+++ /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/csuba/defs.ma".
-
-theorem csuba_gen_abbr:
- \forall (g: G).(\forall (d1: C).(\forall (c: C).(\forall (u: T).((csuba g
-(CHead d1 (Bind Abbr) u) c) \to (ex2 C (\lambda (d2: C).(eq C c (CHead d2
-(Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))))))
-\def
- \lambda (g: G).(\lambda (d1: C).(\lambda (c: C).(\lambda (u: T).(\lambda (H:
-(csuba g (CHead d1 (Bind Abbr) u) c)).(insert_eq C (CHead d1 (Bind Abbr) u)
-(\lambda (c0: C).(csuba g c0 c)) (\lambda (_: C).(ex2 C (\lambda (d2: C).(eq
-C c (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (\lambda
-(y: C).(\lambda (H0: (csuba g y c)).(csuba_ind g (\lambda (c0: C).(\lambda
-(c1: C).((eq C c0 (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda (d2: C).(eq C
-c1 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))))) (\lambda
-(n: nat).(\lambda (H1: (eq C (CSort n) (CHead d1 (Bind Abbr) u))).(let H2
-\def (eq_ind C (CSort n) (\lambda (ee: C).(match ee in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _) \Rightarrow
-False])) I (CHead d1 (Bind Abbr) u) H1) in (False_ind (ex2 C (\lambda (d2:
-C).(eq C (CSort n) (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
-d2))) H2)))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1
-c2)).(\lambda (H2: (((eq C c1 (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda
-(d2: C).(eq C c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
-d2)))))).(\lambda (k: K).(\lambda (u0: T).(\lambda (H3: (eq C (CHead c1 k u0)
-(CHead d1 (Bind Abbr) u))).(let H4 \def (f_equal C C (\lambda (e: C).(match e
-in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c1 | (CHead c0 _
-_) \Rightarrow c0])) (CHead c1 k u0) (CHead d1 (Bind Abbr) u) H3) in ((let H5
-\def (f_equal C K (\lambda (e: C).(match e in C return (\lambda (_: C).K)
-with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c1 k
-u0) (CHead d1 (Bind Abbr) u) H3) in ((let H6 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u0 |
-(CHead _ _ t) \Rightarrow t])) (CHead c1 k u0) (CHead d1 (Bind Abbr) u) H3)
-in (\lambda (H7: (eq K k (Bind Abbr))).(\lambda (H8: (eq C c1 d1)).(eq_ind_r
-T u (\lambda (t: T).(ex2 C (\lambda (d2: C).(eq C (CHead c2 k t) (CHead d2
-(Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (eq_ind_r K (Bind Abbr)
-(\lambda (k0: K).(ex2 C (\lambda (d2: C).(eq C (CHead c2 k0 u) (CHead d2
-(Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (let H9 \def (eq_ind C
-c1 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda
-(d2: C).(eq C c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
-d2))))) H2 d1 H8) in (let H10 \def (eq_ind C c1 (\lambda (c0: C).(csuba g c0
-c2)) H1 d1 H8) in (ex_intro2 C (\lambda (d2: C).(eq C (CHead c2 (Bind Abbr)
-u) (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) c2
-(refl_equal C (CHead c2 (Bind Abbr) u)) H10))) k H7) u0 H6)))) H5))
-H4))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (_: (csuba g c1
-c2)).(\lambda (_: (((eq C c1 (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda
-(d2: C).(eq C c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
-d2)))))).(\lambda (b: B).(\lambda (_: (not (eq B b Void))).(\lambda (u1:
-T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c1 (Bind Void) u1) (CHead d1
-(Bind Abbr) u))).(let H5 \def (eq_ind C (CHead c1 (Bind Void) u1) (\lambda
-(ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _)
-\Rightarrow False | (CHead _ k _) \Rightarrow (match k in K return (\lambda
-(_: K).Prop) with [(Bind b0) \Rightarrow (match b0 in B return (\lambda (_:
-B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow False | Void
-\Rightarrow True]) | (Flat _) \Rightarrow False])])) I (CHead d1 (Bind Abbr)
-u) H4) in (False_ind (ex2 C (\lambda (d2: C).(eq C (CHead c2 (Bind b) u2)
-(CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) H5)))))))))))
-(\lambda (c1: C).(\lambda (c2: C).(\lambda (_: (csuba g c1 c2)).(\lambda (_:
-(((eq C c1 (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda (d2: C).(eq C c2
-(CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))))).(\lambda (t:
-T).(\lambda (a: A).(\lambda (_: (arity g c1 t (asucc g a))).(\lambda (u0:
-T).(\lambda (_: (arity g c2 u0 a)).(\lambda (H5: (eq C (CHead c1 (Bind Abst)
-t) (CHead d1 (Bind Abbr) u))).(let H6 \def (eq_ind C (CHead c1 (Bind Abst) t)
-(\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _)
-\Rightarrow False | (CHead _ k _) \Rightarrow (match k in K return (\lambda
-(_: K).Prop) with [(Bind b) \Rightarrow (match b in B return (\lambda (_:
-B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow True | Void
-\Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead d1 (Bind Abbr)
-u) H5) in (False_ind (ex2 C (\lambda (d2: C).(eq C (CHead c2 (Bind Abbr) u0)
-(CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) H6))))))))))))
-y c H0))) H))))).
-(* COMMENTS
-Initial nodes: 1117
-END *)
-
-theorem csuba_gen_void:
- \forall (g: G).(\forall (d1: C).(\forall (c: C).(\forall (u1: T).((csuba g
-(CHead d1 (Bind Void) u1) c) \to (ex2_3 B C T (\lambda (b: B).(\lambda (d2:
-C).(\lambda (u2: T).(eq C c (CHead d2 (Bind b) u2))))) (\lambda (_:
-B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2)))))))))
-\def
- \lambda (g: G).(\lambda (d1: C).(\lambda (c: C).(\lambda (u1: T).(\lambda
-(H: (csuba g (CHead d1 (Bind Void) u1) c)).(insert_eq C (CHead d1 (Bind Void)
-u1) (\lambda (c0: C).(csuba g c0 c)) (\lambda (_: C).(ex2_3 B C T (\lambda
-(b: B).(\lambda (d2: C).(\lambda (u2: T).(eq C c (CHead d2 (Bind b) u2)))))
-(\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2))))))
-(\lambda (y: C).(\lambda (H0: (csuba g y c)).(csuba_ind g (\lambda (c0:
-C).(\lambda (c1: C).((eq C c0 (CHead d1 (Bind Void) u1)) \to (ex2_3 B C T
-(\lambda (b: B).(\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2 (Bind b)
-u2))))) (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2)))))))) (\lambda (n: nat).(\lambda (H1: (eq C (CSort n) (CHead d1 (Bind
-Void) u1))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee in C
-return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _)
-\Rightarrow False])) I (CHead d1 (Bind Void) u1) H1) in (False_ind (ex2_3 B C
-T (\lambda (b: B).(\lambda (d2: C).(\lambda (u2: T).(eq C (CSort n) (CHead d2
-(Bind b) u2))))) (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2))))) H2)))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1
-c2)).(\lambda (H2: (((eq C c1 (CHead d1 (Bind Void) u1)) \to (ex2_3 B C T
-(\lambda (b: B).(\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind b)
-u2))))) (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2)))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c1 k u)
-(CHead d1 (Bind Void) u1))).(let H4 \def (f_equal C C (\lambda (e: C).(match
-e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c1 | (CHead c0 _
-_) \Rightarrow c0])) (CHead c1 k u) (CHead d1 (Bind Void) u1) H3) in ((let H5
-\def (f_equal C K (\lambda (e: C).(match e in C return (\lambda (_: C).K)
-with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c1 k
-u) (CHead d1 (Bind Void) u1) H3) in ((let H6 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u |
-(CHead _ _ t) \Rightarrow t])) (CHead c1 k u) (CHead d1 (Bind Void) u1) H3)
-in (\lambda (H7: (eq K k (Bind Void))).(\lambda (H8: (eq C c1 d1)).(eq_ind_r
-T u1 (\lambda (t: T).(ex2_3 B C T (\lambda (b: B).(\lambda (d2: C).(\lambda
-(u2: T).(eq C (CHead c2 k t) (CHead d2 (Bind b) u2))))) (\lambda (_:
-B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2)))))) (eq_ind_r K (Bind
-Void) (\lambda (k0: K).(ex2_3 B C T (\lambda (b: B).(\lambda (d2: C).(\lambda
-(u2: T).(eq C (CHead c2 k0 u1) (CHead d2 (Bind b) u2))))) (\lambda (_:
-B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2)))))) (let H9 \def (eq_ind
-C c1 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind Void) u1)) \to (ex2_3 B C T
-(\lambda (b: B).(\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind b)
-u2))))) (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2))))))) H2 d1 H8) in (let H10 \def (eq_ind C c1 (\lambda (c0: C).(csuba g
-c0 c2)) H1 d1 H8) in (ex2_3_intro B C T (\lambda (b: B).(\lambda (d2:
-C).(\lambda (u2: T).(eq C (CHead c2 (Bind Void) u1) (CHead d2 (Bind b)
-u2))))) (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2))))
-Void c2 u1 (refl_equal C (CHead c2 (Bind Void) u1)) H10))) k H7) u H6))))
-H5)) H4))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1
-c2)).(\lambda (H2: (((eq C c1 (CHead d1 (Bind Void) u1)) \to (ex2_3 B C T
-(\lambda (b: B).(\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind b)
-u2))))) (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2)))))))).(\lambda (b: B).(\lambda (_: (not (eq B b Void))).(\lambda (u0:
-T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c1 (Bind Void) u0) (CHead d1
-(Bind Void) u1))).(let H5 \def (f_equal C C (\lambda (e: C).(match e in C
-return (\lambda (_: C).C) with [(CSort _) \Rightarrow c1 | (CHead c0 _ _)
-\Rightarrow c0])) (CHead c1 (Bind Void) u0) (CHead d1 (Bind Void) u1) H4) in
-((let H6 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_:
-C).T) with [(CSort _) \Rightarrow u0 | (CHead _ _ t) \Rightarrow t])) (CHead
-c1 (Bind Void) u0) (CHead d1 (Bind Void) u1) H4) in (\lambda (H7: (eq C c1
-d1)).(let H8 \def (eq_ind C c1 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind
-Void) u1)) \to (ex2_3 B C T (\lambda (b0: B).(\lambda (d2: C).(\lambda (u3:
-T).(eq C c2 (CHead d2 (Bind b0) u3))))) (\lambda (_: B).(\lambda (d2:
-C).(\lambda (_: T).(csuba g d1 d2))))))) H2 d1 H7) in (let H9 \def (eq_ind C
-c1 (\lambda (c0: C).(csuba g c0 c2)) H1 d1 H7) in (ex2_3_intro B C T (\lambda
-(b0: B).(\lambda (d2: C).(\lambda (u3: T).(eq C (CHead c2 (Bind b) u2) (CHead
-d2 (Bind b0) u3))))) (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba
-g d1 d2)))) b c2 u2 (refl_equal C (CHead c2 (Bind b) u2)) H9)))))
-H5))))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (_: (csuba g c1
-c2)).(\lambda (_: (((eq C c1 (CHead d1 (Bind Void) u1)) \to (ex2_3 B C T
-(\lambda (b: B).(\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind b)
-u2))))) (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2)))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (_: (arity g c1 t (asucc
-g a))).(\lambda (u: T).(\lambda (_: (arity g c2 u a)).(\lambda (H5: (eq C
-(CHead c1 (Bind Abst) t) (CHead d1 (Bind Void) u1))).(let H6 \def (eq_ind C
-(CHead c1 (Bind Abst) t) (\lambda (ee: C).(match ee in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match
-k in K return (\lambda (_: K).Prop) with [(Bind b) \Rightarrow (match b in B
-return (\lambda (_: B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow
-True | Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead d1
-(Bind Void) u1) H5) in (False_ind (ex2_3 B C T (\lambda (b: B).(\lambda (d2:
-C).(\lambda (u2: T).(eq C (CHead c2 (Bind Abbr) u) (CHead d2 (Bind b) u2)))))
-(\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2)))))
-H6)))))))))))) y c H0))) H))))).
-(* COMMENTS
-Initial nodes: 1418
-END *)
-
-theorem csuba_gen_abst:
- \forall (g: G).(\forall (d1: C).(\forall (c: C).(\forall (u1: T).((csuba g
-(CHead d1 (Bind Abst) u1) c) \to (or (ex2 C (\lambda (d2: C).(eq C c (CHead
-d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c (CHead d2 (Bind Abbr)
-u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
-(\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
-a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
-a))))))))))
-\def
- \lambda (g: G).(\lambda (d1: C).(\lambda (c: C).(\lambda (u1: T).(\lambda
-(H: (csuba g (CHead d1 (Bind Abst) u1) c)).(insert_eq C (CHead d1 (Bind Abst)
-u1) (\lambda (c0: C).(csuba g c0 c)) (\lambda (_: C).(or (ex2 C (\lambda (d2:
-C).(eq C c (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
-(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c (CHead
-d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
-A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
-g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
-A).(arity g d2 u2 a))))))) (\lambda (y: C).(\lambda (H0: (csuba g y
-c)).(csuba_ind g (\lambda (c0: C).(\lambda (c1: C).((eq C c0 (CHead d1 (Bind
-Abst) u1)) \to (or (ex2 C (\lambda (d2: C).(eq C c1 (CHead d2 (Bind Abst)
-u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
-C).(\lambda (u2: T).(\lambda (_: A).(eq C c1 (CHead d2 (Bind Abbr) u2)))))
-(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
-(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))))))
-(\lambda (n: nat).(\lambda (H1: (eq C (CSort n) (CHead d1 (Bind Abst)
-u1))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee in C return
-(\lambda (_: C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _)
-\Rightarrow False])) I (CHead d1 (Bind Abst) u1) H1) in (False_ind (or (ex2 C
-(\lambda (d2: C).(eq C (CSort n) (CHead d2 (Bind Abst) u1))) (\lambda (d2:
-C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
-(_: A).(eq C (CSort n) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
-C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
-C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) H2))))
-(\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda
-(H2: (((eq C c1 (CHead d1 (Bind Abst) u1)) \to (or (ex2 C (\lambda (d2:
-C).(eq C c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
-(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2
-(CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
-A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
-g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
-A).(arity g d2 u2 a))))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3:
-(eq C (CHead c1 k u) (CHead d1 (Bind Abst) u1))).(let H4 \def (f_equal C C
-(\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
-\Rightarrow c1 | (CHead c0 _ _) \Rightarrow c0])) (CHead c1 k u) (CHead d1
-(Bind Abst) u1) H3) in ((let H5 \def (f_equal C K (\lambda (e: C).(match e in
-C return (\lambda (_: C).K) with [(CSort _) \Rightarrow k | (CHead _ k0 _)
-\Rightarrow k0])) (CHead c1 k u) (CHead d1 (Bind Abst) u1) H3) in ((let H6
-\def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T)
-with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t])) (CHead c1 k u)
-(CHead d1 (Bind Abst) u1) H3) in (\lambda (H7: (eq K k (Bind Abst))).(\lambda
-(H8: (eq C c1 d1)).(eq_ind_r T u1 (\lambda (t: T).(or (ex2 C (\lambda (d2:
-C).(eq C (CHead c2 k t) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g
-d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C
-(CHead c2 k t) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
-T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
-T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
-(u2: T).(\lambda (a: A).(arity g d2 u2 a))))))) (eq_ind_r K (Bind Abst)
-(\lambda (k0: K).(or (ex2 C (\lambda (d2: C).(eq C (CHead c2 k0 u1) (CHead d2
-(Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C (CHead c2 k0 u1) (CHead d2
-(Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
-d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
-(asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
-u2 a))))))) (let H9 \def (eq_ind C c1 (\lambda (c0: C).((eq C c0 (CHead d1
-(Bind Abst) u1)) \to (or (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind
-Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
-C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abbr) u2)))))
-(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
-(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))))) H2
-d1 H8) in (let H10 \def (eq_ind C c1 (\lambda (c0: C).(csuba g c0 c2)) H1 d1
-H8) in (or_introl (ex2 C (\lambda (d2: C).(eq C (CHead c2 (Bind Abst) u1)
-(CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C (CHead c2 (Bind Abst)
-u1) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
-(_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a:
-A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda
-(a: A).(arity g d2 u2 a))))) (ex_intro2 C (\lambda (d2: C).(eq C (CHead c2
-(Bind Abst) u1) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))
-c2 (refl_equal C (CHead c2 (Bind Abst) u1)) H10)))) k H7) u H6)))) H5))
-H4))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (_: (csuba g c1
-c2)).(\lambda (_: (((eq C c1 (CHead d1 (Bind Abst) u1)) \to (or (ex2 C
-(\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba
-g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq
-C c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
-(_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a:
-A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda
-(a: A).(arity g d2 u2 a))))))))).(\lambda (b: B).(\lambda (_: (not (eq B b
-Void))).(\lambda (u0: T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c1 (Bind
-Void) u0) (CHead d1 (Bind Abst) u1))).(let H5 \def (eq_ind C (CHead c1 (Bind
-Void) u0) (\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with
-[(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match k in K return
-(\lambda (_: K).Prop) with [(Bind b0) \Rightarrow (match b0 in B return
-(\lambda (_: B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow False |
-Void \Rightarrow True]) | (Flat _) \Rightarrow False])])) I (CHead d1 (Bind
-Abst) u1) H4) in (False_ind (or (ex2 C (\lambda (d2: C).(eq C (CHead c2 (Bind
-b) u2) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3
-C T A (\lambda (d2: C).(\lambda (u3: T).(\lambda (_: A).(eq C (CHead c2 (Bind
-b) u2) (CHead d2 (Bind Abbr) u3))))) (\lambda (d2: C).(\lambda (_:
-T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
-T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
-(u3: T).(\lambda (a: A).(arity g d2 u3 a)))))) H5))))))))))) (\lambda (c1:
-C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c1
-(CHead d1 (Bind Abst) u1)) \to (or (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2
-(Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abbr)
-u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
-(\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
-a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
-a))))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (H3: (arity g c1 t (asucc
-g a))).(\lambda (u: T).(\lambda (H4: (arity g c2 u a)).(\lambda (H5: (eq C
-(CHead c1 (Bind Abst) t) (CHead d1 (Bind Abst) u1))).(let H6 \def (f_equal C
-C (\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
-\Rightarrow c1 | (CHead c0 _ _) \Rightarrow c0])) (CHead c1 (Bind Abst) t)
-(CHead d1 (Bind Abst) u1) H5) in ((let H7 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow t |
-(CHead _ _ t0) \Rightarrow t0])) (CHead c1 (Bind Abst) t) (CHead d1 (Bind
-Abst) u1) H5) in (\lambda (H8: (eq C c1 d1)).(let H9 \def (eq_ind T t
-(\lambda (t0: T).(arity g c1 t0 (asucc g a))) H3 u1 H7) in (let H10 \def
-(eq_ind C c1 (\lambda (c0: C).(arity g c0 u1 (asucc g a))) H9 d1 H8) in (let
-H11 \def (eq_ind C c1 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind Abst) u1))
-\to (or (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) u1))) (\lambda
-(d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
-T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
-C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
-C).(\lambda (_: T).(\lambda (a0: A).(arity g d1 u1 (asucc g a0))))) (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (a0: A).(arity g d2 u2 a0)))))))) H2 d1 H8)
-in (let H12 \def (eq_ind C c1 (\lambda (c0: C).(csuba g c0 c2)) H1 d1 H8) in
-(or_intror (ex2 C (\lambda (d2: C).(eq C (CHead c2 (Bind Abbr) u) (CHead d2
-(Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C (CHead c2 (Bind Abbr) u)
-(CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
-A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a0: A).(arity
-g d1 u1 (asucc g a0))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a0:
-A).(arity g d2 u2 a0))))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2:
-T).(\lambda (_: A).(eq C (CHead c2 (Bind Abbr) u) (CHead d2 (Bind Abbr)
-u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
-(\lambda (_: C).(\lambda (_: T).(\lambda (a0: A).(arity g d1 u1 (asucc g
-a0))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a0: A).(arity g d2 u2
-a0)))) c2 u a (refl_equal C (CHead c2 (Bind Abbr) u)) H12 H10 H4))))))))
-H6)))))))))))) y c H0))) H))))).
-(* COMMENTS
-Initial nodes: 2550
-END *)
-
-theorem csuba_gen_flat:
- \forall (g: G).(\forall (d1: C).(\forall (c: C).(\forall (u1: T).(\forall
-(f: F).((csuba g (CHead d1 (Flat f) u1) c) \to (ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(eq C c (CHead d2 (Flat f) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d1 d2)))))))))
-\def
- \lambda (g: G).(\lambda (d1: C).(\lambda (c: C).(\lambda (u1: T).(\lambda
-(f: F).(\lambda (H: (csuba g (CHead d1 (Flat f) u1) c)).(insert_eq C (CHead
-d1 (Flat f) u1) (\lambda (c0: C).(csuba g c0 c)) (\lambda (_: C).(ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(eq C c (CHead d2 (Flat f) u2)))) (\lambda
-(d2: C).(\lambda (_: T).(csuba g d1 d2))))) (\lambda (y: C).(\lambda (H0:
-(csuba g y c)).(csuba_ind g (\lambda (c0: C).(\lambda (c1: C).((eq C c0
-(CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
-C c1 (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2))))))) (\lambda (n: nat).(\lambda (H1: (eq C (CSort n) (CHead d1 (Flat f)
-u1))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee in C return
-(\lambda (_: C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _)
-\Rightarrow False])) I (CHead d1 (Flat f) u1) H1) in (False_ind (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(eq C (CSort n) (CHead d2 (Flat f) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2)))) H2)))) (\lambda (c1:
-C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c1
-(CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
-C c2 (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c1 k u)
-(CHead d1 (Flat f) u1))).(let H4 \def (f_equal C C (\lambda (e: C).(match e
-in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c1 | (CHead c0 _
-_) \Rightarrow c0])) (CHead c1 k u) (CHead d1 (Flat f) u1) H3) in ((let H5
-\def (f_equal C K (\lambda (e: C).(match e in C return (\lambda (_: C).K)
-with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c1 k
-u) (CHead d1 (Flat f) u1) H3) in ((let H6 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u |
-(CHead _ _ t) \Rightarrow t])) (CHead c1 k u) (CHead d1 (Flat f) u1) H3) in
-(\lambda (H7: (eq K k (Flat f))).(\lambda (H8: (eq C c1 d1)).(eq_ind_r T u1
-(\lambda (t: T).(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c2
-k t) (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2))))) (eq_ind_r K (Flat f) (\lambda (k0: K).(ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(eq C (CHead c2 k0 u1) (CHead d2 (Flat f) u2)))) (\lambda
-(d2: C).(\lambda (_: T).(csuba g d1 d2))))) (let H9 \def (eq_ind C c1
-(\lambda (c0: C).((eq C c0 (CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda
-(d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Flat f) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d1 d2)))))) H2 d1 H8) in (let H10 \def (eq_ind C
-c1 (\lambda (c0: C).(csuba g c0 c2)) H1 d1 H8) in (ex2_2_intro C T (\lambda
-(d2: C).(\lambda (u2: T).(eq C (CHead c2 (Flat f) u1) (CHead d2 (Flat f)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2))) c2 u1 (refl_equal C
-(CHead c2 (Flat f) u1)) H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
-C).(\lambda (c2: C).(\lambda (_: (csuba g c1 c2)).(\lambda (_: (((eq C c1
-(CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
-C c2 (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2))))))).(\lambda (b: B).(\lambda (_: (not (eq B b Void))).(\lambda (u0:
-T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c1 (Bind Void) u0) (CHead d1
-(Flat f) u1))).(let H5 \def (eq_ind C (CHead c1 (Bind Void) u0) (\lambda (ee:
-C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow
-False | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop)
-with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead d1
-(Flat f) u1) H4) in (False_ind (ex2_2 C T (\lambda (d2: C).(\lambda (u3:
-T).(eq C (CHead c2 (Bind b) u2) (CHead d2 (Flat f) u3)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d1 d2)))) H5))))))))))) (\lambda (c1: C).(\lambda
-(c2: C).(\lambda (_: (csuba g c1 c2)).(\lambda (_: (((eq C c1 (CHead d1 (Flat
-f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2
-(Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (_: (arity g c1 t (asucc g
-a))).(\lambda (u: T).(\lambda (_: (arity g c2 u a)).(\lambda (H5: (eq C
-(CHead c1 (Bind Abst) t) (CHead d1 (Flat f) u1))).(let H6 \def (eq_ind C
-(CHead c1 (Bind Abst) t) (\lambda (ee: C).(match ee in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match
-k in K return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow True | (Flat
-_) \Rightarrow False])])) I (CHead d1 (Flat f) u1) H5) in (False_ind (ex2_2 C
-T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c2 (Bind Abbr) u) (CHead d2
-(Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2))))
-H6)))))))))))) y c H0))) H)))))).
-(* COMMENTS
-Initial nodes: 1183
-END *)
-
-theorem csuba_gen_bind:
- \forall (g: G).(\forall (b1: B).(\forall (e1: C).(\forall (c2: C).(\forall
-(v1: T).((csuba g (CHead e1 (Bind b1) v1) c2) \to (ex2_3 B C T (\lambda (b2:
-B).(\lambda (e2: C).(\lambda (v2: T).(eq C c2 (CHead e2 (Bind b2) v2)))))
-(\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e1 e2))))))))))
-\def
- \lambda (g: G).(\lambda (b1: B).(\lambda (e1: C).(\lambda (c2: C).(\lambda
-(v1: T).(\lambda (H: (csuba g (CHead e1 (Bind b1) v1) c2)).(insert_eq C
-(CHead e1 (Bind b1) v1) (\lambda (c: C).(csuba g c c2)) (\lambda (_:
-C).(ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c2
-(CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csuba g e1 e2)))))) (\lambda (y: C).(\lambda (H0: (csuba g y
-c2)).(csuba_ind g (\lambda (c: C).(\lambda (c0: C).((eq C c (CHead e1 (Bind
-b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2:
-T).(eq C c0 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
-C).(\lambda (_: T).(csuba g e1 e2)))))))) (\lambda (n: nat).(\lambda (H1: (eq
-C (CSort n) (CHead e1 (Bind b1) v1))).(let H2 \def (eq_ind C (CSort n)
-(\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _)
-\Rightarrow True | (CHead _ _ _) \Rightarrow False])) I (CHead e1 (Bind b1)
-v1) H1) in (False_ind (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda
-(v2: T).(eq C (CSort n) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda
-(e2: C).(\lambda (_: T).(csuba g e1 e2))))) H2)))) (\lambda (c1: C).(\lambda
-(c3: C).(\lambda (H1: (csuba g c1 c3)).(\lambda (H2: (((eq C c1 (CHead e1
-(Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda
-(v2: T).(eq C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
-C).(\lambda (_: T).(csuba g e1 e2)))))))).(\lambda (k: K).(\lambda (u:
-T).(\lambda (H3: (eq C (CHead c1 k u) (CHead e1 (Bind b1) v1))).(let H4 \def
-(f_equal C C (\lambda (e: C).(match e in C return (\lambda (_: C).C) with
-[(CSort _) \Rightarrow c1 | (CHead c _ _) \Rightarrow c])) (CHead c1 k u)
-(CHead e1 (Bind b1) v1) H3) in ((let H5 \def (f_equal C K (\lambda (e:
-C).(match e in C return (\lambda (_: C).K) with [(CSort _) \Rightarrow k |
-(CHead _ k0 _) \Rightarrow k0])) (CHead c1 k u) (CHead e1 (Bind b1) v1) H3)
-in ((let H6 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda
-(_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t]))
-(CHead c1 k u) (CHead e1 (Bind b1) v1) H3) in (\lambda (H7: (eq K k (Bind
-b1))).(\lambda (H8: (eq C c1 e1)).(eq_ind_r T v1 (\lambda (t: T).(ex2_3 B C T
-(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 k t)
-(CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csuba g e1 e2)))))) (eq_ind_r K (Bind b1) (\lambda (k0: K).(ex2_3 B C T
-(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 k0 v1)
-(CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csuba g e1 e2)))))) (let H9 \def (eq_ind C c1 (\lambda (c: C).((eq C c
-(CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2:
-C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_:
-B).(\lambda (e2: C).(\lambda (_: T).(csuba g e1 e2))))))) H2 e1 H8) in (let
-H10 \def (eq_ind C c1 (\lambda (c: C).(csuba g c c3)) H1 e1 H8) in
-(ex2_3_intro B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C
-(CHead c3 (Bind b1) v1) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda
-(e2: C).(\lambda (_: T).(csuba g e1 e2)))) b1 c3 v1 (refl_equal C (CHead c3
-(Bind b1) v1)) H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
-C).(\lambda (c3: C).(\lambda (H1: (csuba g c1 c3)).(\lambda (H2: (((eq C c1
-(CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2:
-C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_:
-B).(\lambda (e2: C).(\lambda (_: T).(csuba g e1 e2)))))))).(\lambda (b:
-B).(\lambda (_: (not (eq B b Void))).(\lambda (u1: T).(\lambda (u2:
-T).(\lambda (H4: (eq C (CHead c1 (Bind Void) u1) (CHead e1 (Bind b1)
-v1))).(let H5 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda
-(_: C).C) with [(CSort _) \Rightarrow c1 | (CHead c _ _) \Rightarrow c]))
-(CHead c1 (Bind Void) u1) (CHead e1 (Bind b1) v1) H4) in ((let H6 \def
-(f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with
-[(CSort _) \Rightarrow Void | (CHead _ k _) \Rightarrow (match k in K return
-(\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow
-Void])])) (CHead c1 (Bind Void) u1) (CHead e1 (Bind b1) v1) H4) in ((let H7
-\def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T)
-with [(CSort _) \Rightarrow u1 | (CHead _ _ t) \Rightarrow t])) (CHead c1
-(Bind Void) u1) (CHead e1 (Bind b1) v1) H4) in (\lambda (H8: (eq B Void
-b1)).(\lambda (H9: (eq C c1 e1)).(let H10 \def (eq_ind C c1 (\lambda (c:
-C).((eq C c (CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2:
-B).(\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind b2) v2)))))
-(\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e1 e2))))))) H2 e1
-H9) in (let H11 \def (eq_ind C c1 (\lambda (c: C).(csuba g c c3)) H1 e1 H9)
-in (let H12 \def (eq_ind_r B b1 (\lambda (b0: B).((eq C e1 (CHead e1 (Bind
-b0) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2:
-T).(eq C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
-C).(\lambda (_: T).(csuba g e1 e2))))))) H10 Void H8) in (ex2_3_intro B C T
-(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 (Bind b)
-u2) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csuba g e1 e2)))) b c3 u2 (refl_equal C (CHead c3 (Bind b) u2))
-H11))))))) H6)) H5))))))))))) (\lambda (c1: C).(\lambda (c3: C).(\lambda (H1:
-(csuba g c1 c3)).(\lambda (H2: (((eq C c1 (CHead e1 (Bind b1) v1)) \to (ex2_3
-B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2
-(Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g
-e1 e2)))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (H3: (arity g c1 t
-(asucc g a))).(\lambda (u: T).(\lambda (_: (arity g c3 u a)).(\lambda (H5:
-(eq C (CHead c1 (Bind Abst) t) (CHead e1 (Bind b1) v1))).(let H6 \def
-(f_equal C C (\lambda (e: C).(match e in C return (\lambda (_: C).C) with
-[(CSort _) \Rightarrow c1 | (CHead c _ _) \Rightarrow c])) (CHead c1 (Bind
-Abst) t) (CHead e1 (Bind b1) v1) H5) in ((let H7 \def (f_equal C B (\lambda
-(e: C).(match e in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow
-Abst | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).B) with
-[(Bind b) \Rightarrow b | (Flat _) \Rightarrow Abst])])) (CHead c1 (Bind
-Abst) t) (CHead e1 (Bind b1) v1) H5) in ((let H8 \def (f_equal C T (\lambda
-(e: C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow t
-| (CHead _ _ t0) \Rightarrow t0])) (CHead c1 (Bind Abst) t) (CHead e1 (Bind
-b1) v1) H5) in (\lambda (H9: (eq B Abst b1)).(\lambda (H10: (eq C c1
-e1)).(let H11 \def (eq_ind T t (\lambda (t0: T).(arity g c1 t0 (asucc g a)))
-H3 v1 H8) in (let H12 \def (eq_ind C c1 (\lambda (c: C).(arity g c v1 (asucc
-g a))) H11 e1 H10) in (let H13 \def (eq_ind C c1 (\lambda (c: C).((eq C c
-(CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2:
-C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_:
-B).(\lambda (e2: C).(\lambda (_: T).(csuba g e1 e2))))))) H2 e1 H10) in (let
-H14 \def (eq_ind C c1 (\lambda (c: C).(csuba g c c3)) H1 e1 H10) in (let H15
-\def (eq_ind_r B b1 (\lambda (b: B).((eq C e1 (CHead e1 (Bind b) v1)) \to
-(ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c3
-(CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csuba g e1 e2))))))) H13 Abst H9) in (ex2_3_intro B C T (\lambda (b2:
-B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 (Bind Abbr) u) (CHead e2
-(Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g
-e1 e2)))) Abbr c3 u (refl_equal C (CHead c3 (Bind Abbr) u)) H14))))))))) H7))
-H6)))))))))))) y c2 H0))) H)))))).
-(* COMMENTS
-Initial nodes: 1889
-END *)
-
-theorem csuba_gen_abst_rev:
- \forall (g: G).(\forall (d1: C).(\forall (c: C).(\forall (u: T).((csuba g c
-(CHead d1 (Bind Abst) u)) \to (or (ex2 C (\lambda (d2: C).(eq C c (CHead d2
-(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(eq C c (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1)))))))))
-\def
- \lambda (g: G).(\lambda (d1: C).(\lambda (c: C).(\lambda (u: T).(\lambda (H:
-(csuba g c (CHead d1 (Bind Abst) u))).(insert_eq C (CHead d1 (Bind Abst) u)
-(\lambda (c0: C).(csuba g c c0)) (\lambda (_: C).(or (ex2 C (\lambda (d2:
-C).(eq C c (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (\lambda (y:
-C).(\lambda (H0: (csuba g c y)).(csuba_ind g (\lambda (c0: C).(\lambda (c1:
-C).((eq C c1 (CHead d1 (Bind Abst) u)) \to (or (ex2 C (\lambda (d2: C).(eq C
-c0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(eq C c0 (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))) (\lambda (n:
-nat).(\lambda (H1: (eq C (CSort n) (CHead d1 (Bind Abst) u))).(let H2 \def
-(eq_ind C (CSort n) (\lambda (ee: C).(match ee in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _) \Rightarrow
-False])) I (CHead d1 (Bind Abst) u) H1) in (False_ind (or (ex2 C (\lambda
-(d2: C).(eq C (CSort n) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g
-d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CSort n) (CHead
-d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))
-H2)))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1
-c2)).(\lambda (H2: (((eq C c2 (CHead d1 (Bind Abst) u)) \to (or (ex2 C
-(\lambda (d2: C).(eq C c1 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba
-g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2
-(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))))))).(\lambda (k: K).(\lambda (u0: T).(\lambda (H3: (eq C (CHead c2 k
-u0) (CHead d1 (Bind Abst) u))).(let H4 \def (f_equal C C (\lambda (e:
-C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c2 |
-(CHead c0 _ _) \Rightarrow c0])) (CHead c2 k u0) (CHead d1 (Bind Abst) u) H3)
-in ((let H5 \def (f_equal C K (\lambda (e: C).(match e in C return (\lambda
-(_: C).K) with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0]))
-(CHead c2 k u0) (CHead d1 (Bind Abst) u) H3) in ((let H6 \def (f_equal C T
-(\lambda (e: C).(match e in C return (\lambda (_: C).T) with [(CSort _)
-\Rightarrow u0 | (CHead _ _ t) \Rightarrow t])) (CHead c2 k u0) (CHead d1
-(Bind Abst) u) H3) in (\lambda (H7: (eq K k (Bind Abst))).(\lambda (H8: (eq C
-c2 d1)).(eq_ind_r T u (\lambda (t: T).(or (ex2 C (\lambda (d2: C).(eq C
-(CHead c1 k t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c1 k t) (CHead d2
-(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))
-(eq_ind_r K (Bind Abst) (\lambda (k0: K).(or (ex2 C (\lambda (d2: C).(eq C
-(CHead c1 k0 u) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c1 k0 u) (CHead d2
-(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let
-H9 \def (eq_ind C c2 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind Abst) u)) \to
-(or (ex2 C (\lambda (d2: C).(eq C c1 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1
-(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1))))))) H2 d1 H8) in (let H10 \def (eq_ind C c2 (\lambda (c0: C).(csuba g
-c1 c0)) H1 d1 H8) in (or_introl (ex2 C (\lambda (d2: C).(eq C (CHead c1 (Bind
-Abst) u) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2
-C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c1 (Bind Abst) u) (CHead
-d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))
-(ex_intro2 C (\lambda (d2: C).(eq C (CHead c1 (Bind Abst) u) (CHead d2 (Bind
-Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) c1 (refl_equal C (CHead c1 (Bind
-Abst) u)) H10)))) k H7) u0 H6)))) H5)) H4))))))))) (\lambda (c1: C).(\lambda
-(c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c2 (CHead d1
-(Bind Abst) u)) \to (or (ex2 C (\lambda (d2: C).(eq C c1 (CHead d2 (Bind
-Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(eq C c1 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1)))))))).(\lambda (b: B).(\lambda (H3: (not
-(eq B b Void))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead
-c2 (Bind b) u2) (CHead d1 (Bind Abst) u))).(let H5 \def (f_equal C C (\lambda
-(e: C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c2
-| (CHead c0 _ _) \Rightarrow c0])) (CHead c2 (Bind b) u2) (CHead d1 (Bind
-Abst) u) H4) in ((let H6 \def (f_equal C B (\lambda (e: C).(match e in C
-return (\lambda (_: C).B) with [(CSort _) \Rightarrow b | (CHead _ k _)
-\Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind b0)
-\Rightarrow b0 | (Flat _) \Rightarrow b])])) (CHead c2 (Bind b) u2) (CHead d1
-(Bind Abst) u) H4) in ((let H7 \def (f_equal C T (\lambda (e: C).(match e in
-C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u2 | (CHead _ _ t)
-\Rightarrow t])) (CHead c2 (Bind b) u2) (CHead d1 (Bind Abst) u) H4) in
-(\lambda (H8: (eq B b Abst)).(\lambda (H9: (eq C c2 d1)).(let H10 \def
-(eq_ind B b (\lambda (b0: B).(not (eq B b0 Void))) H3 Abst H8) in (let H11
-\def (eq_ind C c2 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind Abst) u)) \to
-(or (ex2 C (\lambda (d2: C).(eq C c1 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u3: T).(eq C c1
-(CHead d2 (Bind Void) u3)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1))))))) H2 d1 H9) in (let H12 \def (eq_ind C c2 (\lambda (c0: C).(csuba g
-c1 c0)) H1 d1 H9) in (or_intror (ex2 C (\lambda (d2: C).(eq C (CHead c1 (Bind
-Void) u1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u3: T).(eq C (CHead c1 (Bind Void) u1)
-(CHead d2 (Bind Void) u3)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u3: T).(eq C (CHead c1
-(Bind Void) u1) (CHead d2 (Bind Void) u3)))) (\lambda (d2: C).(\lambda (_:
-T).(csuba g d2 d1))) c1 u1 (refl_equal C (CHead c1 (Bind Void) u1))
-H12)))))))) H6)) H5))))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (_:
-(csuba g c1 c2)).(\lambda (_: (((eq C c2 (CHead d1 (Bind Abst) u)) \to (or
-(ex2 C (\lambda (d2: C).(eq C c1 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1
-(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (_: (arity g c1 t (asucc
-g a))).(\lambda (u0: T).(\lambda (_: (arity g c2 u0 a)).(\lambda (H5: (eq C
-(CHead c2 (Bind Abbr) u0) (CHead d1 (Bind Abst) u))).(let H6 \def (eq_ind C
-(CHead c2 (Bind Abbr) u0) (\lambda (ee: C).(match ee in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match
-k in K return (\lambda (_: K).Prop) with [(Bind b) \Rightarrow (match b in B
-return (\lambda (_: B).Prop) with [Abbr \Rightarrow True | Abst \Rightarrow
-False | Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead
-d1 (Bind Abst) u) H5) in (False_ind (or (ex2 C (\lambda (d2: C).(eq C (CHead
-c1 (Bind Abst) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2
-d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c1 (Bind
-Abst) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba
-g d2 d1))))) H6)))))))))))) c y H0))) H))))).
-(* COMMENTS
-Initial nodes: 1980
-END *)
-
-theorem csuba_gen_void_rev:
- \forall (g: G).(\forall (d1: C).(\forall (c: C).(\forall (u: T).((csuba g c
-(CHead d1 (Bind Void) u)) \to (ex2 C (\lambda (d2: C).(eq C c (CHead d2 (Bind
-Void) u))) (\lambda (d2: C).(csuba g d2 d1)))))))
-\def
- \lambda (g: G).(\lambda (d1: C).(\lambda (c: C).(\lambda (u: T).(\lambda (H:
-(csuba g c (CHead d1 (Bind Void) u))).(insert_eq C (CHead d1 (Bind Void) u)
-(\lambda (c0: C).(csuba g c c0)) (\lambda (_: C).(ex2 C (\lambda (d2: C).(eq
-C c (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1)))) (\lambda
-(y: C).(\lambda (H0: (csuba g c y)).(csuba_ind g (\lambda (c0: C).(\lambda
-(c1: C).((eq C c1 (CHead d1 (Bind Void) u)) \to (ex2 C (\lambda (d2: C).(eq C
-c0 (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1)))))) (\lambda
-(n: nat).(\lambda (H1: (eq C (CSort n) (CHead d1 (Bind Void) u))).(let H2
-\def (eq_ind C (CSort n) (\lambda (ee: C).(match ee in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _) \Rightarrow
-False])) I (CHead d1 (Bind Void) u) H1) in (False_ind (ex2 C (\lambda (d2:
-C).(eq C (CSort n) (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2
-d1))) H2)))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1
-c2)).(\lambda (H2: (((eq C c2 (CHead d1 (Bind Void) u)) \to (ex2 C (\lambda
-(d2: C).(eq C c1 (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2
-d1)))))).(\lambda (k: K).(\lambda (u0: T).(\lambda (H3: (eq C (CHead c2 k u0)
-(CHead d1 (Bind Void) u))).(let H4 \def (f_equal C C (\lambda (e: C).(match e
-in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c2 | (CHead c0 _
-_) \Rightarrow c0])) (CHead c2 k u0) (CHead d1 (Bind Void) u) H3) in ((let H5
-\def (f_equal C K (\lambda (e: C).(match e in C return (\lambda (_: C).K)
-with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c2 k
-u0) (CHead d1 (Bind Void) u) H3) in ((let H6 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u0 |
-(CHead _ _ t) \Rightarrow t])) (CHead c2 k u0) (CHead d1 (Bind Void) u) H3)
-in (\lambda (H7: (eq K k (Bind Void))).(\lambda (H8: (eq C c2 d1)).(eq_ind_r
-T u (\lambda (t: T).(ex2 C (\lambda (d2: C).(eq C (CHead c1 k t) (CHead d2
-(Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1)))) (eq_ind_r K (Bind Void)
-(\lambda (k0: K).(ex2 C (\lambda (d2: C).(eq C (CHead c1 k0 u) (CHead d2
-(Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1)))) (let H9 \def (eq_ind C
-c2 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind Void) u)) \to (ex2 C (\lambda
-(d2: C).(eq C c1 (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2
-d1))))) H2 d1 H8) in (let H10 \def (eq_ind C c2 (\lambda (c0: C).(csuba g c1
-c0)) H1 d1 H8) in (ex_intro2 C (\lambda (d2: C).(eq C (CHead c1 (Bind Void)
-u) (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1)) c1
-(refl_equal C (CHead c1 (Bind Void) u)) H10))) k H7) u0 H6)))) H5))
-H4))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1
-c2)).(\lambda (H2: (((eq C c2 (CHead d1 (Bind Void) u)) \to (ex2 C (\lambda
-(d2: C).(eq C c1 (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2
-d1)))))).(\lambda (b: B).(\lambda (H3: (not (eq B b Void))).(\lambda (u1:
-T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c2 (Bind b) u2) (CHead d1
-(Bind Void) u))).(let H5 \def (f_equal C C (\lambda (e: C).(match e in C
-return (\lambda (_: C).C) with [(CSort _) \Rightarrow c2 | (CHead c0 _ _)
-\Rightarrow c0])) (CHead c2 (Bind b) u2) (CHead d1 (Bind Void) u) H4) in
-((let H6 \def (f_equal C B (\lambda (e: C).(match e in C return (\lambda (_:
-C).B) with [(CSort _) \Rightarrow b | (CHead _ k _) \Rightarrow (match k in K
-return (\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _)
-\Rightarrow b])])) (CHead c2 (Bind b) u2) (CHead d1 (Bind Void) u) H4) in
-((let H7 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_:
-C).T) with [(CSort _) \Rightarrow u2 | (CHead _ _ t) \Rightarrow t])) (CHead
-c2 (Bind b) u2) (CHead d1 (Bind Void) u) H4) in (\lambda (H8: (eq B b
-Void)).(\lambda (H9: (eq C c2 d1)).(let H10 \def (eq_ind B b (\lambda (b0:
-B).(not (eq B b0 Void))) H3 Void H8) in (let H11 \def (eq_ind C c2 (\lambda
-(c0: C).((eq C c0 (CHead d1 (Bind Void) u)) \to (ex2 C (\lambda (d2: C).(eq C
-c1 (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1))))) H2 d1 H9)
-in (let H12 \def (eq_ind C c2 (\lambda (c0: C).(csuba g c1 c0)) H1 d1 H9) in
-(let H13 \def (match (H10 (refl_equal B Void)) in False return (\lambda (_:
-False).(ex2 C (\lambda (d2: C).(eq C (CHead c1 (Bind Void) u1) (CHead d2
-(Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1)))) with []) in H13)))))))
-H6)) H5))))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (_: (csuba g c1
-c2)).(\lambda (_: (((eq C c2 (CHead d1 (Bind Void) u)) \to (ex2 C (\lambda
-(d2: C).(eq C c1 (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2
-d1)))))).(\lambda (t: T).(\lambda (a: A).(\lambda (_: (arity g c1 t (asucc g
-a))).(\lambda (u0: T).(\lambda (_: (arity g c2 u0 a)).(\lambda (H5: (eq C
-(CHead c2 (Bind Abbr) u0) (CHead d1 (Bind Void) u))).(let H6 \def (eq_ind C
-(CHead c2 (Bind Abbr) u0) (\lambda (ee: C).(match ee in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match
-k in K return (\lambda (_: K).Prop) with [(Bind b) \Rightarrow (match b in B
-return (\lambda (_: B).Prop) with [Abbr \Rightarrow True | Abst \Rightarrow
-False | Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead
-d1 (Bind Void) u) H5) in (False_ind (ex2 C (\lambda (d2: C).(eq C (CHead c1
-(Bind Abst) t) (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1)))
-H6)))))))))))) c y H0))) H))))).
-(* COMMENTS
-Initial nodes: 1326
-END *)
-
-theorem csuba_gen_abbr_rev:
- \forall (g: G).(\forall (d1: C).(\forall (c: C).(\forall (u1: T).((csuba g c
-(CHead d1 (Bind Abbr) u1)) \to (or3 (ex2 C (\lambda (d2: C).(eq C c (CHead d2
-(Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c (CHead d2 (Bind Abst)
-u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
-a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))))
-\def
- \lambda (g: G).(\lambda (d1: C).(\lambda (c: C).(\lambda (u1: T).(\lambda
-(H: (csuba g c (CHead d1 (Bind Abbr) u1))).(insert_eq C (CHead d1 (Bind Abbr)
-u1) (\lambda (c0: C).(csuba g c c0)) (\lambda (_: C).(or3 (ex2 C (\lambda
-(d2: C).(eq C c (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
-d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c
-(CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
-A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
-A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
-(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
-C c (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))))) (\lambda (y: C).(\lambda (H0: (csuba g c y)).(csuba_ind g (\lambda
-(c0: C).(\lambda (c1: C).((eq C c1 (CHead d1 (Bind Abbr) u1)) \to (or3 (ex2 C
-(\lambda (d2: C).(eq C c0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba
-g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq
-C c0 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
-(_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
-A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
-(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
-C c0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
-d2 d1)))))))) (\lambda (n: nat).(\lambda (H1: (eq C (CSort n) (CHead d1 (Bind
-Abbr) u1))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee in C
-return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _)
-\Rightarrow False])) I (CHead d1 (Bind Abbr) u1) H1) in (False_ind (or3 (ex2
-C (\lambda (d2: C).(eq C (CSort n) (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
-C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
-(_: A).(eq C (CSort n) (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
-C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
-C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
-(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(eq C (CSort n) (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) H2)))) (\lambda
-(c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C
-c2 (CHead d1 (Bind Abbr) u1)) \to (or3 (ex2 C (\lambda (d2: C).(eq C c1
-(CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c1 (CHead d2 (Bind
-Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
-d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
-(asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
-u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2
-(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c2 k u)
-(CHead d1 (Bind Abbr) u1))).(let H4 \def (f_equal C C (\lambda (e: C).(match
-e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c2 | (CHead c0 _
-_) \Rightarrow c0])) (CHead c2 k u) (CHead d1 (Bind Abbr) u1) H3) in ((let H5
-\def (f_equal C K (\lambda (e: C).(match e in C return (\lambda (_: C).K)
-with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c2 k
-u) (CHead d1 (Bind Abbr) u1) H3) in ((let H6 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u |
-(CHead _ _ t) \Rightarrow t])) (CHead c2 k u) (CHead d1 (Bind Abbr) u1) H3)
-in (\lambda (H7: (eq K k (Bind Abbr))).(\lambda (H8: (eq C c2 d1)).(eq_ind_r
-T u1 (\lambda (t: T).(or3 (ex2 C (\lambda (d2: C).(eq C (CHead c1 k t) (CHead
-d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C (CHead c1 k t) (CHead d2 (Bind
-Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
-d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
-(asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
-u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c1 k t)
-(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))))) (eq_ind_r K (Bind Abbr) (\lambda (k0: K).(or3 (ex2 C (\lambda (d2:
-C).(eq C (CHead c1 k0 u1) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba
-g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq
-C (CHead c1 k0 u1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda
-(_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
-T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
-(_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(eq C (CHead c1 k0 u1) (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let H9 \def (eq_ind C
-c2 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind Abbr) u1)) \to (or3 (ex2 C
-(\lambda (d2: C).(eq C c1 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba
-g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq
-C c1 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
-(_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
-A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
-(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
-C c1 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
-d2 d1))))))) H2 d1 H8) in (let H10 \def (eq_ind C c2 (\lambda (c0: C).(csuba
-g c1 c0)) H1 d1 H8) in (or3_intro0 (ex2 C (\lambda (d2: C).(eq C (CHead c1
-(Bind Abbr) u1) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
-d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C
-(CHead c1 (Bind Abbr) u1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
-C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
-C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
-(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c1 (Bind Abbr) u1) (CHead d2
-(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))
-(ex_intro2 C (\lambda (d2: C).(eq C (CHead c1 (Bind Abbr) u1) (CHead d2 (Bind
-Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) c1 (refl_equal C (CHead c1
-(Bind Abbr) u1)) H10)))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
-C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c2
-(CHead d1 (Bind Abbr) u1)) \to (or3 (ex2 C (\lambda (d2: C).(eq C c1 (CHead
-d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c1 (CHead d2 (Bind Abst)
-u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
-a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))).(\lambda (b:
-B).(\lambda (H3: (not (eq B b Void))).(\lambda (u0: T).(\lambda (u2:
-T).(\lambda (H4: (eq C (CHead c2 (Bind b) u2) (CHead d1 (Bind Abbr)
-u1))).(let H5 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda
-(_: C).C) with [(CSort _) \Rightarrow c2 | (CHead c0 _ _) \Rightarrow c0]))
-(CHead c2 (Bind b) u2) (CHead d1 (Bind Abbr) u1) H4) in ((let H6 \def
-(f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with
-[(CSort _) \Rightarrow b | (CHead _ k _) \Rightarrow (match k in K return
-(\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow
-b])])) (CHead c2 (Bind b) u2) (CHead d1 (Bind Abbr) u1) H4) in ((let H7 \def
-(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with
-[(CSort _) \Rightarrow u2 | (CHead _ _ t) \Rightarrow t])) (CHead c2 (Bind b)
-u2) (CHead d1 (Bind Abbr) u1) H4) in (\lambda (H8: (eq B b Abbr)).(\lambda
-(H9: (eq C c2 d1)).(let H10 \def (eq_ind B b (\lambda (b0: B).(not (eq B b0
-Void))) H3 Abbr H8) in (let H11 \def (eq_ind C c2 (\lambda (c0: C).((eq C c0
-(CHead d1 (Bind Abbr) u1)) \to (or3 (ex2 C (\lambda (d2: C).(eq C c1 (CHead
-d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u3: T).(\lambda (_: A).(eq C c1 (CHead d2 (Bind Abst)
-u3))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
-(\lambda (d2: C).(\lambda (u3: T).(\lambda (a: A).(arity g d2 u3 (asucc g
-a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u3: T).(eq C c1 (CHead d2 (Bind Void)
-u3)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))) H2 d1 H9) in
-(let H12 \def (eq_ind C c2 (\lambda (c0: C).(csuba g c1 c0)) H1 d1 H9) in
-(or3_intro2 (ex2 C (\lambda (d2: C).(eq C (CHead c1 (Bind Void) u0) (CHead d2
-(Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u3: T).(\lambda (_: A).(eq C (CHead c1 (Bind Void) u0)
-(CHead d2 (Bind Abst) u3))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
-A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u3: T).(\lambda (a:
-A).(arity g d2 u3 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
-(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u3: T).(eq
-C (CHead c1 (Bind Void) u0) (CHead d2 (Bind Void) u3)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2:
-C).(\lambda (u3: T).(eq C (CHead c1 (Bind Void) u0) (CHead d2 (Bind Void)
-u3)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) c1 u0 (refl_equal C
-(CHead c1 (Bind Void) u0)) H12)))))))) H6)) H5))))))))))) (\lambda (c1:
-C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c2
-(CHead d1 (Bind Abbr) u1)) \to (or3 (ex2 C (\lambda (d2: C).(eq C c1 (CHead
-d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c1 (CHead d2 (Bind Abst)
-u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
-a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))).(\lambda (t:
-T).(\lambda (a: A).(\lambda (H3: (arity g c1 t (asucc g a))).(\lambda (u:
-T).(\lambda (H4: (arity g c2 u a)).(\lambda (H5: (eq C (CHead c2 (Bind Abbr)
-u) (CHead d1 (Bind Abbr) u1))).(let H6 \def (f_equal C C (\lambda (e:
-C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c2 |
-(CHead c0 _ _) \Rightarrow c0])) (CHead c2 (Bind Abbr) u) (CHead d1 (Bind
-Abbr) u1) H5) in ((let H7 \def (f_equal C T (\lambda (e: C).(match e in C
-return (\lambda (_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t0)
-\Rightarrow t0])) (CHead c2 (Bind Abbr) u) (CHead d1 (Bind Abbr) u1) H5) in
-(\lambda (H8: (eq C c2 d1)).(let H9 \def (eq_ind T u (\lambda (t0: T).(arity
-g c2 t0 a)) H4 u1 H7) in (let H10 \def (eq_ind C c2 (\lambda (c0: C).(arity g
-c0 u1 a)) H9 d1 H8) in (let H11 \def (eq_ind C c2 (\lambda (c0: C).((eq C c0
-(CHead d1 (Bind Abbr) u1)) \to (or3 (ex2 C (\lambda (d2: C).(eq C c1 (CHead
-d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c1 (CHead d2 (Bind Abst)
-u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (a0: A).(arity g d2 u2 (asucc g
-a0))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a0: A).(arity g d1 u1
-a0))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2 (Bind
-Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))) H2 d1 H8)
-in (let H12 \def (eq_ind C c2 (\lambda (c0: C).(csuba g c1 c0)) H1 d1 H8) in
-(or3_intro1 (ex2 C (\lambda (d2: C).(eq C (CHead c1 (Bind Abst) t) (CHead d2
-(Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C (CHead c1 (Bind Abst) t)
-(CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
-A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a0:
-A).(arity g d2 u2 (asucc g a0))))) (\lambda (_: C).(\lambda (_: T).(\lambda
-(a0: A).(arity g d1 u1 a0))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
-T).(eq C (CHead c1 (Bind Abst) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1)))) (ex4_3_intro C T A (\lambda (d2:
-C).(\lambda (u2: T).(\lambda (_: A).(eq C (CHead c1 (Bind Abst) t) (CHead d2
-(Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
-d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a0: A).(arity g d2 u2
-(asucc g a0))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a0: A).(arity g d1
-u1 a0)))) c1 t a (refl_equal C (CHead c1 (Bind Abst) t)) H12 H3 H10))))))))
-H6)))))))))))) c y H0))) H))))).
-(* COMMENTS
-Initial nodes: 3459
-END *)
-
-theorem csuba_gen_flat_rev:
- \forall (g: G).(\forall (d1: C).(\forall (c: C).(\forall (u1: T).(\forall
-(f: F).((csuba g c (CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(eq C c (CHead d2 (Flat f) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1)))))))))
-\def
- \lambda (g: G).(\lambda (d1: C).(\lambda (c: C).(\lambda (u1: T).(\lambda
-(f: F).(\lambda (H: (csuba g c (CHead d1 (Flat f) u1))).(insert_eq C (CHead
-d1 (Flat f) u1) (\lambda (c0: C).(csuba g c c0)) (\lambda (_: C).(ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(eq C c (CHead d2 (Flat f) u2)))) (\lambda
-(d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (y: C).(\lambda (H0:
-(csuba g c y)).(csuba_ind g (\lambda (c0: C).(\lambda (c1: C).((eq C c1
-(CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
-C c0 (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1))))))) (\lambda (n: nat).(\lambda (H1: (eq C (CSort n) (CHead d1 (Flat f)
-u1))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee in C return
-(\lambda (_: C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _)
-\Rightarrow False])) I (CHead d1 (Flat f) u1) H1) in (False_ind (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(eq C (CSort n) (CHead d2 (Flat f) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) H2)))) (\lambda (c1:
-C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c2
-(CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
-C c1 (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c2 k u)
-(CHead d1 (Flat f) u1))).(let H4 \def (f_equal C C (\lambda (e: C).(match e
-in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c2 | (CHead c0 _
-_) \Rightarrow c0])) (CHead c2 k u) (CHead d1 (Flat f) u1) H3) in ((let H5
-\def (f_equal C K (\lambda (e: C).(match e in C return (\lambda (_: C).K)
-with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c2 k
-u) (CHead d1 (Flat f) u1) H3) in ((let H6 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u |
-(CHead _ _ t) \Rightarrow t])) (CHead c2 k u) (CHead d1 (Flat f) u1) H3) in
-(\lambda (H7: (eq K k (Flat f))).(\lambda (H8: (eq C c2 d1)).(eq_ind_r T u1
-(\lambda (t: T).(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c1
-k t) (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1))))) (eq_ind_r K (Flat f) (\lambda (k0: K).(ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(eq C (CHead c1 k0 u1) (CHead d2 (Flat f) u2)))) (\lambda
-(d2: C).(\lambda (_: T).(csuba g d2 d1))))) (let H9 \def (eq_ind C c2
-(\lambda (c0: C).((eq C c0 (CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda
-(d2: C).(\lambda (u2: T).(eq C c1 (CHead d2 (Flat f) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1)))))) H2 d1 H8) in (let H10 \def (eq_ind C
-c2 (\lambda (c0: C).(csuba g c1 c0)) H1 d1 H8) in (ex2_2_intro C T (\lambda
-(d2: C).(\lambda (u2: T).(eq C (CHead c1 (Flat f) u1) (CHead d2 (Flat f)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) c1 u1 (refl_equal C
-(CHead c1 (Flat f) u1)) H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
-C).(\lambda (c2: C).(\lambda (_: (csuba g c1 c2)).(\lambda (_: (((eq C c2
-(CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
-C c1 (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1))))))).(\lambda (b: B).(\lambda (_: (not (eq B b Void))).(\lambda (u0:
-T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c2 (Bind b) u2) (CHead d1
-(Flat f) u1))).(let H5 \def (eq_ind C (CHead c2 (Bind b) u2) (\lambda (ee:
-C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow
-False | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop)
-with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead d1
-(Flat f) u1) H4) in (False_ind (ex2_2 C T (\lambda (d2: C).(\lambda (u3:
-T).(eq C (CHead c1 (Bind Void) u0) (CHead d2 (Flat f) u3)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1)))) H5))))))))))) (\lambda (c1: C).(\lambda
-(c2: C).(\lambda (_: (csuba g c1 c2)).(\lambda (_: (((eq C c2 (CHead d1 (Flat
-f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2
-(Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (_: (arity g c1 t (asucc g
-a))).(\lambda (u: T).(\lambda (_: (arity g c2 u a)).(\lambda (H5: (eq C
-(CHead c2 (Bind Abbr) u) (CHead d1 (Flat f) u1))).(let H6 \def (eq_ind C
-(CHead c2 (Bind Abbr) u) (\lambda (ee: C).(match ee in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match
-k in K return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow True | (Flat
-_) \Rightarrow False])])) I (CHead d1 (Flat f) u1) H5) in (False_ind (ex2_2 C
-T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c1 (Bind Abst) t) (CHead d2
-(Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))
-H6)))))))))))) c y H0))) H)))))).
-(* COMMENTS
-Initial nodes: 1183
-END *)
-
-theorem csuba_gen_bind_rev:
- \forall (g: G).(\forall (b1: B).(\forall (e1: C).(\forall (c2: C).(\forall
-(v1: T).((csuba g c2 (CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2:
-B).(\lambda (e2: C).(\lambda (v2: T).(eq C c2 (CHead e2 (Bind b2) v2)))))
-(\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2 e1))))))))))
-\def
- \lambda (g: G).(\lambda (b1: B).(\lambda (e1: C).(\lambda (c2: C).(\lambda
-(v1: T).(\lambda (H: (csuba g c2 (CHead e1 (Bind b1) v1))).(insert_eq C
-(CHead e1 (Bind b1) v1) (\lambda (c: C).(csuba g c2 c)) (\lambda (_:
-C).(ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c2
-(CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csuba g e2 e1)))))) (\lambda (y: C).(\lambda (H0: (csuba g c2
-y)).(csuba_ind g (\lambda (c: C).(\lambda (c0: C).((eq C c0 (CHead e1 (Bind
-b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2:
-T).(eq C c (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
-C).(\lambda (_: T).(csuba g e2 e1)))))))) (\lambda (n: nat).(\lambda (H1: (eq
-C (CSort n) (CHead e1 (Bind b1) v1))).(let H2 \def (eq_ind C (CSort n)
-(\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _)
-\Rightarrow True | (CHead _ _ _) \Rightarrow False])) I (CHead e1 (Bind b1)
-v1) H1) in (False_ind (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda
-(v2: T).(eq C (CSort n) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda
-(e2: C).(\lambda (_: T).(csuba g e2 e1))))) H2)))) (\lambda (c1: C).(\lambda
-(c3: C).(\lambda (H1: (csuba g c1 c3)).(\lambda (H2: (((eq C c3 (CHead e1
-(Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda
-(v2: T).(eq C c1 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
-C).(\lambda (_: T).(csuba g e2 e1)))))))).(\lambda (k: K).(\lambda (u:
-T).(\lambda (H3: (eq C (CHead c3 k u) (CHead e1 (Bind b1) v1))).(let H4 \def
-(f_equal C C (\lambda (e: C).(match e in C return (\lambda (_: C).C) with
-[(CSort _) \Rightarrow c3 | (CHead c _ _) \Rightarrow c])) (CHead c3 k u)
-(CHead e1 (Bind b1) v1) H3) in ((let H5 \def (f_equal C K (\lambda (e:
-C).(match e in C return (\lambda (_: C).K) with [(CSort _) \Rightarrow k |
-(CHead _ k0 _) \Rightarrow k0])) (CHead c3 k u) (CHead e1 (Bind b1) v1) H3)
-in ((let H6 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda
-(_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t]))
-(CHead c3 k u) (CHead e1 (Bind b1) v1) H3) in (\lambda (H7: (eq K k (Bind
-b1))).(\lambda (H8: (eq C c3 e1)).(eq_ind_r T v1 (\lambda (t: T).(ex2_3 B C T
-(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c1 k t)
-(CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csuba g e2 e1)))))) (eq_ind_r K (Bind b1) (\lambda (k0: K).(ex2_3 B C T
-(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c1 k0 v1)
-(CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csuba g e2 e1)))))) (let H9 \def (eq_ind C c3 (\lambda (c: C).((eq C c
-(CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2:
-C).(\lambda (v2: T).(eq C c1 (CHead e2 (Bind b2) v2))))) (\lambda (_:
-B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2 e1))))))) H2 e1 H8) in (let
-H10 \def (eq_ind C c3 (\lambda (c: C).(csuba g c1 c)) H1 e1 H8) in
-(ex2_3_intro B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C
-(CHead c1 (Bind b1) v1) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda
-(e2: C).(\lambda (_: T).(csuba g e2 e1)))) b1 c1 v1 (refl_equal C (CHead c1
-(Bind b1) v1)) H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
-C).(\lambda (c3: C).(\lambda (H1: (csuba g c1 c3)).(\lambda (H2: (((eq C c3
-(CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2:
-C).(\lambda (v2: T).(eq C c1 (CHead e2 (Bind b2) v2))))) (\lambda (_:
-B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2 e1)))))))).(\lambda (b:
-B).(\lambda (H3: (not (eq B b Void))).(\lambda (u1: T).(\lambda (u2:
-T).(\lambda (H4: (eq C (CHead c3 (Bind b) u2) (CHead e1 (Bind b1) v1))).(let
-H5 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda (_: C).C)
-with [(CSort _) \Rightarrow c3 | (CHead c _ _) \Rightarrow c])) (CHead c3
-(Bind b) u2) (CHead e1 (Bind b1) v1) H4) in ((let H6 \def (f_equal C B
-(\lambda (e: C).(match e in C return (\lambda (_: C).B) with [(CSort _)
-\Rightarrow b | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_:
-K).B) with [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow b])])) (CHead c3
-(Bind b) u2) (CHead e1 (Bind b1) v1) H4) in ((let H7 \def (f_equal C T
-(\lambda (e: C).(match e in C return (\lambda (_: C).T) with [(CSort _)
-\Rightarrow u2 | (CHead _ _ t) \Rightarrow t])) (CHead c3 (Bind b) u2) (CHead
-e1 (Bind b1) v1) H4) in (\lambda (H8: (eq B b b1)).(\lambda (H9: (eq C c3
-e1)).(let H10 \def (eq_ind B b (\lambda (b0: B).(not (eq B b0 Void))) H3 b1
-H8) in (let H11 \def (eq_ind C c3 (\lambda (c: C).((eq C c (CHead e1 (Bind
-b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2:
-T).(eq C c1 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
-C).(\lambda (_: T).(csuba g e2 e1))))))) H2 e1 H9) in (let H12 \def (eq_ind C
-c3 (\lambda (c: C).(csuba g c1 c)) H1 e1 H9) in (ex2_3_intro B C T (\lambda
-(b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c1 (Bind Void) u1)
-(CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csuba g e2 e1)))) Void c1 u1 (refl_equal C (CHead c1 (Bind Void) u1))
-H12))))))) H6)) H5))))))))))) (\lambda (c1: C).(\lambda (c3: C).(\lambda (H1:
-(csuba g c1 c3)).(\lambda (H2: (((eq C c3 (CHead e1 (Bind b1) v1)) \to (ex2_3
-B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c1 (CHead e2
-(Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g
-e2 e1)))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (_: (arity g c1 t
-(asucc g a))).(\lambda (u: T).(\lambda (H4: (arity g c3 u a)).(\lambda (H5:
-(eq C (CHead c3 (Bind Abbr) u) (CHead e1 (Bind b1) v1))).(let H6 \def
-(f_equal C C (\lambda (e: C).(match e in C return (\lambda (_: C).C) with
-[(CSort _) \Rightarrow c3 | (CHead c _ _) \Rightarrow c])) (CHead c3 (Bind
-Abbr) u) (CHead e1 (Bind b1) v1) H5) in ((let H7 \def (f_equal C B (\lambda
-(e: C).(match e in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow
-Abbr | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).B) with
-[(Bind b) \Rightarrow b | (Flat _) \Rightarrow Abbr])])) (CHead c3 (Bind
-Abbr) u) (CHead e1 (Bind b1) v1) H5) in ((let H8 \def (f_equal C T (\lambda
-(e: C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u
-| (CHead _ _ t0) \Rightarrow t0])) (CHead c3 (Bind Abbr) u) (CHead e1 (Bind
-b1) v1) H5) in (\lambda (H9: (eq B Abbr b1)).(\lambda (H10: (eq C c3
-e1)).(let H11 \def (eq_ind T u (\lambda (t0: T).(arity g c3 t0 a)) H4 v1 H8)
-in (let H12 \def (eq_ind C c3 (\lambda (c: C).(arity g c v1 a)) H11 e1 H10)
-in (let H13 \def (eq_ind C c3 (\lambda (c: C).((eq C c (CHead e1 (Bind b1)
-v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq
-C c1 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda
-(_: T).(csuba g e2 e1))))))) H2 e1 H10) in (let H14 \def (eq_ind C c3
-(\lambda (c: C).(csuba g c1 c)) H1 e1 H10) in (let H15 \def (eq_ind_r B b1
-(\lambda (b: B).((eq C e1 (CHead e1 (Bind b) v1)) \to (ex2_3 B C T (\lambda
-(b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c1 (CHead e2 (Bind b2)
-v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2
-e1))))))) H13 Abbr H9) in (ex2_3_intro B C T (\lambda (b2: B).(\lambda (e2:
-C).(\lambda (v2: T).(eq C (CHead c1 (Bind Abst) t) (CHead e2 (Bind b2)
-v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2 e1))))
-Abst c1 t (refl_equal C (CHead c1 (Bind Abst) t)) H14))))))))) H7))
-H6)))))))))))) c2 y H0))) H)))))).
-(* COMMENTS
-Initial nodes: 1831
-END *)
-
projects / helm.git / blobdiff