+++ /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/T/defs.ma".
-
-theorem terms_props__bind_dec:
- \forall (b1: B).(\forall (b2: B).(or (eq B b1 b2) ((eq B b1 b2) \to (\forall
-(P: Prop).P))))
-\def
- \lambda (b1: B).(B_ind (\lambda (b: B).(\forall (b2: B).(or (eq B b b2) ((eq
-B b b2) \to (\forall (P: Prop).P))))) (\lambda (b2: B).(B_ind (\lambda (b:
-B).(or (eq B Abbr b) ((eq B Abbr b) \to (\forall (P: Prop).P)))) (or_introl
-(eq B Abbr Abbr) ((eq B Abbr Abbr) \to (\forall (P: Prop).P)) (refl_equal B
-Abbr)) (or_intror (eq B Abbr Abst) ((eq B Abbr Abst) \to (\forall (P:
-Prop).P)) (\lambda (H: (eq B Abbr Abst)).(\lambda (P: Prop).(let H0 \def
-(eq_ind B Abbr (\lambda (ee: B).(match ee in B return (\lambda (_: B).Prop)
-with [Abbr \Rightarrow True | Abst \Rightarrow False | Void \Rightarrow
-False])) I Abst H) in (False_ind P H0))))) (or_intror (eq B Abbr Void) ((eq B
-Abbr Void) \to (\forall (P: Prop).P)) (\lambda (H: (eq B Abbr Void)).(\lambda
-(P: Prop).(let H0 \def (eq_ind B Abbr (\lambda (ee: B).(match ee in B return
-(\lambda (_: B).Prop) with [Abbr \Rightarrow True | Abst \Rightarrow False |
-Void \Rightarrow False])) I Void H) in (False_ind P H0))))) b2)) (\lambda
-(b2: B).(B_ind (\lambda (b: B).(or (eq B Abst b) ((eq B Abst b) \to (\forall
-(P: Prop).P)))) (or_intror (eq B Abst Abbr) ((eq B Abst Abbr) \to (\forall
-(P: Prop).P)) (\lambda (H: (eq B Abst Abbr)).(\lambda (P: Prop).(let H0 \def
-(eq_ind B Abst (\lambda (ee: B).(match ee in B return (\lambda (_: B).Prop)
-with [Abbr \Rightarrow False | Abst \Rightarrow True | Void \Rightarrow
-False])) I Abbr H) in (False_ind P H0))))) (or_introl (eq B Abst Abst) ((eq B
-Abst Abst) \to (\forall (P: Prop).P)) (refl_equal B Abst)) (or_intror (eq B
-Abst Void) ((eq B Abst Void) \to (\forall (P: Prop).P)) (\lambda (H: (eq B
-Abst Void)).(\lambda (P: Prop).(let H0 \def (eq_ind B Abst (\lambda (ee:
-B).(match ee in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow False |
-Abst \Rightarrow True | Void \Rightarrow False])) I Void H) in (False_ind P
-H0))))) b2)) (\lambda (b2: B).(B_ind (\lambda (b: B).(or (eq B Void b) ((eq B
-Void b) \to (\forall (P: Prop).P)))) (or_intror (eq B Void Abbr) ((eq B Void
-Abbr) \to (\forall (P: Prop).P)) (\lambda (H: (eq B Void Abbr)).(\lambda (P:
-Prop).(let H0 \def (eq_ind B Void (\lambda (ee: B).(match ee in B return
-(\lambda (_: B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow False |
-Void \Rightarrow True])) I Abbr H) in (False_ind P H0))))) (or_intror (eq B
-Void Abst) ((eq B Void Abst) \to (\forall (P: Prop).P)) (\lambda (H: (eq B
-Void Abst)).(\lambda (P: Prop).(let H0 \def (eq_ind B Void (\lambda (ee:
-B).(match ee in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow False |
-Abst \Rightarrow False | Void \Rightarrow True])) I Abst H) in (False_ind P
-H0))))) (or_introl (eq B Void Void) ((eq B Void Void) \to (\forall (P:
-Prop).P)) (refl_equal B Void)) b2)) b1).
-(* COMMENTS
-Initial nodes: 559
-END *)
-
-theorem bind_dec_not:
- \forall (b1: B).(\forall (b2: B).(or (eq B b1 b2) (not (eq B b1 b2))))
-\def
- \lambda (b1: B).(\lambda (b2: B).(let H_x \def (terms_props__bind_dec b1 b2)
-in (let H \def H_x in (or_ind (eq B b1 b2) ((eq B b1 b2) \to (\forall (P:
-Prop).P)) (or (eq B b1 b2) ((eq B b1 b2) \to False)) (\lambda (H0: (eq B b1
-b2)).(or_introl (eq B b1 b2) ((eq B b1 b2) \to False) H0)) (\lambda (H0:
-(((eq B b1 b2) \to (\forall (P: Prop).P)))).(or_intror (eq B b1 b2) ((eq B b1
-b2) \to False) (\lambda (H1: (eq B b1 b2)).(H0 H1 False)))) H)))).
-(* COMMENTS
-Initial nodes: 131
-END *)
-
-theorem terms_props__flat_dec:
- \forall (f1: F).(\forall (f2: F).(or (eq F f1 f2) ((eq F f1 f2) \to (\forall
-(P: Prop).P))))
-\def
- \lambda (f1: F).(F_ind (\lambda (f: F).(\forall (f2: F).(or (eq F f f2) ((eq
-F f f2) \to (\forall (P: Prop).P))))) (\lambda (f2: F).(F_ind (\lambda (f:
-F).(or (eq F Appl f) ((eq F Appl f) \to (\forall (P: Prop).P)))) (or_introl
-(eq F Appl Appl) ((eq F Appl Appl) \to (\forall (P: Prop).P)) (refl_equal F
-Appl)) (or_intror (eq F Appl Cast) ((eq F Appl Cast) \to (\forall (P:
-Prop).P)) (\lambda (H: (eq F Appl Cast)).(\lambda (P: Prop).(let H0 \def
-(eq_ind F Appl (\lambda (ee: F).(match ee in F return (\lambda (_: F).Prop)
-with [Appl \Rightarrow True | Cast \Rightarrow False])) I Cast H) in
-(False_ind P H0))))) f2)) (\lambda (f2: F).(F_ind (\lambda (f: F).(or (eq F
-Cast f) ((eq F Cast f) \to (\forall (P: Prop).P)))) (or_intror (eq F Cast
-Appl) ((eq F Cast Appl) \to (\forall (P: Prop).P)) (\lambda (H: (eq F Cast
-Appl)).(\lambda (P: Prop).(let H0 \def (eq_ind F Cast (\lambda (ee: F).(match
-ee in F return (\lambda (_: F).Prop) with [Appl \Rightarrow False | Cast
-\Rightarrow True])) I Appl H) in (False_ind P H0))))) (or_introl (eq F Cast
-Cast) ((eq F Cast Cast) \to (\forall (P: Prop).P)) (refl_equal F Cast)) f2))
-f1).
-(* COMMENTS
-Initial nodes: 263
-END *)
-
-theorem terms_props__kind_dec:
- \forall (k1: K).(\forall (k2: K).(or (eq K k1 k2) ((eq K k1 k2) \to (\forall
-(P: Prop).P))))
-\def
- \lambda (k1: K).(K_ind (\lambda (k: K).(\forall (k2: K).(or (eq K k k2) ((eq
-K k k2) \to (\forall (P: Prop).P))))) (\lambda (b: B).(\lambda (k2: K).(K_ind
-(\lambda (k: K).(or (eq K (Bind b) k) ((eq K (Bind b) k) \to (\forall (P:
-Prop).P)))) (\lambda (b0: B).(let H_x \def (terms_props__bind_dec b b0) in
-(let H \def H_x in (or_ind (eq B b b0) ((eq B b b0) \to (\forall (P:
-Prop).P)) (or (eq K (Bind b) (Bind b0)) ((eq K (Bind b) (Bind b0)) \to
-(\forall (P: Prop).P))) (\lambda (H0: (eq B b b0)).(eq_ind B b (\lambda (b1:
-B).(or (eq K (Bind b) (Bind b1)) ((eq K (Bind b) (Bind b1)) \to (\forall (P:
-Prop).P)))) (or_introl (eq K (Bind b) (Bind b)) ((eq K (Bind b) (Bind b)) \to
-(\forall (P: Prop).P)) (refl_equal K (Bind b))) b0 H0)) (\lambda (H0: (((eq B
-b b0) \to (\forall (P: Prop).P)))).(or_intror (eq K (Bind b) (Bind b0)) ((eq
-K (Bind b) (Bind b0)) \to (\forall (P: Prop).P)) (\lambda (H1: (eq K (Bind b)
-(Bind b0))).(\lambda (P: Prop).(let H2 \def (f_equal K B (\lambda (e:
-K).(match e in K return (\lambda (_: K).B) with [(Bind b1) \Rightarrow b1 |
-(Flat _) \Rightarrow b])) (Bind b) (Bind b0) H1) in (let H3 \def (eq_ind_r B
-b0 (\lambda (b1: B).((eq B b b1) \to (\forall (P0: Prop).P0))) H0 b H2) in
-(H3 (refl_equal B b) P))))))) H)))) (\lambda (f: F).(or_intror (eq K (Bind b)
-(Flat f)) ((eq K (Bind b) (Flat f)) \to (\forall (P: Prop).P)) (\lambda (H:
-(eq K (Bind b) (Flat f))).(\lambda (P: Prop).(let H0 \def (eq_ind K (Bind b)
-(\lambda (ee: K).(match ee in K return (\lambda (_: K).Prop) with [(Bind _)
-\Rightarrow True | (Flat _) \Rightarrow False])) I (Flat f) H) in (False_ind
-P H0)))))) k2))) (\lambda (f: F).(\lambda (k2: K).(K_ind (\lambda (k: K).(or
-(eq K (Flat f) k) ((eq K (Flat f) k) \to (\forall (P: Prop).P)))) (\lambda
-(b: B).(or_intror (eq K (Flat f) (Bind b)) ((eq K (Flat f) (Bind b)) \to
-(\forall (P: Prop).P)) (\lambda (H: (eq K (Flat f) (Bind b))).(\lambda (P:
-Prop).(let H0 \def (eq_ind K (Flat f) (\lambda (ee: K).(match ee in K return
-(\lambda (_: K).Prop) with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow
-True])) I (Bind b) H) in (False_ind P H0)))))) (\lambda (f0: F).(let H_x \def
-(terms_props__flat_dec f f0) in (let H \def H_x in (or_ind (eq F f f0) ((eq F
-f f0) \to (\forall (P: Prop).P)) (or (eq K (Flat f) (Flat f0)) ((eq K (Flat
-f) (Flat f0)) \to (\forall (P: Prop).P))) (\lambda (H0: (eq F f f0)).(eq_ind
-F f (\lambda (f1: F).(or (eq K (Flat f) (Flat f1)) ((eq K (Flat f) (Flat f1))
-\to (\forall (P: Prop).P)))) (or_introl (eq K (Flat f) (Flat f)) ((eq K (Flat
-f) (Flat f)) \to (\forall (P: Prop).P)) (refl_equal K (Flat f))) f0 H0))
-(\lambda (H0: (((eq F f f0) \to (\forall (P: Prop).P)))).(or_intror (eq K
-(Flat f) (Flat f0)) ((eq K (Flat f) (Flat f0)) \to (\forall (P: Prop).P))
-(\lambda (H1: (eq K (Flat f) (Flat f0))).(\lambda (P: Prop).(let H2 \def
-(f_equal K F (\lambda (e: K).(match e in K return (\lambda (_: K).F) with
-[(Bind _) \Rightarrow f | (Flat f1) \Rightarrow f1])) (Flat f) (Flat f0) H1)
-in (let H3 \def (eq_ind_r F f0 (\lambda (f1: F).((eq F f f1) \to (\forall
-(P0: Prop).P0))) H0 f H2) in (H3 (refl_equal F f) P))))))) H)))) k2))) k1).
-(* COMMENTS
-Initial nodes: 799
-END *)
-
-theorem term_dec:
- \forall (t1: T).(\forall (t2: T).(or (eq T t1 t2) ((eq T t1 t2) \to (\forall
-(P: Prop).P))))
-\def
- \lambda (t1: T).(T_ind (\lambda (t: T).(\forall (t2: T).(or (eq T t t2) ((eq
-T t t2) \to (\forall (P: Prop).P))))) (\lambda (n: nat).(\lambda (t2:
-T).(T_ind (\lambda (t: T).(or (eq T (TSort n) t) ((eq T (TSort n) t) \to
-(\forall (P: Prop).P)))) (\lambda (n0: nat).(let H_x \def (nat_dec n n0) in
-(let H \def H_x in (or_ind (eq nat n n0) ((eq nat n n0) \to (\forall (P:
-Prop).P)) (or (eq T (TSort n) (TSort n0)) ((eq T (TSort n) (TSort n0)) \to
-(\forall (P: Prop).P))) (\lambda (H0: (eq nat n n0)).(eq_ind nat n (\lambda
-(n1: nat).(or (eq T (TSort n) (TSort n1)) ((eq T (TSort n) (TSort n1)) \to
-(\forall (P: Prop).P)))) (or_introl (eq T (TSort n) (TSort n)) ((eq T (TSort
-n) (TSort n)) \to (\forall (P: Prop).P)) (refl_equal T (TSort n))) n0 H0))
-(\lambda (H0: (((eq nat n n0) \to (\forall (P: Prop).P)))).(or_intror (eq T
-(TSort n) (TSort n0)) ((eq T (TSort n) (TSort n0)) \to (\forall (P: Prop).P))
-(\lambda (H1: (eq T (TSort n) (TSort n0))).(\lambda (P: Prop).(let H2 \def
-(f_equal T nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat) with
-[(TSort n1) \Rightarrow n1 | (TLRef _) \Rightarrow n | (THead _ _ _)
-\Rightarrow n])) (TSort n) (TSort n0) H1) in (let H3 \def (eq_ind_r nat n0
-(\lambda (n1: nat).((eq nat n n1) \to (\forall (P0: Prop).P0))) H0 n H2) in
-(H3 (refl_equal nat n) P))))))) H)))) (\lambda (n0: nat).(or_intror (eq T
-(TSort n) (TLRef n0)) ((eq T (TSort n) (TLRef n0)) \to (\forall (P: Prop).P))
-(\lambda (H: (eq T (TSort n) (TLRef n0))).(\lambda (P: Prop).(let H0 \def
-(eq_ind T (TSort n) (\lambda (ee: T).(match ee in T return (\lambda (_:
-T).Prop) with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False |
-(THead _ _ _) \Rightarrow False])) I (TLRef n0) H) in (False_ind P H0))))))
-(\lambda (k: K).(\lambda (t: T).(\lambda (_: (or (eq T (TSort n) t) ((eq T
-(TSort n) t) \to (\forall (P: Prop).P)))).(\lambda (t0: T).(\lambda (_: (or
-(eq T (TSort n) t0) ((eq T (TSort n) t0) \to (\forall (P:
-Prop).P)))).(or_intror (eq T (TSort n) (THead k t t0)) ((eq T (TSort n)
-(THead k t t0)) \to (\forall (P: Prop).P)) (\lambda (H1: (eq T (TSort n)
-(THead k t t0))).(\lambda (P: Prop).(let H2 \def (eq_ind T (TSort n) (\lambda
-(ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _)
-\Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow
-False])) I (THead k t t0) H1) in (False_ind P H2)))))))))) t2))) (\lambda (n:
-nat).(\lambda (t2: T).(T_ind (\lambda (t: T).(or (eq T (TLRef n) t) ((eq T
-(TLRef n) t) \to (\forall (P: Prop).P)))) (\lambda (n0: nat).(or_intror (eq T
-(TLRef n) (TSort n0)) ((eq T (TLRef n) (TSort n0)) \to (\forall (P: Prop).P))
-(\lambda (H: (eq T (TLRef n) (TSort n0))).(\lambda (P: Prop).(let H0 \def
-(eq_ind T (TLRef n) (\lambda (ee: T).(match ee in T return (\lambda (_:
-T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True |
-(THead _ _ _) \Rightarrow False])) I (TSort n0) H) in (False_ind P H0))))))
-(\lambda (n0: nat).(let H_x \def (nat_dec n n0) in (let H \def H_x in (or_ind
-(eq nat n n0) ((eq nat n n0) \to (\forall (P: Prop).P)) (or (eq T (TLRef n)
-(TLRef n0)) ((eq T (TLRef n) (TLRef n0)) \to (\forall (P: Prop).P))) (\lambda
-(H0: (eq nat n n0)).(eq_ind nat n (\lambda (n1: nat).(or (eq T (TLRef n)
-(TLRef n1)) ((eq T (TLRef n) (TLRef n1)) \to (\forall (P: Prop).P))))
-(or_introl (eq T (TLRef n) (TLRef n)) ((eq T (TLRef n) (TLRef n)) \to
-(\forall (P: Prop).P)) (refl_equal T (TLRef n))) n0 H0)) (\lambda (H0: (((eq
-nat n n0) \to (\forall (P: Prop).P)))).(or_intror (eq T (TLRef n) (TLRef n0))
-((eq T (TLRef n) (TLRef n0)) \to (\forall (P: Prop).P)) (\lambda (H1: (eq T
-(TLRef n) (TLRef n0))).(\lambda (P: Prop).(let H2 \def (f_equal T nat
-(\lambda (e: T).(match e in T return (\lambda (_: T).nat) with [(TSort _)
-\Rightarrow n | (TLRef n1) \Rightarrow n1 | (THead _ _ _) \Rightarrow n]))
-(TLRef n) (TLRef n0) H1) in (let H3 \def (eq_ind_r nat n0 (\lambda (n1:
-nat).((eq nat n n1) \to (\forall (P0: Prop).P0))) H0 n H2) in (H3 (refl_equal
-nat n) P))))))) H)))) (\lambda (k: K).(\lambda (t: T).(\lambda (_: (or (eq T
-(TLRef n) t) ((eq T (TLRef n) t) \to (\forall (P: Prop).P)))).(\lambda (t0:
-T).(\lambda (_: (or (eq T (TLRef n) t0) ((eq T (TLRef n) t0) \to (\forall (P:
-Prop).P)))).(or_intror (eq T (TLRef n) (THead k t t0)) ((eq T (TLRef n)
-(THead k t t0)) \to (\forall (P: Prop).P)) (\lambda (H1: (eq T (TLRef n)
-(THead k t t0))).(\lambda (P: Prop).(let H2 \def (eq_ind T (TLRef n) (\lambda
-(ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _)
-\Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow
-False])) I (THead k t t0) H1) in (False_ind P H2)))))))))) t2))) (\lambda (k:
-K).(\lambda (t: T).(\lambda (H: ((\forall (t2: T).(or (eq T t t2) ((eq T t
-t2) \to (\forall (P: Prop).P)))))).(\lambda (t0: T).(\lambda (H0: ((\forall
-(t2: T).(or (eq T t0 t2) ((eq T t0 t2) \to (\forall (P:
-Prop).P)))))).(\lambda (t2: T).(T_ind (\lambda (t3: T).(or (eq T (THead k t
-t0) t3) ((eq T (THead k t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (n:
-nat).(or_intror (eq T (THead k t t0) (TSort n)) ((eq T (THead k t t0) (TSort
-n)) \to (\forall (P: Prop).P)) (\lambda (H1: (eq T (THead k t t0) (TSort
-n))).(\lambda (P: Prop).(let H2 \def (eq_ind T (THead k t t0) (\lambda (ee:
-T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
-False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) I
-(TSort n) H1) in (False_ind P H2)))))) (\lambda (n: nat).(or_intror (eq T
-(THead k t t0) (TLRef n)) ((eq T (THead k t t0) (TLRef n)) \to (\forall (P:
-Prop).P)) (\lambda (H1: (eq T (THead k t t0) (TLRef n))).(\lambda (P:
-Prop).(let H2 \def (eq_ind T (THead k t t0) (\lambda (ee: T).(match ee in T
-return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TLRef n) H1) in
-(False_ind P H2)))))) (\lambda (k0: K).(\lambda (t3: T).(\lambda (H1: (or (eq
-T (THead k t t0) t3) ((eq T (THead k t t0) t3) \to (\forall (P:
-Prop).P)))).(\lambda (t4: T).(\lambda (H2: (or (eq T (THead k t t0) t4) ((eq
-T (THead k t t0) t4) \to (\forall (P: Prop).P)))).(let H_x \def (H t3) in
-(let H3 \def H_x in (or_ind (eq T t t3) ((eq T t t3) \to (\forall (P:
-Prop).P)) (or (eq T (THead k t t0) (THead k0 t3 t4)) ((eq T (THead k t t0)
-(THead k0 t3 t4)) \to (\forall (P: Prop).P))) (\lambda (H4: (eq T t t3)).(let
-H5 \def (eq_ind_r T t3 (\lambda (t5: T).(or (eq T (THead k t t0) t5) ((eq T
-(THead k t t0) t5) \to (\forall (P: Prop).P)))) H1 t H4) in (eq_ind T t
-(\lambda (t5: T).(or (eq T (THead k t t0) (THead k0 t5 t4)) ((eq T (THead k t
-t0) (THead k0 t5 t4)) \to (\forall (P: Prop).P)))) (let H_x0 \def (H0 t4) in
-(let H6 \def H_x0 in (or_ind (eq T t0 t4) ((eq T t0 t4) \to (\forall (P:
-Prop).P)) (or (eq T (THead k t t0) (THead k0 t t4)) ((eq T (THead k t t0)
-(THead k0 t t4)) \to (\forall (P: Prop).P))) (\lambda (H7: (eq T t0 t4)).(let
-H8 \def (eq_ind_r T t4 (\lambda (t5: T).(or (eq T (THead k t t0) t5) ((eq T
-(THead k t t0) t5) \to (\forall (P: Prop).P)))) H2 t0 H7) in (eq_ind T t0
-(\lambda (t5: T).(or (eq T (THead k t t0) (THead k0 t t5)) ((eq T (THead k t
-t0) (THead k0 t t5)) \to (\forall (P: Prop).P)))) (let H_x1 \def
-(terms_props__kind_dec k k0) in (let H9 \def H_x1 in (or_ind (eq K k k0) ((eq
-K k k0) \to (\forall (P: Prop).P)) (or (eq T (THead k t t0) (THead k0 t t0))
-((eq T (THead k t t0) (THead k0 t t0)) \to (\forall (P: Prop).P))) (\lambda
-(H10: (eq K k k0)).(eq_ind K k (\lambda (k1: K).(or (eq T (THead k t t0)
-(THead k1 t t0)) ((eq T (THead k t t0) (THead k1 t t0)) \to (\forall (P:
-Prop).P)))) (or_introl (eq T (THead k t t0) (THead k t t0)) ((eq T (THead k t
-t0) (THead k t t0)) \to (\forall (P: Prop).P)) (refl_equal T (THead k t t0)))
-k0 H10)) (\lambda (H10: (((eq K k k0) \to (\forall (P: Prop).P)))).(or_intror
-(eq T (THead k t t0) (THead k0 t t0)) ((eq T (THead k t t0) (THead k0 t t0))
-\to (\forall (P: Prop).P)) (\lambda (H11: (eq T (THead k t t0) (THead k0 t
-t0))).(\lambda (P: Prop).(let H12 \def (f_equal T K (\lambda (e: T).(match e
-in T return (\lambda (_: T).K) with [(TSort _) \Rightarrow k | (TLRef _)
-\Rightarrow k | (THead k1 _ _) \Rightarrow k1])) (THead k t t0) (THead k0 t
-t0) H11) in (let H13 \def (eq_ind_r K k0 (\lambda (k1: K).((eq K k k1) \to
-(\forall (P0: Prop).P0))) H10 k H12) in (H13 (refl_equal K k) P))))))) H9)))
-t4 H7))) (\lambda (H7: (((eq T t0 t4) \to (\forall (P: Prop).P)))).(or_intror
-(eq T (THead k t t0) (THead k0 t t4)) ((eq T (THead k t t0) (THead k0 t t4))
-\to (\forall (P: Prop).P)) (\lambda (H8: (eq T (THead k t t0) (THead k0 t
-t4))).(\lambda (P: Prop).(let H9 \def (f_equal T K (\lambda (e: T).(match e
-in T return (\lambda (_: T).K) with [(TSort _) \Rightarrow k | (TLRef _)
-\Rightarrow k | (THead k1 _ _) \Rightarrow k1])) (THead k t t0) (THead k0 t
-t4) H8) in ((let H10 \def (f_equal T T (\lambda (e: T).(match e in T return
-(\lambda (_: T).T) with [(TSort _) \Rightarrow t0 | (TLRef _) \Rightarrow t0
-| (THead _ _ t5) \Rightarrow t5])) (THead k t t0) (THead k0 t t4) H8) in
-(\lambda (_: (eq K k k0)).(let H12 \def (eq_ind_r T t4 (\lambda (t5: T).((eq
-T t0 t5) \to (\forall (P0: Prop).P0))) H7 t0 H10) in (let H13 \def (eq_ind_r
-T t4 (\lambda (t5: T).(or (eq T (THead k t t0) t5) ((eq T (THead k t t0) t5)
-\to (\forall (P0: Prop).P0)))) H2 t0 H10) in (H12 (refl_equal T t0) P)))))
-H9)))))) H6))) t3 H4))) (\lambda (H4: (((eq T t t3) \to (\forall (P:
-Prop).P)))).(or_intror (eq T (THead k t t0) (THead k0 t3 t4)) ((eq T (THead k
-t t0) (THead k0 t3 t4)) \to (\forall (P: Prop).P)) (\lambda (H5: (eq T (THead
-k t t0) (THead k0 t3 t4))).(\lambda (P: Prop).(let H6 \def (f_equal T K
-(\lambda (e: T).(match e in T return (\lambda (_: T).K) with [(TSort _)
-\Rightarrow k | (TLRef _) \Rightarrow k | (THead k1 _ _) \Rightarrow k1]))
-(THead k t t0) (THead k0 t3 t4) H5) in ((let H7 \def (f_equal T T (\lambda
-(e: T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow t
-| (TLRef _) \Rightarrow t | (THead _ t5 _) \Rightarrow t5])) (THead k t t0)
-(THead k0 t3 t4) H5) in ((let H8 \def (f_equal T T (\lambda (e: T).(match e
-in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow t0 | (TLRef _)
-\Rightarrow t0 | (THead _ _ t5) \Rightarrow t5])) (THead k t t0) (THead k0 t3
-t4) H5) in (\lambda (H9: (eq T t t3)).(\lambda (_: (eq K k k0)).(let H11 \def
-(eq_ind_r T t4 (\lambda (t5: T).(or (eq T (THead k t t0) t5) ((eq T (THead k
-t t0) t5) \to (\forall (P0: Prop).P0)))) H2 t0 H8) in (let H12 \def (eq_ind_r
-T t3 (\lambda (t5: T).((eq T t t5) \to (\forall (P0: Prop).P0))) H4 t H9) in
-(let H13 \def (eq_ind_r T t3 (\lambda (t5: T).(or (eq T (THead k t t0) t5)
-((eq T (THead k t t0) t5) \to (\forall (P0: Prop).P0)))) H1 t H9) in (H12
-(refl_equal T t) P))))))) H7)) H6)))))) H3)))))))) t2))))))) t1).
-(* COMMENTS
-Initial nodes: 2821
-END *)
-
-theorem binder_dec:
- \forall (t: T).(or (ex_3 B T T (\lambda (b: B).(\lambda (w: T).(\lambda (u:
-T).(eq T t (THead (Bind b) w u)))))) (\forall (b: B).(\forall (w: T).(\forall
-(u: T).((eq T t (THead (Bind b) w u)) \to (\forall (P: Prop).P))))))
-\def
- \lambda (t: T).(T_ind (\lambda (t0: T).(or (ex_3 B T T (\lambda (b:
-B).(\lambda (w: T).(\lambda (u: T).(eq T t0 (THead (Bind b) w u))))))
-(\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T t0 (THead (Bind b) w
-u)) \to (\forall (P: Prop).P))))))) (\lambda (n: nat).(or_intror (ex_3 B T T
-(\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(eq T (TSort n) (THead (Bind
-b) w u)))))) (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T (TSort n)
-(THead (Bind b) w u)) \to (\forall (P: Prop).P))))) (\lambda (b: B).(\lambda
-(w: T).(\lambda (u: T).(\lambda (H: (eq T (TSort n) (THead (Bind b) w
-u))).(\lambda (P: Prop).(let H0 \def (eq_ind T (TSort n) (\lambda (ee:
-T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
-True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow False])) I
-(THead (Bind b) w u) H) in (False_ind P H0))))))))) (\lambda (n:
-nat).(or_intror (ex_3 B T T (\lambda (b: B).(\lambda (w: T).(\lambda (u:
-T).(eq T (TLRef n) (THead (Bind b) w u)))))) (\forall (b: B).(\forall (w:
-T).(\forall (u: T).((eq T (TLRef n) (THead (Bind b) w u)) \to (\forall (P:
-Prop).P))))) (\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(\lambda (H: (eq
-T (TLRef n) (THead (Bind b) w u))).(\lambda (P: Prop).(let H0 \def (eq_ind T
-(TLRef n) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with
-[(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _)
-\Rightarrow False])) I (THead (Bind b) w u) H) in (False_ind P H0)))))))))
-(\lambda (k: K).(K_ind (\lambda (k0: K).(\forall (t0: T).((or (ex_3 B T T
-(\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(eq T t0 (THead (Bind b) w
-u)))))) (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T t0 (THead
-(Bind b) w u)) \to (\forall (P: Prop).P)))))) \to (\forall (t1: T).((or (ex_3
-B T T (\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(eq T t1 (THead (Bind
-b) w u)))))) (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T t1 (THead
-(Bind b) w u)) \to (\forall (P: Prop).P)))))) \to (or (ex_3 B T T (\lambda
-(b: B).(\lambda (w: T).(\lambda (u: T).(eq T (THead k0 t0 t1) (THead (Bind b)
-w u)))))) (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T (THead k0 t0
-t1) (THead (Bind b) w u)) \to (\forall (P: Prop).P))))))))))) (\lambda (b:
-B).(\lambda (t0: T).(\lambda (_: (or (ex_3 B T T (\lambda (b0: B).(\lambda
-(w: T).(\lambda (u: T).(eq T t0 (THead (Bind b0) w u)))))) (\forall (b0:
-B).(\forall (w: T).(\forall (u: T).((eq T t0 (THead (Bind b0) w u)) \to
-(\forall (P: Prop).P))))))).(\lambda (t1: T).(\lambda (_: (or (ex_3 B T T
-(\lambda (b0: B).(\lambda (w: T).(\lambda (u: T).(eq T t1 (THead (Bind b0) w
-u)))))) (\forall (b0: B).(\forall (w: T).(\forall (u: T).((eq T t1 (THead
-(Bind b0) w u)) \to (\forall (P: Prop).P))))))).(or_introl (ex_3 B T T
-(\lambda (b0: B).(\lambda (w: T).(\lambda (u: T).(eq T (THead (Bind b) t0 t1)
-(THead (Bind b0) w u)))))) (\forall (b0: B).(\forall (w: T).(\forall (u:
-T).((eq T (THead (Bind b) t0 t1) (THead (Bind b0) w u)) \to (\forall (P:
-Prop).P))))) (ex_3_intro B T T (\lambda (b0: B).(\lambda (w: T).(\lambda (u:
-T).(eq T (THead (Bind b) t0 t1) (THead (Bind b0) w u))))) b t0 t1 (refl_equal
-T (THead (Bind b) t0 t1))))))))) (\lambda (f: F).(\lambda (t0: T).(\lambda
-(_: (or (ex_3 B T T (\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(eq T t0
-(THead (Bind b) w u)))))) (\forall (b: B).(\forall (w: T).(\forall (u:
-T).((eq T t0 (THead (Bind b) w u)) \to (\forall (P: Prop).P))))))).(\lambda
-(t1: T).(\lambda (_: (or (ex_3 B T T (\lambda (b: B).(\lambda (w: T).(\lambda
-(u: T).(eq T t1 (THead (Bind b) w u)))))) (\forall (b: B).(\forall (w:
-T).(\forall (u: T).((eq T t1 (THead (Bind b) w u)) \to (\forall (P:
-Prop).P))))))).(or_intror (ex_3 B T T (\lambda (b: B).(\lambda (w:
-T).(\lambda (u: T).(eq T (THead (Flat f) t0 t1) (THead (Bind b) w u))))))
-(\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T (THead (Flat f) t0 t1)
-(THead (Bind b) w u)) \to (\forall (P: Prop).P))))) (\lambda (b: B).(\lambda
-(w: T).(\lambda (u: T).(\lambda (H1: (eq T (THead (Flat f) t0 t1) (THead
-(Bind b) w u))).(\lambda (P: Prop).(let H2 \def (eq_ind T (THead (Flat f) t0
-t1) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort
-_) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k0 _ _)
-\Rightarrow (match k0 in K return (\lambda (_: K).Prop) with [(Bind _)
-\Rightarrow False | (Flat _) \Rightarrow True])])) I (THead (Bind b) w u) H1)
-in (False_ind P H2))))))))))))) k)) t).
-(* COMMENTS
-Initial nodes: 1063
-END *)
-
-theorem abst_dec:
- \forall (u: T).(\forall (v: T).(or (ex T (\lambda (t: T).(eq T u (THead
-(Bind Abst) v t)))) (\forall (t: T).((eq T u (THead (Bind Abst) v t)) \to
-(\forall (P: Prop).P)))))
-\def
- \lambda (u: T).(T_ind (\lambda (t: T).(\forall (v: T).(or (ex T (\lambda
-(t0: T).(eq T t (THead (Bind Abst) v t0)))) (\forall (t0: T).((eq T t (THead
-(Bind Abst) v t0)) \to (\forall (P: Prop).P)))))) (\lambda (n: nat).(\lambda
-(v: T).(or_intror (ex T (\lambda (t: T).(eq T (TSort n) (THead (Bind Abst) v
-t)))) (\forall (t: T).((eq T (TSort n) (THead (Bind Abst) v t)) \to (\forall
-(P: Prop).P))) (\lambda (t: T).(\lambda (H: (eq T (TSort n) (THead (Bind
-Abst) v t))).(\lambda (P: Prop).(let H0 \def (eq_ind T (TSort n) (\lambda
-(ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _)
-\Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow
-False])) I (THead (Bind Abst) v t) H) in (False_ind P H0)))))))) (\lambda (n:
-nat).(\lambda (v: T).(or_intror (ex T (\lambda (t: T).(eq T (TLRef n) (THead
-(Bind Abst) v t)))) (\forall (t: T).((eq T (TLRef n) (THead (Bind Abst) v t))
-\to (\forall (P: Prop).P))) (\lambda (t: T).(\lambda (H: (eq T (TLRef n)
-(THead (Bind Abst) v t))).(\lambda (P: Prop).(let H0 \def (eq_ind T (TLRef n)
-(\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _)
-\Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow
-False])) I (THead (Bind Abst) v t) H) in (False_ind P H0)))))))) (\lambda (k:
-K).(\lambda (t: T).(\lambda (_: ((\forall (v: T).(or (ex T (\lambda (t0:
-T).(eq T t (THead (Bind Abst) v t0)))) (\forall (t0: T).((eq T t (THead (Bind
-Abst) v t0)) \to (\forall (P: Prop).P))))))).(\lambda (t0: T).(\lambda (_:
-((\forall (v: T).(or (ex T (\lambda (t1: T).(eq T t0 (THead (Bind Abst) v
-t1)))) (\forall (t1: T).((eq T t0 (THead (Bind Abst) v t1)) \to (\forall (P:
-Prop).P))))))).(\lambda (v: T).(let H_x \def (terms_props__kind_dec k (Bind
-Abst)) in (let H1 \def H_x in (or_ind (eq K k (Bind Abst)) ((eq K k (Bind
-Abst)) \to (\forall (P: Prop).P)) (or (ex T (\lambda (t1: T).(eq T (THead k t
-t0) (THead (Bind Abst) v t1)))) (\forall (t1: T).((eq T (THead k t t0) (THead
-(Bind Abst) v t1)) \to (\forall (P: Prop).P)))) (\lambda (H2: (eq K k (Bind
-Abst))).(eq_ind_r K (Bind Abst) (\lambda (k0: K).(or (ex T (\lambda (t1:
-T).(eq T (THead k0 t t0) (THead (Bind Abst) v t1)))) (\forall (t1: T).((eq T
-(THead k0 t t0) (THead (Bind Abst) v t1)) \to (\forall (P: Prop).P))))) (let
-H_x0 \def (term_dec t v) in (let H3 \def H_x0 in (or_ind (eq T t v) ((eq T t
-v) \to (\forall (P: Prop).P)) (or (ex T (\lambda (t1: T).(eq T (THead (Bind
-Abst) t t0) (THead (Bind Abst) v t1)))) (\forall (t1: T).((eq T (THead (Bind
-Abst) t t0) (THead (Bind Abst) v t1)) \to (\forall (P: Prop).P)))) (\lambda
-(H4: (eq T t v)).(eq_ind T t (\lambda (t1: T).(or (ex T (\lambda (t2: T).(eq
-T (THead (Bind Abst) t t0) (THead (Bind Abst) t1 t2)))) (\forall (t2: T).((eq
-T (THead (Bind Abst) t t0) (THead (Bind Abst) t1 t2)) \to (\forall (P:
-Prop).P))))) (or_introl (ex T (\lambda (t1: T).(eq T (THead (Bind Abst) t t0)
-(THead (Bind Abst) t t1)))) (\forall (t1: T).((eq T (THead (Bind Abst) t t0)
-(THead (Bind Abst) t t1)) \to (\forall (P: Prop).P))) (ex_intro T (\lambda
-(t1: T).(eq T (THead (Bind Abst) t t0) (THead (Bind Abst) t t1))) t0
-(refl_equal T (THead (Bind Abst) t t0)))) v H4)) (\lambda (H4: (((eq T t v)
-\to (\forall (P: Prop).P)))).(or_intror (ex T (\lambda (t1: T).(eq T (THead
-(Bind Abst) t t0) (THead (Bind Abst) v t1)))) (\forall (t1: T).((eq T (THead
-(Bind Abst) t t0) (THead (Bind Abst) v t1)) \to (\forall (P: Prop).P)))
-(\lambda (t1: T).(\lambda (H5: (eq T (THead (Bind Abst) t t0) (THead (Bind
-Abst) v t1))).(\lambda (P: Prop).(let H6 \def (f_equal T T (\lambda (e:
-T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow t |
-(TLRef _) \Rightarrow t | (THead _ t2 _) \Rightarrow t2])) (THead (Bind Abst)
-t t0) (THead (Bind Abst) v t1) H5) in ((let H7 \def (f_equal T T (\lambda (e:
-T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow t0 |
-(TLRef _) \Rightarrow t0 | (THead _ _ t2) \Rightarrow t2])) (THead (Bind
-Abst) t t0) (THead (Bind Abst) v t1) H5) in (\lambda (H8: (eq T t v)).(H4 H8
-P))) H6))))))) H3))) k H2)) (\lambda (H2: (((eq K k (Bind Abst)) \to (\forall
-(P: Prop).P)))).(or_intror (ex T (\lambda (t1: T).(eq T (THead k t t0) (THead
-(Bind Abst) v t1)))) (\forall (t1: T).((eq T (THead k t t0) (THead (Bind
-Abst) v t1)) \to (\forall (P: Prop).P))) (\lambda (t1: T).(\lambda (H3: (eq T
-(THead k t t0) (THead (Bind Abst) v t1))).(\lambda (P: Prop).(let H4 \def
-(f_equal T K (\lambda (e: T).(match e in T return (\lambda (_: T).K) with
-[(TSort _) \Rightarrow k | (TLRef _) \Rightarrow k | (THead k0 _ _)
-\Rightarrow k0])) (THead k t t0) (THead (Bind Abst) v t1) H3) in ((let H5
-\def (f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T)
-with [(TSort _) \Rightarrow t | (TLRef _) \Rightarrow t | (THead _ t2 _)
-\Rightarrow t2])) (THead k t t0) (THead (Bind Abst) v t1) H3) in ((let H6
-\def (f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T)
-with [(TSort _) \Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t2)
-\Rightarrow t2])) (THead k t t0) (THead (Bind Abst) v t1) H3) in (\lambda (_:
-(eq T t v)).(\lambda (H8: (eq K k (Bind Abst))).(H2 H8 P)))) H5)) H4)))))))
-H1))))))))) u).
-(* COMMENTS
-Initial nodes: 1305
-END *)
-
projects / helm.git / blobdiff