -_) \Rightarrow True | (THead _ _ _) \Rightarrow False])) I (TSort n2) H0) in -(False_ind ((eq T (TLRef i2) t3) \to (iso (TSort n1) t3)) H2)) H1))) | -(iso_head k v1 v2 t1 t2) \Rightarrow (\lambda (H0: (eq T (THead k v1 t1) -(TSort n2))).(\lambda (H1: (eq T (THead k v2 t2) t3)).((let H2 \def (eq_ind T -(THead k v1 t1) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) -with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ -_) \Rightarrow True])) I (TSort n2) H0) in (False_ind ((eq T (THead k v2 t2) -t3) \to (iso (TSort n1) t3)) H2)) H1)))]) in (H1 (refl_equal T (TSort n2)) -(refl_equal T t3))))))) (\lambda (i1: nat).(\lambda (i2: nat).(\lambda (t3: -T).(\lambda (H0: (iso (TLRef i2) t3)).(let H1 \def (match H0 in iso return -(\lambda (t: T).(\lambda (t0: T).(\lambda (_: (iso t t0)).((eq T t (TLRef -i2)) \to ((eq T t0 t3) \to (iso (TLRef i1) t3)))))) with [(iso_sort n1 n2) -\Rightarrow (\lambda (H0: (eq T (TSort n1) (TLRef i2))).(\lambda (H1: (eq T -(TSort n2) t3)).((let H2 \def (eq_ind T (TSort n1) (\lambda (e: T).(match e -in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow True | (TLRef -_) \Rightarrow False | (THead _ _ _) \Rightarrow False])) I (TLRef i2) H0) in -(False_ind ((eq T (TSort n2) t3) \to (iso (TLRef i1) t3)) H2)) H1))) | -(iso_lref i0 i3) \Rightarrow (\lambda (H0: (eq T (TLRef i0) (TLRef -i2))).(\lambda (H1: (eq T (TLRef i3) t3)).((let H2 \def (f_equal T nat -(\lambda (e: T).(match e in T return (\lambda (_: T).nat) with [(TSort _) -\Rightarrow i0 | (TLRef n) \Rightarrow n | (THead _ _ _) \Rightarrow i0])) -(TLRef i0) (TLRef i2) H0) in (eq_ind nat i2 (\lambda (_: nat).((eq T (TLRef -i3) t3) \to (iso (TLRef i1) t3))) (\lambda (H3: (eq T (TLRef i3) t3)).(eq_ind -T (TLRef i3) (\lambda (t: T).(iso (TLRef i1) t)) (iso_lref i1 i3) t3 H3)) i0 -(sym_eq nat i0 i2 H2))) H1))) | (iso_head k v1 v2 t1 t2) \Rightarrow (\lambda -(H0: (eq T (THead k v1 t1) (TLRef i2))).(\lambda (H1: (eq T (THead k v2 t2) -t3)).((let H2 \def (eq_ind T (THead k v1 t1) (\lambda (e: T).(match e in T -return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) -\Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TLRef i2) H0) in -(False_ind ((eq T (THead k v2 t2) t3) \to (iso (TLRef i1) t3)) H2)) H1)))]) -in (H1 (refl_equal T (TLRef i2)) (refl_equal T t3))))))) (\lambda (k: -K).(\lambda (v1: T).(\lambda (v2: T).(\lambda (t3: T).(\lambda (t4: -T).(\lambda (t5: T).(\lambda (H0: (iso (THead k v2 t4) t5)).(let H1 \def -(match H0 in iso return (\lambda (t: T).(\lambda (t0: T).(\lambda (_: (iso t -t0)).((eq T t (THead k v2 t4)) \to ((eq T t0 t5) \to (iso (THead k v1 t3) -t5)))))) with [(iso_sort n1 n2) \Rightarrow (\lambda (H0: (eq T (TSort n1) -(THead k v2 t4))).(\lambda (H1: (eq T (TSort n2) t5)).((let H2 \def (eq_ind T -(TSort n1) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with -[(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) -\Rightarrow False])) I (THead k v2 t4) H0) in (False_ind ((eq T (TSort n2) -t5) \to (iso (THead k v1 t3) t5)) H2)) H1))) | (iso_lref i1 i2) \Rightarrow -(\lambda (H0: (eq T (TLRef i1) (THead k v2 t4))).(\lambda (H1: (eq T (TLRef -i2) t5)).((let H2 \def (eq_ind T (TLRef i1) (\lambda (e: T).(match e in T -return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) -\Rightarrow True | (THead _ _ _) \Rightarrow False])) I (THead k v2 t4) H0) -in (False_ind ((eq T (TLRef i2) t5) \to (iso (THead k v1 t3) t5)) H2)) H1))) -| (iso_head k0 v0 v3 t0 t4) \Rightarrow (\lambda (H0: (eq T (THead k0 v0 t0) -(THead k v2 t4))).(\lambda (H1: (eq T (THead k0 v3 t4) t5)).((let H2 \def -(f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with -[(TSort _) \Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t) -\Rightarrow t])) (THead k0 v0 t0) (THead k v2 t4) H0) in ((let H3 \def -(f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with -[(TSort _) \Rightarrow v0 | (TLRef _) \Rightarrow v0 | (THead _ t _) -\Rightarrow t])) (THead k0 v0 t0) (THead k v2 t4) H0) in ((let H4 \def -(f_equal T K (\lambda (e: T).(match e in T return (\lambda (_: T).K) with -[(TSort _) \Rightarrow k0 | (TLRef _) \Rightarrow k0 | (THead k _ _) -\Rightarrow k])) (THead k0 v0 t0) (THead k v2 t4) H0) in (eq_ind K k (\lambda -(k1: K).((eq T v0 v2) \to ((eq T t0 t4) \to ((eq T (THead k1 v3 t4) t5) \to -(iso (THead k v1 t3) t5))))) (\lambda (H5: (eq T v0 v2)).(eq_ind T v2 -(\lambda (_: T).((eq T t0 t4) \to ((eq T (THead k v3 t4) t5) \to (iso (THead -k v1 t3) t5)))) (\lambda (H6: (eq T t0 t4)).(eq_ind T t4 (\lambda (_: T).((eq -T (THead k v3 t4) t5) \to (iso (THead k v1 t3) t5))) (\lambda (H7: (eq T -(THead k v3 t4) t5)).(eq_ind T (THead k v3 t4) (\lambda (t: T).(iso (THead k -v1 t3) t)) (iso_head k v1 v3 t3 t4) t5 H7)) t0 (sym_eq T t0 t4 H6))) v0 -(sym_eq T v0 v2 H5))) k0 (sym_eq K k0 k H4))) H3)) H2)) H1)))]) in (H1 -(refl_equal T (THead k v2 t4)) (refl_equal T t5)))))))))) t1 t2 H))). diff --git a/matita/contribs/LAMBDA-TYPES/Level-1/problems-2.ma~ b/matita/contribs/LAMBDA-TYPES/Level-1/problems-2.ma~ deleted file mode 100644 index a0f6f0275..000000000 --- a/matita/contribs/LAMBDA-TYPES/Level-1/problems-2.ma~ +++ /dev/null @@ -1,158 +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 *) -(* *) -(**************************************************************************) - -(* Problematic objects for disambiguation/typechecking ********************) -(* FG: PLEASE COMMENT THE NON WORKING OBJECTS *****************************) - -set "baseuri" "cic:/matita/LAMBDA-TYPES/Level-1/problems". - -include "LambdaDelta/theory.ma". - -theorem drop1_getl_trans: - \forall (hds: PList).(\forall (c1: C).(\forall (c2: C).((drop1 hds c2 c1) -\to (\forall (b: B).(\forall (e1: C).(\forall (v: T).(\forall (i: nat).((getl -i c1 (CHead e1 (Bind b) v)) \to (ex C (\lambda (e2: C).(getl (trans hds i) c2 -(CHead e2 (Bind b) (ctrans hds i v))))))))))))) -\def - \lambda (hds: PList).(PList_ind (\lambda (p: PList).(\forall (c1: -C).(\forall (c2: C).((drop1 p c2 c1) \to (\forall (b: B).(\forall (e1: -C).(\forall (v: T).(\forall (i: nat).((getl i c1 (CHead e1 (Bind b) v)) \to -(ex C (\lambda (e2: C).(getl (trans p i) c2 (CHead e2 (Bind b) (ctrans p i -v)))))))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H: (drop1 PNil c2 -c1)).(\lambda (b: B).(\lambda (e1: C).(\lambda (v: T).(\lambda (i: -nat).(\lambda (H0: (getl i c1 (CHead e1 (Bind b) v))).(let H1 \def (match H -in drop1 return (\lambda (p: PList).(\lambda (c: C).(\lambda (c0: C).(\lambda -(_: (drop1 p c c0)).((eq PList p PNil) \to ((eq C c c2) \to ((eq C c0 c1) \to -(ex C (\lambda (e2: C).(getl i c2 (CHead e2 (Bind b) v))))))))))) with -[(drop1_nil c) \Rightarrow (\lambda (_: (eq PList PNil PNil)).(\lambda (H2: -(eq C c c2)).(\lambda (H3: (eq C c c1)).(eq_ind C c2 (\lambda (c0: C).((eq C -c0 c1) \to (ex C (\lambda (e2: C).(getl i c2 (CHead e2 (Bind b) v)))))) -(\lambda (H4: (eq C c2 c1)).(eq_ind C c1 (\lambda (c0: C).(ex C (\lambda (e2: -C).(getl i c0 (CHead e2 (Bind b) v))))) (ex_intro C (\lambda (e2: C).(getl i -c1 (CHead e2 (Bind b) v))) e1 H0) c2 (sym_eq C c2 c1 H4))) c (sym_eq C c c2 -H2) H3)))) | (drop1_cons c0 c3 h d H1 c4 hds H2) \Rightarrow (\lambda (H3: -(eq PList (PCons h d hds) PNil)).(\lambda (H4: (eq C c0 c2)).(\lambda (H5: -(eq C c4 c1)).((let H6 \def (eq_ind PList (PCons h d hds) (\lambda (e: -PList).(match e in PList return (\lambda (_: PList).Prop) with [PNil -\Rightarrow False | (PCons _ _ _) \Rightarrow True])) I PNil H3) in -(False_ind ((eq C c0 c2) \to ((eq C c4 c1) \to ((drop h d c0 c3) \to ((drop1 -hds c3 c4) \to (ex C (\lambda (e2: C).(getl i c2 (CHead e2 (Bind b) v)))))))) -H6)) H4 H5 H1 H2))))]) in (H1 (refl_equal PList PNil) (refl_equal C c2) -(refl_equal C c1))))))))))) (\lambda (h: nat).(\lambda (d: nat).(\lambda -(hds0: PList).(\lambda (H: ((\forall (c1: C).(\forall (c2: C).((drop1 hds0 c2 -c1) \to (\forall (b: B).(\forall (e1: C).(\forall (v: T).(\forall (i: -nat).((getl i c1 (CHead e1 (Bind b) v)) \to (ex C (\lambda (e2: C).(getl -(trans hds0 i) c2 (CHead e2 (Bind b) (ctrans hds0 i v))))))))))))))).(\lambda -(c1: C).(\lambda (c2: C).(\lambda (H0: (drop1 (PCons h d hds0) c2 -c1)).(\lambda (b: B).(\lambda (e1: C).(\lambda (v: T).(\lambda (i: -nat).(\lambda (H1: (getl i c1 (CHead e1 (Bind b) v))).(let H2 \def (match H0 -in drop1 return (\lambda (p: PList).(\lambda (c: C).(\lambda (c0: C).(\lambda -(_: (drop1 p c c0)).((eq PList p (PCons h d hds0)) \to ((eq C c c2) \to ((eq -C c0 c1) \to (ex C (\lambda (e2: C).(getl (match (blt (trans hds0 i) d) with -[true \Rightarrow (trans hds0 i) | false \Rightarrow (plus (trans hds0 i) -h)]) c2 (CHead e2 (Bind b) (match (blt (trans hds0 i) d) with [true -\Rightarrow (lift h (minus d (S (trans hds0 i))) (ctrans hds0 i v)) | false -\Rightarrow (ctrans hds0 i v)])))))))))))) with [(drop1_nil c) \Rightarrow -(\lambda (H2: (eq PList PNil (PCons h d hds0))).(\lambda (H3: (eq C c -c2)).(\lambda (H4: (eq C c c1)).((let H5 \def (eq_ind PList PNil (\lambda (e: -PList).(match e in PList return (\lambda (_: PList).Prop) with [PNil -\Rightarrow True | (PCons _ _ _) \Rightarrow False])) I (PCons h d hds0) H2) -in (False_ind ((eq C c c2) \to ((eq C c c1) \to (ex C (\lambda (e2: C).(getl -(match (blt (trans hds0 i) d) with [true \Rightarrow (trans hds0 i) | false -\Rightarrow (plus (trans hds0 i) h)]) c2 (CHead e2 (Bind b) (match (blt -(trans hds0 i) d) with [true \Rightarrow (lift h (minus d (S (trans hds0 i))) -(ctrans hds0 i v)) | false \Rightarrow (ctrans hds0 i v)]))))))) H5)) H3 -H4)))) | (drop1_cons c0 c3 h0 d0 H2 c4 hds0 H3) \Rightarrow (\lambda (H4: (eq -PList (PCons h0 d0 hds0) (PCons h d hds0))).(\lambda (H5: (eq C c0 -c2)).(\lambda (H6: (eq C c4 c1)).((let H7 \def (f_equal PList PList (\lambda -(e: PList).(match e in PList return (\lambda (_: PList).PList) with [PNil -\Rightarrow hds0 | (PCons _ _ p) \Rightarrow p])) (PCons h0 d0 hds0) (PCons h -d hds0) H4) in ((let H8 \def (f_equal PList nat (\lambda (e: PList).(match e -in PList return (\lambda (_: PList).nat) with [PNil \Rightarrow d0 | (PCons _ -n _) \Rightarrow n])) (PCons h0 d0 hds0) (PCons h d hds0) H4) in ((let H9 -\def (f_equal PList nat (\lambda (e: PList).(match e in PList return (\lambda -(_: PList).nat) with [PNil \Rightarrow h0 | (PCons n _ _) \Rightarrow n])) -(PCons h0 d0 hds0) (PCons h d hds0) H4) in (eq_ind nat h (\lambda (n: -nat).((eq nat d0 d) \to ((eq PList hds0 hds0) \to ((eq C c0 c2) \to ((eq C c4 -c1) \to ((drop n d0 c0 c3) \to ((drop1 hds0 c3 c4) \to (ex C (\lambda (e2: -C).(getl (match (blt (trans hds0 i) d) with [true \Rightarrow (trans hds0 i) -| false \Rightarrow (plus (trans hds0 i) h)]) c2 (CHead e2 (Bind b) (match -(blt (trans hds0 i) d) with [true \Rightarrow (lift h (minus d (S (trans hds0 -i))) (ctrans hds0 i v)) | false \Rightarrow (ctrans hds0 i v)])))))))))))) -(\lambda (H10: (eq nat d0 d)).(eq_ind nat d (\lambda (n: nat).((eq PList hds0 -hds0) \to ((eq C c0 c2) \to ((eq C c4 c1) \to ((drop h n c0 c3) \to ((drop1 -hds0 c3 c4) \to (ex C (\lambda (e2: C).(getl (match (blt (trans hds0 i) d) -with [true \Rightarrow (trans hds0 i) | false \Rightarrow (plus (trans hds0 -i) h)]) c2 (CHead e2 (Bind b) (match (blt (trans hds0 i) d) with [true -\Rightarrow (lift h (minus d (S (trans hds0 i))) (ctrans hds0 i v)) | false -\Rightarrow (ctrans hds0 i v)]))))))))))) (\lambda (H11: (eq PList hds0 -hds0)).(eq_ind PList hds0 (\lambda (p: PList).((eq C c0 c2) \to ((eq C c4 c1) -\to ((drop h d c0 c3) \to ((drop1 p c3 c4) \to (ex C (\lambda (e2: C).(getl -(match (blt (trans hds0 i) d) with [true \Rightarrow (trans hds0 i) | false -\Rightarrow (plus (trans hds0 i) h)]) c2 (CHead e2 (Bind b) (match (blt -(trans hds0 i) d) with [true \Rightarrow (lift h (minus d (S (trans hds0 i))) -(ctrans hds0 i v)) | false \Rightarrow (ctrans hds0 i v)])))))))))) (\lambda -(H12: (eq C c0 c2)).(eq_ind C c2 (\lambda (c: C).((eq C c4 c1) \to ((drop h d -c c3) \to ((drop1 hds0 c3 c4) \to (ex C (\lambda (e2: C).(getl (match (blt -(trans hds0 i) d) with [true \Rightarrow (trans hds0 i) | false \Rightarrow -(plus (trans hds0 i) h)]) c2 (CHead e2 (Bind b) (match (blt (trans hds0 i) d) -with [true \Rightarrow (lift h (minus d (S (trans hds0 i))) (ctrans hds0 i -v)) | false \Rightarrow (ctrans hds0 i v)]))))))))) (\lambda (H13: (eq C c4 -c1)).(eq_ind C c1 (\lambda (c: C).((drop h d c2 c3) \to ((drop1 hds0 c3 c) -\to (ex C (\lambda (e2: C).(getl (match (blt (trans hds0 i) d) with [true -\Rightarrow (trans hds0 i) | false \Rightarrow (plus (trans hds0 i) h)]) c2 -(CHead e2 (Bind b) (match (blt (trans hds0 i) d) with [true \Rightarrow (lift -h (minus d (S (trans hds0 i))) (ctrans hds0 i v)) | false \Rightarrow (ctrans -hds0 i v)])))))))) (\lambda (H14: (drop h d c2 c3)).(\lambda (H15: (drop1 -hds0 c3 c1)).(xinduction bool (blt (trans hds0 i) d) (\lambda (b0: bool).(ex -C (\lambda (e2: C).(getl (match b0 with [true \Rightarrow (trans hds0 i) | -false \Rightarrow (plus (trans hds0 i) h)]) c2 (CHead e2 (Bind b) (match b0 -with [true \Rightarrow (lift h (minus d (S (trans hds0 i))) (ctrans hds0 i -v)) | false \Rightarrow (ctrans hds0 i v)])))))) (\lambda (x_x: -bool).(bool_ind (\lambda (b0: bool).((eq bool (blt (trans hds0 i) d) b0) \to -(ex C (\lambda (e2: C).(getl (match b0 with [true \Rightarrow (trans hds0 i) -| false \Rightarrow (plus (trans hds0 i) h)]) c2 (CHead e2 (Bind b) (match b0 -with [true \Rightarrow (lift h (minus d (S (trans hds0 i))) (ctrans hds0 i -v)) | false \Rightarrow (ctrans hds0 i v)]))))))) (\lambda (H0: (eq bool (blt -(trans hds0 i) d) true)).(let H_x \def (H c1 c3 H15 b e1 v i H1) in (let H16 -\def H_x in (ex_ind C (\lambda (e2: C).(getl (trans hds0 i) c3 (CHead e2 -(Bind b) (ctrans hds0 i v)))) (ex C (\lambda (e2: C).(getl (trans hds0 i) c2 -(CHead e2 (Bind b) (lift h (minus d (S (trans hds0 i))) (ctrans hds0 i -v)))))) (\lambda (x: C).(\lambda (H17: (getl (trans hds0 i) c3 (CHead x (Bind -b) (ctrans hds0 i v)))).(let H_x0 \def (drop_getl_trans_lt (trans hds0 i) d -(le_S_n (S (trans hds0 i)) d (lt_le_S (S (trans hds0 i)) (S d) (blt_lt (S d) -(S (trans hds0 i)) H0))) c2 c3 h H14 b x (ctrans hds0 i v) H17) in (let H -\def H_x0 in (ex2_ind C (\lambda (e1: C).(getl (trans hds0 i) c2 (CHead e1 -(Bind b) (lift h (minus d (S (trans hds0 i))) (ctrans hds0 i v))))) (\lambda -(e1: C).(drop h (minus d (S (trans hds0 i))) e1 x)) (ex C (\lambda (e2: -C).(getl (trans hds0 i) c2 (CHead e2 (Bind b) (lift h (minus d (S (trans hds0 -i))) (ctrans hds0 i v)))))) (\lambda (x0: C).(\lambda (H1: (getl (trans hds0 -i) c2 (CHead x0 (Bind b) (lift h (minus d (S (trans hds0 i))) (ctrans hds0 i -v))))).(\lambda (_: (drop h (minus d (S (trans hds0 i))) x0 x)).(ex_intro C -(\lambda (e2: C).(getl (trans hds0 i) c2 (CHead e2 (Bind b) (lift h (minus d -(S (trans hds0 i))) (ctrans hds0 i v))))) x0 H1)))) H))))) H16)))) (\lambda -(H0: (eq bool (blt (trans hds0 i) d) false)).(let H_x \def (H c1 c3 H15 b e1 -v i H1) in (let H16 \def H_x in (ex_ind C (\lambda (e2: C).(getl (trans hds0 -i) c3 (CHead e2 (Bind b) (ctrans hds0 i v)))) (ex C (\lambda (e2: C).(getl -(plus (trans hds0 i) h) c2 (CHead e2 (Bind b) (ctrans hds0 i v))))) (\lambda -(x: C).(\lambda (H17: (getl (trans hds0 i) c3 (CHead x (Bind b) (ctrans hds0 -i v)))).(let H \def (drop_getl_trans_ge (trans hds0 i) c2 c3 d h H14 (CHead x -(Bind b) (ctrans hds0 i v)) H17) in (ex_intro C (\lambda (e2: C).(getl (plus -(trans hds0 i) h) c2 (CHead e2 (Bind b) (ctrans hds0 i v)))) x (H (bge_le d -(trans hds0 i) H0)))))) H16)))) x_x))))) c4 (sym_eq C c4 c1 H13))) c0 (sym_eq -C c0 c2 H12))) hds0 (sym_eq PList hds0 hds0 H11))) d0 (sym_eq nat d0 d H10))) -h0 (sym_eq nat h0 h H9))) H8)) H7)) H5 H6 H2 H3))))]) in (H2 (refl_equal -PList (PCons h d hds0)) (refl_equal C c2) (refl_equal C c1))))))))))))))) -hds). - diff --git a/matita/contribs/LAMBDA-TYPES/Level-1/problems.ma~ b/matita/contribs/LAMBDA-TYPES/Level-1/problems.ma~ deleted file mode 100644 index c727f77db..000000000 --- a/matita/contribs/LAMBDA-TYPES/Level-1/problems.ma~ +++ /dev/null @@ -1,32 +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 *) -(* *) -(**************************************************************************) - -(* Problematic objects for disambiguation/typechecking ********************) - -set "baseuri" "cic:/matita/LAMBDA-TYPES/Level-1/problems". - -include "LambdaDelta/theory.ma". - -(* Problem 1: disambiguation errors with these objects *) - -(* iso_trans (in problems-1) - * drop1_getl_trans (in problems-2) - *) - -(* Problem 2: assertion failure raised by type checker on this object *) - -inductive tau1 (g:G) (c:C) (t1:T): T \to Prop \def -| tau1_tau0: \forall (t2: T).((tau0 g c t1 t2) \to (tau1 g c t1 t2)) -| tau1_sing: \forall (t: T).((tau1 g c t1 t) \to (\forall (t2: T).((tau0 g c -t t2) \to (tau1 g c t1 t2)))). -- 2.39.2