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 b) \Rightarrow b |
+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 (b0: B).((eq B b b0) \to (\forall (P: Prop).P))) H0 b H2) in (H3
-(refl_equal B b) P))))))) H)))) (\lambda (f: F).(or_intror (eq K (Bind 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 _)
(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 f) \Rightarrow f])) (Flat f) (Flat f0) H1) in
-(let H3 \def (eq_ind_r F f0 (\lambda (f0: F).((eq F f f0) \to (\forall (P:
-Prop).P))) H0 f H2) in (H3 (refl_equal F f) P))))))) H)))) k2))) k1).
+[(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).
theorem term_dec:
\forall (t1: T).(\forall (t2: T).(or (eq T t1 t2) ((eq T t1 t2) \to (\forall
(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 n) \Rightarrow n | (TLRef _) \Rightarrow n | (THead _ _ _)
+[(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 (n0: nat).((eq nat n n0) \to (\forall (P: Prop).P))) 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 (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 |
((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 n) \Rightarrow n | (THead _ _ _) \Rightarrow n]))
-(TLRef n) (TLRef n0) H1) in (let H3 \def (eq_ind_r nat n0 (\lambda (n0:
-nat).((eq nat n n0) \to (\forall (P: Prop).P))) H0 n H2) in (H3 (refl_equal
+\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:
(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 (t1: T).(or (eq T (THead k t t0) t1) ((eq T
-(THead k t t0) t1) \to (\forall (P: Prop).P)))) H1 t H4) in (eq_ind T t
+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 (t1: T).(or (eq T (THead k t t0) t1) ((eq T
-(THead k t t0) t1) \to (\forall (P: Prop).P)))) H2 t0 H7) in (eq_ind T t0
+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
\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 k _ _) \Rightarrow k])) (THead k t t0) (THead k0 t t0)
-H11) in (let H13 \def (eq_ind_r K k0 (\lambda (k0: K).((eq K k k0) \to
-(\forall (P: Prop).P))) 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
+\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 k _ _) \Rightarrow k])) (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
+\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 _ _ t) \Rightarrow t])) (THead k t t0) (THead k0 t t4) H8) in
-(\lambda (_: (eq K k k0)).(let H12 \def (eq_ind_r T t4 (\lambda (t: T).((eq T
-t0 t) \to (\forall (P: Prop).P))) H7 t0 H10) in (let H13 \def (eq_ind_r T t4
-(\lambda (t1: T).(or (eq T (THead k t t0) t1) ((eq T (THead k t t0) t1) \to
-(\forall (P: Prop).P)))) H2 t0 H10) in (H12 (refl_equal T t0) P))))) H9))))))
-H6))) t3 H4))) (\lambda (H4: (((eq T t t3) \to (\forall (P:
+| (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 k _ _) \Rightarrow k]))
+\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 _ t _) \Rightarrow t])) (THead k t t0)
+| (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 _ _ t) \Rightarrow t])) (THead k t t0) (THead k0 t3
+\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 (t1: T).(or (eq T (THead k t t0) t1) ((eq T (THead k
-t t0) t1) \to (\forall (P: Prop).P)))) H2 t0 H8) in (let H12 \def (eq_ind_r T
-t3 (\lambda (t0: T).((eq T t t0) \to (\forall (P: Prop).P))) H4 t H9) in (let
-H13 \def (eq_ind_r T t3 (\lambda (t1: T).(or (eq T (THead k t t0) t1) ((eq T
-(THead k t t0) t1) \to (\forall (P: Prop).P)))) H1 t H9) in (H12 (refl_equal
-T t) P))))))) H7)) H6)))))) H3)))))))) t2))))))) t1).
+(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).
theorem binder_dec:
\forall (t: T).(or (ex_3 B T T (\lambda (b: B).(\lambda (w: T).(\lambda (u:
(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).(match k in K return (\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))))))))))) with [(Bind b) \Rightarrow (\lambda (t0: T).(\lambda (_:
-(or (ex_3 B T T (\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(eq T t0
+(\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_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))))))))
-| (Flat f) \Rightarrow (\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 k _ _) \Rightarrow (match k 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))))))))))))])) t).
+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).
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).(match u in T return (\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)))))) with [(TSort n)
-\Rightarrow (\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))))))) |
-(TLRef n) \Rightarrow (\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))))))) | (THead k t t0) \Rightarrow (\lambda (v: T).(let H_x \def
-(terms_props__kind_dec k (Bind Abst)) in (let H \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 (H0: (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 H1 \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 (H2: (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 H2)) (\lambda (H2: (((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 (H3: (eq T (THead (Bind Abst) t t0) (THead (Bind Abst) v
-t1))).(\lambda (P: Prop).(let H4 \def (f_equal T T (\lambda (e: T).(match e
-in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow t | (TLRef _)
-\Rightarrow t | (THead _ t _) \Rightarrow t])) (THead (Bind Abst) t t0)
-(THead (Bind Abst) v t1) H3) in ((let H5 \def (f_equal T T (\lambda (e:
+ \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 _ _ t) \Rightarrow t])) (THead (Bind Abst)
-t t0) (THead (Bind Abst) v t1) H3) in (\lambda (H6: (eq T t v)).(H2 H6 P)))
-H4))))))) H1))) k H0)) (\lambda (H0: (((eq K k (Bind Abst)) \to (\forall (P:
-Prop).P)))).(or_intror (ex T (\lambda (t1: T).(eq T (THead k t t0) (THead
+(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 (H1: (eq T
-(THead k t t0) (THead (Bind Abst) v t1))).(\lambda (P: Prop).(let H2 \def
+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 k _ _)
-\Rightarrow k])) (THead k t t0) (THead (Bind Abst) v t1) H1) in ((let H3 \def
-(f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with
-[(TSort _) \Rightarrow t | (TLRef _) \Rightarrow t | (THead _ t _)
-\Rightarrow t])) (THead k t t0) (THead (Bind Abst) v t1) H1) in ((let H4 \def
-(f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with
-[(TSort _) \Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t)
-\Rightarrow t])) (THead k t t0) (THead (Bind Abst) v t1) H1) in (\lambda (_:
-(eq T t v)).(\lambda (H6: (eq K k (Bind Abst))).(H0 H6 P)))) H3)) H2)))))))
-H))))]).
+[(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).
projects / helm.git / blobdiff