+++ /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 *********************)
-
-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)).
-
+++ /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 *)
-(* *)
-(**************************************************************************)
-
-(* 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))).
+++ /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 *)
-(* *)
-(**************************************************************************)
-
-(* 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).
-
+++ /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 *)
-(* *)
-(**************************************************************************)
-
-(* 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)))).
projects / helm.git / commitdiff