include "basic_1/flt/props.ma".
-theorem getl_flt:
+lemma getl_flt:
\forall (b: B).(\forall (c: C).(\forall (e: C).(\forall (u: T).(\forall (i:
nat).((getl i c (CHead e (Bind b) u)) \to (flt e u c (TLRef i)))))))
\def
- \lambda (b: B).(\lambda (c: C).(let TMP_2 \def (\lambda (c0: C).(\forall (e:
+ \lambda (b: B).(\lambda (c: C).(C_ind (\lambda (c0: C).(\forall (e:
C).(\forall (u: T).(\forall (i: nat).((getl i c0 (CHead e (Bind b) u)) \to
-(let TMP_1 \def (TLRef i) in (flt e u c0 TMP_1))))))) in (let TMP_8 \def
-(\lambda (n: nat).(\lambda (e: C).(\lambda (u: T).(\lambda (i: nat).(\lambda
-(H: (getl i (CSort n) (CHead e (Bind b) u))).(let TMP_3 \def (Bind b) in (let
-TMP_4 \def (CHead e TMP_3 u) in (let TMP_5 \def (CSort n) in (let TMP_6 \def
-(TLRef i) in (let TMP_7 \def (flt e u TMP_5 TMP_6) in (getl_gen_sort n i
-TMP_4 H TMP_7))))))))))) in (let TMP_79 \def (\lambda (c0: C).(\lambda (H:
-((\forall (e: C).(\forall (u: T).(\forall (i: nat).((getl i c0 (CHead e (Bind
-b) u)) \to (flt e u c0 (TLRef i)))))))).(\lambda (k: K).(\lambda (t:
-T).(\lambda (e: C).(\lambda (u: T).(\lambda (i: nat).(let TMP_11 \def
-(\lambda (n: nat).((getl n (CHead c0 k t) (CHead e (Bind b) u)) \to (let
-TMP_9 \def (CHead c0 k t) in (let TMP_10 \def (TLRef n) in (flt e u TMP_9
-TMP_10))))) in (let TMP_71 \def (\lambda (H0: (getl O (CHead c0 k t) (CHead e
-(Bind b) u))).(let TMP_14 \def (\lambda (k0: K).((clear (CHead c0 k0 t)
-(CHead e (Bind b) u)) \to (let TMP_12 \def (CHead c0 k0 t) in (let TMP_13
-\def (TLRef O) in (flt e u TMP_12 TMP_13))))) in (let TMP_57 \def (\lambda
-(b0: B).(\lambda (H1: (clear (CHead c0 (Bind b0) t) (CHead e (Bind b)
-u))).(let TMP_15 \def (\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow
-e | (CHead c1 _ _) \Rightarrow c1])) in (let TMP_16 \def (Bind b) in (let
-TMP_17 \def (CHead e TMP_16 u) in (let TMP_18 \def (Bind b0) in (let TMP_19
-\def (CHead c0 TMP_18 t) in (let TMP_20 \def (Bind b) in (let TMP_21 \def
-(CHead e TMP_20 u) in (let TMP_22 \def (clear_gen_bind b0 c0 TMP_21 t H1) in
-(let H2 \def (f_equal C C TMP_15 TMP_17 TMP_19 TMP_22) in (let TMP_23 \def
-(\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow b | (CHead _ k0 _)
-\Rightarrow (match k0 with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow
-b])])) in (let TMP_24 \def (Bind b) in (let TMP_25 \def (CHead e TMP_24 u) in
-(let TMP_26 \def (Bind b0) in (let TMP_27 \def (CHead c0 TMP_26 t) in (let
-TMP_28 \def (Bind b) in (let TMP_29 \def (CHead e TMP_28 u) in (let TMP_30
-\def (clear_gen_bind b0 c0 TMP_29 t H1) in (let H3 \def (f_equal C B TMP_23
-TMP_25 TMP_27 TMP_30) in (let TMP_31 \def (\lambda (e0: C).(match e0 with
-[(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) in (let TMP_32
-\def (Bind b) in (let TMP_33 \def (CHead e TMP_32 u) in (let TMP_34 \def
-(Bind b0) in (let TMP_35 \def (CHead c0 TMP_34 t) in (let TMP_36 \def (Bind
-b) in (let TMP_37 \def (CHead e TMP_36 u) in (let TMP_38 \def (clear_gen_bind
-b0 c0 TMP_37 t H1) in (let H4 \def (f_equal C T TMP_31 TMP_33 TMP_35 TMP_38)
-in (let TMP_55 \def (\lambda (H5: (eq B b b0)).(\lambda (H6: (eq C e
-c0)).(let TMP_42 \def (\lambda (t0: T).(let TMP_39 \def (Bind b0) in (let
-TMP_40 \def (CHead c0 TMP_39 t) in (let TMP_41 \def (TLRef O) in (flt e t0
-TMP_40 TMP_41))))) in (let TMP_46 \def (\lambda (c1: C).(let TMP_43 \def
-(Bind b0) in (let TMP_44 \def (CHead c0 TMP_43 t) in (let TMP_45 \def (TLRef
-O) in (flt c1 t TMP_44 TMP_45))))) in (let TMP_50 \def (\lambda (b1: B).(let
-TMP_47 \def (Bind b1) in (let TMP_48 \def (CHead c0 TMP_47 t) in (let TMP_49
-\def (TLRef O) in (flt c0 t TMP_48 TMP_49))))) in (let TMP_51 \def (Bind b)
-in (let TMP_52 \def (flt_arith0 TMP_51 c0 t O) in (let TMP_53 \def (eq_ind B
-b TMP_50 TMP_52 b0 H5) in (let TMP_54 \def (eq_ind_r C c0 TMP_46 TMP_53 e H6)
-in (eq_ind_r T t TMP_42 TMP_54 u H4)))))))))) in (let TMP_56 \def (TMP_55 H3)
-in (TMP_56 H2)))))))))))))))))))))))))))))))) in (let TMP_66 \def (\lambda
-(f: F).(\lambda (H1: (clear (CHead c0 (Flat f) t) (CHead e (Bind b) u))).(let
-TMP_58 \def (Bind b) in (let TMP_59 \def (Bind b) in (let TMP_60 \def (CHead
-e TMP_59 u) in (let TMP_61 \def (Bind b) in (let TMP_62 \def (CHead e TMP_61
-u) in (let TMP_63 \def (clear_gen_flat f c0 TMP_62 t H1) in (let TMP_64 \def
-(clear_cle c0 TMP_60 TMP_63) in (let TMP_65 \def (Flat f) in (flt_arith1
-TMP_58 e c0 u TMP_64 TMP_65 t O))))))))))) in (let TMP_67 \def (CHead c0 k t)
-in (let TMP_68 \def (Bind b) in (let TMP_69 \def (CHead e TMP_68 u) in (let
-TMP_70 \def (getl_gen_O TMP_67 TMP_69 H0) in (K_ind TMP_14 TMP_57 TMP_66 k
-TMP_70))))))))) in (let TMP_78 \def (\lambda (n: nat).(\lambda (_: (((getl n
-(CHead c0 k t) (CHead e (Bind b) u)) \to (flt e u (CHead c0 k t) (TLRef
-n))))).(\lambda (H1: (getl (S n) (CHead c0 k t) (CHead e (Bind b) u))).(let
-TMP_72 \def (r k n) in (let TMP_73 \def (Bind b) in (let TMP_74 \def (CHead e
-TMP_73 u) in (let TMP_75 \def (getl_gen_S k c0 TMP_74 t n H1) in (let H_y
-\def (H e u TMP_72 TMP_75) in (let TMP_76 \def (r k n) in (let TMP_77 \def (S
-n) in (flt_arith2 e c0 u TMP_76 H_y k t TMP_77))))))))))) in (nat_ind TMP_11
-TMP_71 TMP_78 i))))))))))) in (C_ind TMP_2 TMP_8 TMP_79 c))))).
+(flt e u c0 (TLRef i))))))) (\lambda (n: nat).(\lambda (e: C).(\lambda (u:
+T).(\lambda (i: nat).(\lambda (H: (getl i (CSort n) (CHead e (Bind b)
+u))).(getl_gen_sort n i (CHead e (Bind b) u) H (flt e u (CSort n) (TLRef
+i)))))))) (\lambda (c0: C).(\lambda (H: ((\forall (e: C).(\forall (u:
+T).(\forall (i: nat).((getl i c0 (CHead e (Bind b) u)) \to (flt e u c0 (TLRef
+i)))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (e: C).(\lambda (u:
+T).(\lambda (i: nat).(nat_ind (\lambda (n: nat).((getl n (CHead c0 k t)
+(CHead e (Bind b) u)) \to (flt e u (CHead c0 k t) (TLRef n)))) (\lambda (H0:
+(getl O (CHead c0 k t) (CHead e (Bind b) u))).(K_ind (\lambda (k0: K).((clear
+(CHead c0 k0 t) (CHead e (Bind b) u)) \to (flt e u (CHead c0 k0 t) (TLRef
+O)))) (\lambda (b0: B).(\lambda (H1: (clear (CHead c0 (Bind b0) t) (CHead e
+(Bind b) u))).(let H2 \def (f_equal C C (\lambda (e0: C).(match e0 with
+[(CSort _) \Rightarrow e | (CHead c1 _ _) \Rightarrow c1])) (CHead e (Bind b)
+u) (CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead e (Bind b) u) t H1))
+in ((let H3 \def (f_equal C B (\lambda (e0: C).(match e0 with [(CSort _)
+\Rightarrow b | (CHead _ k0 _) \Rightarrow (match k0 with [(Bind b1)
+\Rightarrow b1 | (Flat _) \Rightarrow b])])) (CHead e (Bind b) u) (CHead c0
+(Bind b0) t) (clear_gen_bind b0 c0 (CHead e (Bind b) u) t H1)) in ((let H4
+\def (f_equal C T (\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow u |
+(CHead _ _ t0) \Rightarrow t0])) (CHead e (Bind b) u) (CHead c0 (Bind b0) t)
+(clear_gen_bind b0 c0 (CHead e (Bind b) u) t H1)) in (\lambda (H5: (eq B b
+b0)).(\lambda (H6: (eq C e c0)).(eq_ind_r T t (\lambda (t0: T).(flt e t0
+(CHead c0 (Bind b0) t) (TLRef O))) (eq_ind_r C c0 (\lambda (c1: C).(flt c1 t
+(CHead c0 (Bind b0) t) (TLRef O))) (eq_ind B b (\lambda (b1: B).(flt c0 t
+(CHead c0 (Bind b1) t) (TLRef O))) (flt_arith0 (Bind b) c0 t O) b0 H5) e H6)
+u H4)))) H3)) H2)))) (\lambda (f: F).(\lambda (H1: (clear (CHead c0 (Flat f)
+t) (CHead e (Bind b) u))).(flt_arith1 (Bind b) e c0 u (clear_cle c0 (CHead e
+(Bind b) u) (clear_gen_flat f c0 (CHead e (Bind b) u) t H1)) (Flat f) t O)))
+k (getl_gen_O (CHead c0 k t) (CHead e (Bind b) u) H0))) (\lambda (n:
+nat).(\lambda (_: (((getl n (CHead c0 k t) (CHead e (Bind b) u)) \to (flt e u
+(CHead c0 k t) (TLRef n))))).(\lambda (H1: (getl (S n) (CHead c0 k t) (CHead
+e (Bind b) u))).(let H_y \def (H e u (r k n) (getl_gen_S k c0 (CHead e (Bind
+b) u) t n H1)) in (flt_arith2 e c0 u (r k n) H_y k t (S n)))))) i)))))))) c)).
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