(* This file was automatically generated: do not edit *********************)
-include "Basic-1/ty3/props.ma".
+include "basic_1/ty3/props.ma".
-include "Basic-1/pc3/fsubst0.ma".
+include "basic_1/pc3/fsubst0.ma".
-include "Basic-1/getl/getl.ma".
+include "basic_1/getl/getl.ma".
-theorem ty3_fsubst0:
+lemma ty3_fsubst0:
\forall (g: G).(\forall (c1: C).(\forall (t1: T).(\forall (t: T).((ty3 g c1
t1 t) \to (\forall (i: nat).(\forall (u: T).(\forall (c2: C).(\forall (t2:
T).((fsubst0 i u c1 t1 c2 t2) \to (\forall (e: C).((getl i c1 (CHead e (Bind
nat).(getl n0 c (CHead e (Bind Abbr) u0))) H5 n H6) in (let H9 \def (eq_ind C
(CHead d (Bind Abbr) u) (\lambda (c0: C).(getl n c c0)) H0 (CHead e (Bind
Abbr) u0) (getl_mono c (CHead d (Bind Abbr) u) n H0 (CHead e (Bind Abbr) u0)
-H8)) in (let H10 \def (f_equal C C (\lambda (e0: C).(match e0 in C return
-(\lambda (_: C).C) with [(CSort _) \Rightarrow d | (CHead c0 _ _) \Rightarrow
-c0])) (CHead d (Bind Abbr) u) (CHead e (Bind Abbr) u0) (getl_mono c (CHead d
-(Bind Abbr) u) n H0 (CHead e (Bind Abbr) u0) H8)) in ((let H11 \def (f_equal
-C T (\lambda (e0: C).(match e0 in C return (\lambda (_: C).T) with [(CSort _)
-\Rightarrow u | (CHead _ _ t4) \Rightarrow t4])) (CHead d (Bind Abbr) u)
+H8)) in (let H10 \def (f_equal C C (\lambda (e0: C).(match e0 with [(CSort _)
+\Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind Abbr) u)
(CHead e (Bind Abbr) u0) (getl_mono c (CHead d (Bind Abbr) u) n H0 (CHead e
-(Bind Abbr) u0) H8)) in (\lambda (H12: (eq C d e)).(let H13 \def (eq_ind_r C
-e (\lambda (c0: C).(getl n c (CHead c0 (Bind Abbr) u0))) H9 d H12) in (let
-H14 \def (eq_ind_r T u0 (\lambda (t4: T).(getl n c (CHead d (Bind Abbr) t4)))
-H13 u H11) in (eq_ind T u (\lambda (t4: T).(ty3 g c (lift (S n) O t4) (lift
-(S n) O t0))) (ty3_lift g d u t0 H1 c O (S n) (getl_drop Abbr c d u n H14))
-u0 H11))))) H10)))) t3 H7))) (subst0_gen_lref u0 t3 i n H4)))))) (\lambda
-(c3: C).(\lambda (H4: (csubst0 i u0 c c3)).(\lambda (e: C).(\lambda (H5:
-(getl i c (CHead e (Bind Abbr) u0))).(lt_le_e n i (ty3 g c3 (TLRef n) (lift
-(S n) O t0)) (\lambda (H6: (lt n i)).(let H7 \def (csubst0_getl_lt i n H6 c
-c3 u0 H4 (CHead d (Bind Abbr) u) H0) in (or4_ind (getl n c3 (CHead d (Bind
-Abbr) u)) (ex3_4 B C T T (\lambda (b: B).(\lambda (e0: C).(\lambda (u1:
-T).(\lambda (_: T).(eq C (CHead d (Bind Abbr) u) (CHead e0 (Bind b) u1))))))
-(\lambda (b: B).(\lambda (e0: C).(\lambda (_: T).(\lambda (w: T).(getl n c3
-(CHead e0 (Bind b) w)))))) (\lambda (_: B).(\lambda (_: C).(\lambda (u1:
-T).(\lambda (w: T).(subst0 (minus i (S n)) u0 u1 w)))))) (ex3_4 B C C T
-(\lambda (b: B).(\lambda (e1: C).(\lambda (_: C).(\lambda (u1: T).(eq C
-(CHead d (Bind Abbr) u) (CHead e1 (Bind b) u1)))))) (\lambda (b: B).(\lambda
-(_: C).(\lambda (e2: C).(\lambda (u1: T).(getl n c3 (CHead e2 (Bind b)
-u1)))))) (\lambda (_: B).(\lambda (e1: C).(\lambda (e2: C).(\lambda (_:
-T).(csubst0 (minus i (S n)) u0 e1 e2)))))) (ex4_5 B C C T T (\lambda (b:
-B).(\lambda (e1: C).(\lambda (_: C).(\lambda (u1: T).(\lambda (_: T).(eq C
-(CHead d (Bind Abbr) u) (CHead e1 (Bind b) u1))))))) (\lambda (b: B).(\lambda
-(_: C).(\lambda (e2: C).(\lambda (_: T).(\lambda (w: T).(getl n c3 (CHead e2
-(Bind b) w))))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_: C).(\lambda
-(u1: T).(\lambda (w: T).(subst0 (minus i (S n)) u0 u1 w)))))) (\lambda (_:
-B).(\lambda (e1: C).(\lambda (e2: C).(\lambda (_: T).(\lambda (_: T).(csubst0
-(minus i (S n)) u0 e1 e2))))))) (ty3 g c3 (TLRef n) (lift (S n) O t0))
-(\lambda (H8: (getl n c3 (CHead d (Bind Abbr) u))).(ty3_abbr g n c3 d u H8 t0
-H1)) (\lambda (H8: (ex3_4 B C T T (\lambda (b: B).(\lambda (e0: C).(\lambda
-(u1: T).(\lambda (_: T).(eq C (CHead d (Bind Abbr) u) (CHead e0 (Bind b)
-u1)))))) (\lambda (b: B).(\lambda (e0: C).(\lambda (_: T).(\lambda (w:
-T).(getl n c3 (CHead e0 (Bind b) w)))))) (\lambda (_: B).(\lambda (_:
+(Bind Abbr) u0) H8)) in ((let H11 \def (f_equal C T (\lambda (e0: C).(match
+e0 with [(CSort _) \Rightarrow u | (CHead _ _ t4) \Rightarrow t4])) (CHead d
+(Bind Abbr) u) (CHead e (Bind Abbr) u0) (getl_mono c (CHead d (Bind Abbr) u)
+n H0 (CHead e (Bind Abbr) u0) H8)) in (\lambda (H12: (eq C d e)).(let H13
+\def (eq_ind_r C e (\lambda (c0: C).(getl n c (CHead c0 (Bind Abbr) u0))) H9
+d H12) in (let H14 \def (eq_ind_r T u0 (\lambda (t4: T).(getl n c (CHead d
+(Bind Abbr) t4))) H13 u H11) in (eq_ind T u (\lambda (t4: T).(ty3 g c (lift
+(S n) O t4) (lift (S n) O t0))) (ty3_lift g d u t0 H1 c O (S n) (getl_drop
+Abbr c d u n H14)) u0 H11))))) H10)))) t3 H7))) (subst0_gen_lref u0 t3 i n
+H4)))))) (\lambda (c3: C).(\lambda (H4: (csubst0 i u0 c c3)).(\lambda (e:
+C).(\lambda (H5: (getl i c (CHead e (Bind Abbr) u0))).(lt_le_e n i (ty3 g c3
+(TLRef n) (lift (S n) O t0)) (\lambda (H6: (lt n i)).(let H7 \def
+(csubst0_getl_lt i n H6 c c3 u0 H4 (CHead d (Bind Abbr) u) H0) in (or4_ind
+(getl n c3 (CHead d (Bind Abbr) u)) (ex3_4 B C T T (\lambda (b: B).(\lambda
+(e0: C).(\lambda (u1: T).(\lambda (_: T).(eq C (CHead d (Bind Abbr) u) (CHead
+e0 (Bind b) u1)))))) (\lambda (b: B).(\lambda (e0: C).(\lambda (_:
+T).(\lambda (w: T).(getl n c3 (CHead e0 (Bind b) w)))))) (\lambda (_:
+B).(\lambda (_: C).(\lambda (u1: T).(\lambda (w: T).(subst0 (minus i (S n))
+u0 u1 w)))))) (ex3_4 B C C T (\lambda (b: B).(\lambda (e1: C).(\lambda (_:
+C).(\lambda (u1: T).(eq C (CHead d (Bind Abbr) u) (CHead e1 (Bind b) u1))))))
+(\lambda (b: B).(\lambda (_: C).(\lambda (e2: C).(\lambda (u1: T).(getl n c3
+(CHead e2 (Bind b) u1)))))) (\lambda (_: B).(\lambda (e1: C).(\lambda (e2:
+C).(\lambda (_: T).(csubst0 (minus i (S n)) u0 e1 e2)))))) (ex4_5 B C C T T
+(\lambda (b: B).(\lambda (e1: C).(\lambda (_: C).(\lambda (u1: T).(\lambda
+(_: T).(eq C (CHead d (Bind Abbr) u) (CHead e1 (Bind b) u1))))))) (\lambda
+(b: B).(\lambda (_: C).(\lambda (e2: C).(\lambda (_: T).(\lambda (w: T).(getl
+n c3 (CHead e2 (Bind b) w))))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_:
+C).(\lambda (u1: T).(\lambda (w: T).(subst0 (minus i (S n)) u0 u1 w))))))
+(\lambda (_: B).(\lambda (e1: C).(\lambda (e2: C).(\lambda (_: T).(\lambda
+(_: T).(csubst0 (minus i (S n)) u0 e1 e2))))))) (ty3 g c3 (TLRef n) (lift (S
+n) O t0)) (\lambda (H8: (getl n c3 (CHead d (Bind Abbr) u))).(ty3_abbr g n c3
+d u H8 t0 H1)) (\lambda (H8: (ex3_4 B C T T (\lambda (b: B).(\lambda (e0:
+C).(\lambda (u1: T).(\lambda (_: T).(eq C (CHead d (Bind Abbr) u) (CHead e0
+(Bind b) u1)))))) (\lambda (b: B).(\lambda (e0: C).(\lambda (_: T).(\lambda
+(w: T).(getl n c3 (CHead e0 (Bind b) w)))))) (\lambda (_: B).(\lambda (_:
C).(\lambda (u1: T).(\lambda (w: T).(subst0 (minus i (S n)) u0 u1
w))))))).(ex3_4_ind B C T T (\lambda (b: B).(\lambda (e0: C).(\lambda (u1:
T).(\lambda (_: T).(eq C (CHead d (Bind Abbr) u) (CHead e0 (Bind b) u1))))))
T).(\lambda (x3: T).(\lambda (H9: (eq C (CHead d (Bind Abbr) u) (CHead x1
(Bind x0) x2))).(\lambda (H10: (getl n c3 (CHead x1 (Bind x0) x3))).(\lambda
(H11: (subst0 (minus i (S n)) u0 x2 x3)).(let H12 \def (f_equal C C (\lambda
-(e0: C).(match e0 in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow
-d | (CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind Abbr) u) (CHead x1 (Bind
-x0) x2) H9) in ((let H13 \def (f_equal C B (\lambda (e0: C).(match e0 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 d (Bind Abbr) u) (CHead
-x1 (Bind x0) x2) H9) in ((let H14 \def (f_equal C T (\lambda (e0: C).(match
-e0 in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _
-t3) \Rightarrow t3])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x2) H9) in
-(\lambda (H15: (eq B Abbr x0)).(\lambda (H16: (eq C d x1)).(let H17 \def
-(eq_ind_r T x2 (\lambda (t3: T).(subst0 (minus i (S n)) u0 t3 x3)) H11 u H14)
-in (let H18 \def (eq_ind_r C x1 (\lambda (c0: C).(getl n c3 (CHead c0 (Bind
-x0) x3))) H10 d H16) in (let H19 \def (eq_ind_r B x0 (\lambda (b: B).(getl n
-c3 (CHead d (Bind b) x3))) H18 Abbr H15) in (let H20 \def (eq_ind nat (minus
-i n) (\lambda (n0: nat).(getl n0 (CHead d (Bind Abbr) x3) (CHead e (Bind
-Abbr) u0))) (getl_conf_le i (CHead e (Bind Abbr) u0) c3 (csubst0_getl_ge i i
-(le_n i) c c3 u0 H4 (CHead e (Bind Abbr) u0) H5) (CHead d (Bind Abbr) x3) n
-H19 (le_S_n n i (le_S (S n) i H6))) (S (minus i (S n))) (minus_x_Sy i n H6))
-in (ty3_abbr g n c3 d x3 H19 t0 (H2 (minus i (S n)) u0 d x3 (fsubst0_snd
-(minus i (S n)) u0 d u x3 H17) e (getl_gen_S (Bind Abbr) d (CHead e (Bind
-Abbr) u0) x3 (minus i (S n)) H20)))))))))) H13)) H12))))))))) H8)) (\lambda
-(H8: (ex3_4 B C C T (\lambda (b: B).(\lambda (e1: C).(\lambda (_: C).(\lambda
-(u1: T).(eq C (CHead d (Bind Abbr) u) (CHead e1 (Bind b) u1)))))) (\lambda
-(b: B).(\lambda (_: C).(\lambda (e2: C).(\lambda (u1: T).(getl n c3 (CHead e2
+(e0: C).(match e0 with [(CSort _) \Rightarrow d | (CHead c0 _ _) \Rightarrow
+c0])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x2) H9) in ((let H13 \def
+(f_equal C B (\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow Abbr |
+(CHead _ k _) \Rightarrow (match k with [(Bind b) \Rightarrow b | (Flat _)
+\Rightarrow Abbr])])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x2) H9) in
+((let H14 \def (f_equal C T (\lambda (e0: C).(match e0 with [(CSort _)
+\Rightarrow u | (CHead _ _ t3) \Rightarrow t3])) (CHead d (Bind Abbr) u)
+(CHead x1 (Bind x0) x2) H9) in (\lambda (H15: (eq B Abbr x0)).(\lambda (H16:
+(eq C d x1)).(let H17 \def (eq_ind_r T x2 (\lambda (t3: T).(subst0 (minus i
+(S n)) u0 t3 x3)) H11 u H14) in (let H18 \def (eq_ind_r C x1 (\lambda (c0:
+C).(getl n c3 (CHead c0 (Bind x0) x3))) H10 d H16) in (let H19 \def (eq_ind_r
+B x0 (\lambda (b: B).(getl n c3 (CHead d (Bind b) x3))) H18 Abbr H15) in (let
+H20 \def (eq_ind nat (minus i n) (\lambda (n0: nat).(getl n0 (CHead d (Bind
+Abbr) x3) (CHead e (Bind Abbr) u0))) (getl_conf_le i (CHead e (Bind Abbr) u0)
+c3 (csubst0_getl_ge i i (le_n i) c c3 u0 H4 (CHead e (Bind Abbr) u0) H5)
+(CHead d (Bind Abbr) x3) n H19 (le_S_n n i (le_S_n (S n) (S i) (le_S (S (S
+n)) (S i) (le_n_S (S n) i H6))))) (S (minus i (S n))) (minus_x_Sy i n H6)) in
+(ty3_abbr g n c3 d x3 H19 t0 (H2 (minus i (S n)) u0 d x3 (fsubst0_snd (minus
+i (S n)) u0 d u x3 H17) e (getl_gen_S (Bind Abbr) d (CHead e (Bind Abbr) u0)
+x3 (minus i (S n)) H20)))))))))) H13)) H12))))))))) H8)) (\lambda (H8: (ex3_4
+B C C T (\lambda (b: B).(\lambda (e1: C).(\lambda (_: C).(\lambda (u1: T).(eq
+C (CHead d (Bind Abbr) u) (CHead e1 (Bind b) u1)))))) (\lambda (b:
+B).(\lambda (_: C).(\lambda (e2: C).(\lambda (u1: T).(getl n c3 (CHead e2
(Bind b) u1)))))) (\lambda (_: B).(\lambda (e1: C).(\lambda (e2: C).(\lambda
(_: T).(csubst0 (minus i (S n)) u0 e1 e2))))))).(ex3_4_ind B C C T (\lambda
(b: B).(\lambda (e1: C).(\lambda (_: C).(\lambda (u1: T).(eq C (CHead d (Bind
B).(\lambda (x1: C).(\lambda (x2: C).(\lambda (x3: T).(\lambda (H9: (eq C
(CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x3))).(\lambda (H10: (getl n c3
(CHead x2 (Bind x0) x3))).(\lambda (H11: (csubst0 (minus i (S n)) u0 x1
-x2)).(let H12 \def (f_equal C C (\lambda (e0: C).(match e0 in C return
-(\lambda (_: C).C) with [(CSort _) \Rightarrow d | (CHead c0 _ _) \Rightarrow
-c0])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x3) H9) in ((let H13 \def
-(f_equal C B (\lambda (e0: C).(match e0 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 d (Bind Abbr) u) (CHead x1 (Bind x0) x3) H9) in ((let H14
-\def (f_equal C T (\lambda (e0: C).(match e0 in C return (\lambda (_: C).T)
-with [(CSort _) \Rightarrow u | (CHead _ _ t3) \Rightarrow t3])) (CHead d
-(Bind Abbr) u) (CHead x1 (Bind x0) x3) H9) in (\lambda (H15: (eq B Abbr
-x0)).(\lambda (H16: (eq C d x1)).(let H17 \def (eq_ind_r T x3 (\lambda (t3:
-T).(getl n c3 (CHead x2 (Bind x0) t3))) H10 u H14) in (let H18 \def (eq_ind_r
-C x1 (\lambda (c0: C).(csubst0 (minus i (S n)) u0 c0 x2)) H11 d H16) in (let
-H19 \def (eq_ind_r B x0 (\lambda (b: B).(getl n c3 (CHead x2 (Bind b) u)))
-H17 Abbr H15) in (let H20 \def (eq_ind nat (minus i n) (\lambda (n0:
-nat).(getl n0 (CHead x2 (Bind Abbr) u) (CHead e (Bind Abbr) u0)))
-(getl_conf_le i (CHead e (Bind Abbr) u0) c3 (csubst0_getl_ge i i (le_n i) c
-c3 u0 H4 (CHead e (Bind Abbr) u0) H5) (CHead x2 (Bind Abbr) u) n H19 (le_S_n
-n i (le_S (S n) i H6))) (S (minus i (S n))) (minus_x_Sy i n H6)) in (ty3_abbr
+x2)).(let H12 \def (f_equal C C (\lambda (e0: C).(match e0 with [(CSort _)
+\Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind Abbr) u)
+(CHead x1 (Bind x0) x3) H9) in ((let H13 \def (f_equal C B (\lambda (e0:
+C).(match e0 with [(CSort _) \Rightarrow Abbr | (CHead _ k _) \Rightarrow
+(match k with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow Abbr])])) (CHead
+d (Bind Abbr) u) (CHead x1 (Bind x0) x3) H9) in ((let H14 \def (f_equal C T
+(\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow u | (CHead _ _ t3)
+\Rightarrow t3])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x3) H9) in
+(\lambda (H15: (eq B Abbr x0)).(\lambda (H16: (eq C d x1)).(let H17 \def
+(eq_ind_r T x3 (\lambda (t3: T).(getl n c3 (CHead x2 (Bind x0) t3))) H10 u
+H14) in (let H18 \def (eq_ind_r C x1 (\lambda (c0: C).(csubst0 (minus i (S
+n)) u0 c0 x2)) H11 d H16) in (let H19 \def (eq_ind_r B x0 (\lambda (b:
+B).(getl n c3 (CHead x2 (Bind b) u))) H17 Abbr H15) in (let H20 \def (eq_ind
+nat (minus i n) (\lambda (n0: nat).(getl n0 (CHead x2 (Bind Abbr) u) (CHead e
+(Bind Abbr) u0))) (getl_conf_le i (CHead e (Bind Abbr) u0) c3
+(csubst0_getl_ge i i (le_n i) c c3 u0 H4 (CHead e (Bind Abbr) u0) H5) (CHead
+x2 (Bind Abbr) u) n H19 (le_S_n n i (le_S_n (S n) (S i) (le_S (S (S n)) (S i)
+(le_n_S (S n) i H6))))) (S (minus i (S n))) (minus_x_Sy i n H6)) in (ty3_abbr
g n c3 x2 u H19 t0 (H2 (minus i (S n)) u0 x2 u (fsubst0_fst (minus i (S n))
u0 d u x2 H18) e (csubst0_getl_ge_back (minus i (S n)) (minus i (S n)) (le_n
(minus i (S n))) d x2 u0 H18 (CHead e (Bind Abbr) u0) (getl_gen_S (Bind Abbr)
(x4: T).(\lambda (H9: (eq C (CHead d (Bind Abbr) u) (CHead x1 (Bind x0)
x3))).(\lambda (H10: (getl n c3 (CHead x2 (Bind x0) x4))).(\lambda (H11:
(subst0 (minus i (S n)) u0 x3 x4)).(\lambda (H12: (csubst0 (minus i (S n)) u0
-x1 x2)).(let H13 \def (f_equal C C (\lambda (e0: C).(match e0 in C return
-(\lambda (_: C).C) with [(CSort _) \Rightarrow d | (CHead c0 _ _) \Rightarrow
-c0])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x3) H9) in ((let H14 \def
-(f_equal C B (\lambda (e0: C).(match e0 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 d (Bind Abbr) u) (CHead x1 (Bind x0) x3) H9) in ((let H15
-\def (f_equal C T (\lambda (e0: C).(match e0 in C return (\lambda (_: C).T)
-with [(CSort _) \Rightarrow u | (CHead _ _ t3) \Rightarrow t3])) (CHead d
-(Bind Abbr) u) (CHead x1 (Bind x0) x3) H9) in (\lambda (H16: (eq B Abbr
-x0)).(\lambda (H17: (eq C d x1)).(let H18 \def (eq_ind_r T x3 (\lambda (t3:
-T).(subst0 (minus i (S n)) u0 t3 x4)) H11 u H15) in (let H19 \def (eq_ind_r C
-x1 (\lambda (c0: C).(csubst0 (minus i (S n)) u0 c0 x2)) H12 d H17) in (let
-H20 \def (eq_ind_r B x0 (\lambda (b: B).(getl n c3 (CHead x2 (Bind b) x4)))
-H10 Abbr H16) in (let H21 \def (eq_ind nat (minus i n) (\lambda (n0:
-nat).(getl n0 (CHead x2 (Bind Abbr) x4) (CHead e (Bind Abbr) u0)))
-(getl_conf_le i (CHead e (Bind Abbr) u0) c3 (csubst0_getl_ge i i (le_n i) c
-c3 u0 H4 (CHead e (Bind Abbr) u0) H5) (CHead x2 (Bind Abbr) x4) n H20 (le_S_n
-n i (le_S (S n) i H6))) (S (minus i (S n))) (minus_x_Sy i n H6)) in (ty3_abbr
-g n c3 x2 x4 H20 t0 (H2 (minus i (S n)) u0 x2 x4 (fsubst0_both (minus i (S
-n)) u0 d u x4 H18 x2 H19) e (csubst0_getl_ge_back (minus i (S n)) (minus i (S
-n)) (le_n (minus i (S n))) d x2 u0 H19 (CHead e (Bind Abbr) u0) (getl_gen_S
-(Bind Abbr) x2 (CHead e (Bind Abbr) u0) x4 (minus i (S n)) H21)))))))))))
-H14)) H13))))))))))) H8)) H7))) (\lambda (H6: (le i n)).(ty3_abbr g n c3 d u
-(csubst0_getl_ge i n H6 c c3 u0 H4 (CHead d (Bind Abbr) u) H0) t0 H1)))))))
-(\lambda (t3: T).(\lambda (H4: (subst0 i u0 (TLRef n) t3)).(\lambda (c3:
-C).(\lambda (H5: (csubst0 i u0 c c3)).(\lambda (e: C).(\lambda (H6: (getl i c
-(CHead e (Bind Abbr) u0))).(land_ind (eq nat n i) (eq T t3 (lift (S n) O u0))
-(ty3 g c3 t3 (lift (S n) O t0)) (\lambda (H7: (eq nat n i)).(\lambda (H8: (eq
-T t3 (lift (S n) O u0))).(eq_ind_r T (lift (S n) O u0) (\lambda (t4: T).(ty3
-g c3 t4 (lift (S n) O t0))) (let H9 \def (eq_ind_r nat i (\lambda (n0:
-nat).(getl n0 c (CHead e (Bind Abbr) u0))) H6 n H7) in (let H10 \def
-(eq_ind_r nat i (\lambda (n0: nat).(csubst0 n0 u0 c c3)) H5 n H7) in (let H11
-\def (eq_ind C (CHead d (Bind Abbr) u) (\lambda (c0: C).(getl n c c0)) H0
+x1 x2)).(let H13 \def (f_equal C C (\lambda (e0: C).(match e0 with [(CSort _)
+\Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind Abbr) u)
+(CHead x1 (Bind x0) x3) H9) in ((let H14 \def (f_equal C B (\lambda (e0:
+C).(match e0 with [(CSort _) \Rightarrow Abbr | (CHead _ k _) \Rightarrow
+(match k with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow Abbr])])) (CHead
+d (Bind Abbr) u) (CHead x1 (Bind x0) x3) H9) in ((let H15 \def (f_equal C T
+(\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow u | (CHead _ _ t3)
+\Rightarrow t3])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x3) H9) in
+(\lambda (H16: (eq B Abbr x0)).(\lambda (H17: (eq C d x1)).(let H18 \def
+(eq_ind_r T x3 (\lambda (t3: T).(subst0 (minus i (S n)) u0 t3 x4)) H11 u H15)
+in (let H19 \def (eq_ind_r C x1 (\lambda (c0: C).(csubst0 (minus i (S n)) u0
+c0 x2)) H12 d H17) in (let H20 \def (eq_ind_r B x0 (\lambda (b: B).(getl n c3
+(CHead x2 (Bind b) x4))) H10 Abbr H16) in (let H21 \def (eq_ind nat (minus i
+n) (\lambda (n0: nat).(getl n0 (CHead x2 (Bind Abbr) x4) (CHead e (Bind Abbr)
+u0))) (getl_conf_le i (CHead e (Bind Abbr) u0) c3 (csubst0_getl_ge i i (le_n
+i) c c3 u0 H4 (CHead e (Bind Abbr) u0) H5) (CHead x2 (Bind Abbr) x4) n H20
+(le_S_n n i (le_S_n (S n) (S i) (le_S (S (S n)) (S i) (le_n_S (S n) i H6)))))
+(S (minus i (S n))) (minus_x_Sy i n H6)) in (ty3_abbr g n c3 x2 x4 H20 t0 (H2
+(minus i (S n)) u0 x2 x4 (fsubst0_both (minus i (S n)) u0 d u x4 H18 x2 H19)
+e (csubst0_getl_ge_back (minus i (S n)) (minus i (S n)) (le_n (minus i (S
+n))) d x2 u0 H19 (CHead e (Bind Abbr) u0) (getl_gen_S (Bind Abbr) x2 (CHead e
+(Bind Abbr) u0) x4 (minus i (S n)) H21))))))))))) H14)) H13))))))))))) H8))
+H7))) (\lambda (H6: (le i n)).(ty3_abbr g n c3 d u (csubst0_getl_ge i n H6 c
+c3 u0 H4 (CHead d (Bind Abbr) u) H0) t0 H1))))))) (\lambda (t3: T).(\lambda
+(H4: (subst0 i u0 (TLRef n) t3)).(\lambda (c3: C).(\lambda (H5: (csubst0 i u0
+c c3)).(\lambda (e: C).(\lambda (H6: (getl i c (CHead e (Bind Abbr)
+u0))).(land_ind (eq nat n i) (eq T t3 (lift (S n) O u0)) (ty3 g c3 t3 (lift
+(S n) O t0)) (\lambda (H7: (eq nat n i)).(\lambda (H8: (eq T t3 (lift (S n) O
+u0))).(eq_ind_r T (lift (S n) O u0) (\lambda (t4: T).(ty3 g c3 t4 (lift (S n)
+O t0))) (let H9 \def (eq_ind_r nat i (\lambda (n0: nat).(getl n0 c (CHead e
+(Bind Abbr) u0))) H6 n H7) in (let H10 \def (eq_ind_r nat i (\lambda (n0:
+nat).(csubst0 n0 u0 c c3)) H5 n H7) in (let H11 \def (eq_ind C (CHead d (Bind
+Abbr) u) (\lambda (c0: C).(getl n c c0)) H0 (CHead e (Bind Abbr) u0)
+(getl_mono c (CHead d (Bind Abbr) u) n H0 (CHead e (Bind Abbr) u0) H9)) in
+(let H12 \def (f_equal C C (\lambda (e0: C).(match e0 with [(CSort _)
+\Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind Abbr) u)
(CHead e (Bind Abbr) u0) (getl_mono c (CHead d (Bind Abbr) u) n H0 (CHead e
-(Bind Abbr) u0) H9)) in (let H12 \def (f_equal C C (\lambda (e0: C).(match e0
-in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d | (CHead c0 _ _)
-\Rightarrow c0])) (CHead d (Bind Abbr) u) (CHead e (Bind Abbr) u0) (getl_mono
-c (CHead d (Bind Abbr) u) n H0 (CHead e (Bind Abbr) u0) H9)) in ((let H13
-\def (f_equal C T (\lambda (e0: C).(match e0 in C return (\lambda (_: C).T)
-with [(CSort _) \Rightarrow u | (CHead _ _ t4) \Rightarrow t4])) (CHead d
+(Bind Abbr) u0) H9)) in ((let H13 \def (f_equal C T (\lambda (e0: C).(match
+e0 with [(CSort _) \Rightarrow u | (CHead _ _ t4) \Rightarrow t4])) (CHead d
(Bind Abbr) u) (CHead e (Bind Abbr) u0) (getl_mono c (CHead d (Bind Abbr) u)
n H0 (CHead e (Bind Abbr) u0) H9)) in (\lambda (H14: (eq C d e)).(let H15
\def (eq_ind_r C e (\lambda (c0: C).(getl n c (CHead c0 (Bind Abbr) u0))) H11
(Bind Abbr) u0))) H5 n H6) in (let H9 \def (eq_ind C (CHead d (Bind Abst) u)
(\lambda (c0: C).(getl n c c0)) H0 (CHead e (Bind Abbr) u0) (getl_mono c
(CHead d (Bind Abst) u) n H0 (CHead e (Bind Abbr) u0) H8)) in (let H10 \def
-(eq_ind C (CHead d (Bind Abst) 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 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 e (Bind Abbr) u0) (getl_mono c (CHead d (Bind
-Abst) u) n H0 (CHead e (Bind Abbr) u0) H8)) in (False_ind (ty3 g c (lift (S
-n) O u0) (lift (S n) O u)) H10)))) t3 H7))) (subst0_gen_lref u0 t3 i n
-H4)))))) (\lambda (c3: C).(\lambda (H4: (csubst0 i u0 c c3)).(\lambda (e:
-C).(\lambda (H5: (getl i c (CHead e (Bind Abbr) u0))).(lt_le_e n i (ty3 g c3
-(TLRef n) (lift (S n) O u)) (\lambda (H6: (lt n i)).(let H7 \def
-(csubst0_getl_lt i n H6 c c3 u0 H4 (CHead d (Bind Abst) u) H0) in (or4_ind
-(getl n c3 (CHead d (Bind Abst) u)) (ex3_4 B C T T (\lambda (b: B).(\lambda
+(eq_ind C (CHead d (Bind Abst) u) (\lambda (ee: C).(match ee with [(CSort _)
+\Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind b)
+\Rightarrow (match b with [Abbr \Rightarrow False | Abst \Rightarrow True |
+Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead e (Bind
+Abbr) u0) (getl_mono c (CHead d (Bind Abst) u) n H0 (CHead e (Bind Abbr) u0)
+H8)) in (False_ind (ty3 g c (lift (S n) O u0) (lift (S n) O u)) H10)))) t3
+H7))) (subst0_gen_lref u0 t3 i n H4)))))) (\lambda (c3: C).(\lambda (H4:
+(csubst0 i u0 c c3)).(\lambda (e: C).(\lambda (H5: (getl i c (CHead e (Bind
+Abbr) u0))).(lt_le_e n i (ty3 g c3 (TLRef n) (lift (S n) O u)) (\lambda (H6:
+(lt n i)).(let H7 \def (csubst0_getl_lt i n H6 c c3 u0 H4 (CHead d (Bind
+Abst) u) H0) in (or4_ind (getl n c3 (CHead d (Bind Abst) u)) (ex3_4 B C T T
+(\lambda (b: B).(\lambda (e0: C).(\lambda (u1: T).(\lambda (_: T).(eq C
+(CHead d (Bind Abst) u) (CHead e0 (Bind b) u1)))))) (\lambda (b: B).(\lambda
+(e0: C).(\lambda (_: T).(\lambda (w: T).(getl n c3 (CHead e0 (Bind b) w))))))
+(\lambda (_: B).(\lambda (_: C).(\lambda (u1: T).(\lambda (w: T).(subst0
+(minus i (S n)) u0 u1 w)))))) (ex3_4 B C C T (\lambda (b: B).(\lambda (e1:
+C).(\lambda (_: C).(\lambda (u1: T).(eq C (CHead d (Bind Abst) u) (CHead e1
+(Bind b) u1)))))) (\lambda (b: B).(\lambda (_: C).(\lambda (e2: C).(\lambda
+(u1: T).(getl n c3 (CHead e2 (Bind b) u1)))))) (\lambda (_: B).(\lambda (e1:
+C).(\lambda (e2: C).(\lambda (_: T).(csubst0 (minus i (S n)) u0 e1 e2))))))
+(ex4_5 B C C T T (\lambda (b: B).(\lambda (e1: C).(\lambda (_: C).(\lambda
+(u1: T).(\lambda (_: T).(eq C (CHead d (Bind Abst) u) (CHead e1 (Bind b)
+u1))))))) (\lambda (b: B).(\lambda (_: C).(\lambda (e2: C).(\lambda (_:
+T).(\lambda (w: T).(getl n c3 (CHead e2 (Bind b) w))))))) (\lambda (_:
+B).(\lambda (_: C).(\lambda (_: C).(\lambda (u1: T).(\lambda (w: T).(subst0
+(minus i (S n)) u0 u1 w)))))) (\lambda (_: B).(\lambda (e1: C).(\lambda (e2:
+C).(\lambda (_: T).(\lambda (_: T).(csubst0 (minus i (S n)) u0 e1 e2)))))))
+(ty3 g c3 (TLRef n) (lift (S n) O u)) (\lambda (H8: (getl n c3 (CHead d (Bind
+Abst) u))).(ty3_abst g n c3 d u H8 t0 H1)) (\lambda (H8: (ex3_4 B C T T
+(\lambda (b: B).(\lambda (e0: C).(\lambda (u1: T).(\lambda (_: T).(eq C
+(CHead d (Bind Abst) u) (CHead e0 (Bind b) u1)))))) (\lambda (b: B).(\lambda
+(e0: C).(\lambda (_: T).(\lambda (w: T).(getl n c3 (CHead e0 (Bind b) w))))))
+(\lambda (_: B).(\lambda (_: C).(\lambda (u1: T).(\lambda (w: T).(subst0
+(minus i (S n)) u0 u1 w))))))).(ex3_4_ind B C T T (\lambda (b: B).(\lambda
(e0: C).(\lambda (u1: T).(\lambda (_: T).(eq C (CHead d (Bind Abst) u) (CHead
e0 (Bind b) u1)))))) (\lambda (b: B).(\lambda (e0: C).(\lambda (_:
T).(\lambda (w: T).(getl n c3 (CHead e0 (Bind b) w)))))) (\lambda (_:
B).(\lambda (_: C).(\lambda (u1: T).(\lambda (w: T).(subst0 (minus i (S n))
-u0 u1 w)))))) (ex3_4 B C C T (\lambda (b: B).(\lambda (e1: C).(\lambda (_:
+u0 u1 w))))) (ty3 g c3 (TLRef n) (lift (S n) O u)) (\lambda (x0: B).(\lambda
+(x1: C).(\lambda (x2: T).(\lambda (x3: T).(\lambda (H9: (eq C (CHead d (Bind
+Abst) u) (CHead x1 (Bind x0) x2))).(\lambda (H10: (getl n c3 (CHead x1 (Bind
+x0) x3))).(\lambda (H11: (subst0 (minus i (S n)) u0 x2 x3)).(let H12 \def
+(f_equal C C (\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow d |
+(CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0)
+x2) H9) in ((let H13 \def (f_equal C B (\lambda (e0: C).(match e0 with
+[(CSort _) \Rightarrow Abst | (CHead _ k _) \Rightarrow (match k with [(Bind
+b) \Rightarrow b | (Flat _) \Rightarrow Abst])])) (CHead d (Bind Abst) u)
+(CHead x1 (Bind x0) x2) H9) in ((let H14 \def (f_equal C T (\lambda (e0:
+C).(match e0 with [(CSort _) \Rightarrow u | (CHead _ _ t3) \Rightarrow t3]))
+(CHead d (Bind Abst) u) (CHead x1 (Bind x0) x2) H9) in (\lambda (H15: (eq B
+Abst x0)).(\lambda (H16: (eq C d x1)).(let H17 \def (eq_ind_r T x2 (\lambda
+(t3: T).(subst0 (minus i (S n)) u0 t3 x3)) H11 u H14) in (let H18 \def
+(eq_ind_r C x1 (\lambda (c0: C).(getl n c3 (CHead c0 (Bind x0) x3))) H10 d
+H16) in (let H19 \def (eq_ind_r B x0 (\lambda (b: B).(getl n c3 (CHead d
+(Bind b) x3))) H18 Abst H15) in (let H20 \def (eq_ind nat (minus i n)
+(\lambda (n0: nat).(getl n0 (CHead d (Bind Abst) x3) (CHead e (Bind Abbr)
+u0))) (getl_conf_le i (CHead e (Bind Abbr) u0) c3 (csubst0_getl_ge i i (le_n
+i) c c3 u0 H4 (CHead e (Bind Abbr) u0) H5) (CHead d (Bind Abst) x3) n H19
+(le_S_n n i (le_S_n (S n) (S i) (le_S (S (S n)) (S i) (le_n_S (S n) i H6)))))
+(S (minus i (S n))) (minus_x_Sy i n H6)) in (ty3_conv g c3 (lift (S n) O u)
+(lift (S n) O t0) (ty3_lift g d u t0 H1 c3 O (S n) (getl_drop Abst c3 d x3 n
+H19)) (TLRef n) (lift (S n) O x3) (ty3_abst g n c3 d x3 H19 t0 (H2 (minus i
+(S n)) u0 d x3 (fsubst0_snd (minus i (S n)) u0 d u x3 H17) e (getl_gen_S
+(Bind Abst) d (CHead e (Bind Abbr) u0) x3 (minus i (S n)) H20))) (pc3_lift c3
+d (S n) O (getl_drop Abst c3 d x3 n H19) x3 u (pc3_pr2_x d x3 u (pr2_delta d
+e u0 (r (Bind Abst) (minus i (S n))) (getl_gen_S (Bind Abst) d (CHead e (Bind
+Abbr) u0) x3 (minus i (S n)) H20) u u (pr0_refl u) x3 H17))))))))))) H13))
+H12))))))))) H8)) (\lambda (H8: (ex3_4 B C C T (\lambda (b: B).(\lambda (e1:
+C).(\lambda (_: C).(\lambda (u1: T).(eq C (CHead d (Bind Abst) u) (CHead e1
+(Bind b) u1)))))) (\lambda (b: B).(\lambda (_: C).(\lambda (e2: C).(\lambda
+(u1: T).(getl n c3 (CHead e2 (Bind b) u1)))))) (\lambda (_: B).(\lambda (e1:
+C).(\lambda (e2: C).(\lambda (_: T).(csubst0 (minus i (S n)) u0 e1
+e2))))))).(ex3_4_ind B C C T (\lambda (b: B).(\lambda (e1: C).(\lambda (_:
C).(\lambda (u1: T).(eq C (CHead d (Bind Abst) u) (CHead e1 (Bind b) u1))))))
(\lambda (b: B).(\lambda (_: C).(\lambda (e2: C).(\lambda (u1: T).(getl n c3
(CHead e2 (Bind b) u1)))))) (\lambda (_: B).(\lambda (e1: C).(\lambda (e2:
-C).(\lambda (_: T).(csubst0 (minus i (S n)) u0 e1 e2)))))) (ex4_5 B C C T T
-(\lambda (b: B).(\lambda (e1: C).(\lambda (_: C).(\lambda (u1: T).(\lambda
-(_: T).(eq C (CHead d (Bind Abst) u) (CHead e1 (Bind b) u1))))))) (\lambda
-(b: B).(\lambda (_: C).(\lambda (e2: C).(\lambda (_: T).(\lambda (w: T).(getl
-n c3 (CHead e2 (Bind b) w))))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_:
-C).(\lambda (u1: T).(\lambda (w: T).(subst0 (minus i (S n)) u0 u1 w))))))
-(\lambda (_: B).(\lambda (e1: C).(\lambda (e2: C).(\lambda (_: T).(\lambda
-(_: T).(csubst0 (minus i (S n)) u0 e1 e2))))))) (ty3 g c3 (TLRef n) (lift (S
-n) O u)) (\lambda (H8: (getl n c3 (CHead d (Bind Abst) u))).(ty3_abst g n c3
-d u H8 t0 H1)) (\lambda (H8: (ex3_4 B C T T (\lambda (b: B).(\lambda (e0:
-C).(\lambda (u1: T).(\lambda (_: T).(eq C (CHead d (Bind Abst) u) (CHead e0
-(Bind b) u1)))))) (\lambda (b: B).(\lambda (e0: C).(\lambda (_: T).(\lambda
-(w: T).(getl n c3 (CHead e0 (Bind b) w)))))) (\lambda (_: B).(\lambda (_:
-C).(\lambda (u1: T).(\lambda (w: T).(subst0 (minus i (S n)) u0 u1
-w))))))).(ex3_4_ind B C T T (\lambda (b: B).(\lambda (e0: C).(\lambda (u1:
-T).(\lambda (_: T).(eq C (CHead d (Bind Abst) u) (CHead e0 (Bind b) u1))))))
-(\lambda (b: B).(\lambda (e0: C).(\lambda (_: T).(\lambda (w: T).(getl n c3
-(CHead e0 (Bind b) w)))))) (\lambda (_: B).(\lambda (_: C).(\lambda (u1:
-T).(\lambda (w: T).(subst0 (minus i (S n)) u0 u1 w))))) (ty3 g c3 (TLRef n)
-(lift (S n) O u)) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda
+C).(\lambda (_: T).(csubst0 (minus i (S n)) u0 e1 e2))))) (ty3 g c3 (TLRef n)
+(lift (S n) O u)) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: C).(\lambda
(x3: T).(\lambda (H9: (eq C (CHead d (Bind Abst) u) (CHead x1 (Bind x0)
-x2))).(\lambda (H10: (getl n c3 (CHead x1 (Bind x0) x3))).(\lambda (H11:
-(subst0 (minus i (S n)) u0 x2 x3)).(let H12 \def (f_equal C C (\lambda (e0:
-C).(match e0 in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d |
-(CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0)
-x2) H9) in ((let H13 \def (f_equal C B (\lambda (e0: C).(match e0 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 d (Bind Abst) u) (CHead
-x1 (Bind x0) x2) H9) in ((let H14 \def (f_equal C T (\lambda (e0: C).(match
-e0 in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _
-t3) \Rightarrow t3])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0) x2) H9) in
-(\lambda (H15: (eq B Abst x0)).(\lambda (H16: (eq C d x1)).(let H17 \def
-(eq_ind_r T x2 (\lambda (t3: T).(subst0 (minus i (S n)) u0 t3 x3)) H11 u H14)
-in (let H18 \def (eq_ind_r C x1 (\lambda (c0: C).(getl n c3 (CHead c0 (Bind
-x0) x3))) H10 d H16) in (let H19 \def (eq_ind_r B x0 (\lambda (b: B).(getl n
-c3 (CHead d (Bind b) x3))) H18 Abst H15) in (let H20 \def (eq_ind nat (minus
-i n) (\lambda (n0: nat).(getl n0 (CHead d (Bind Abst) x3) (CHead e (Bind
-Abbr) u0))) (getl_conf_le i (CHead e (Bind Abbr) u0) c3 (csubst0_getl_ge i i
-(le_n i) c c3 u0 H4 (CHead e (Bind Abbr) u0) H5) (CHead d (Bind Abst) x3) n
-H19 (le_S_n n i (le_S (S n) i H6))) (S (minus i (S n))) (minus_x_Sy i n H6))
-in (ty3_conv g c3 (lift (S n) O u) (lift (S n) O t0) (ty3_lift g d u t0 H1 c3
-O (S n) (getl_drop Abst c3 d x3 n H19)) (TLRef n) (lift (S n) O x3) (ty3_abst
-g n c3 d x3 H19 t0 (H2 (minus i (S n)) u0 d x3 (fsubst0_snd (minus i (S n))
-u0 d u x3 H17) e (getl_gen_S (Bind Abst) d (CHead e (Bind Abbr) u0) x3 (minus
-i (S n)) H20))) (pc3_lift c3 d (S n) O (getl_drop Abst c3 d x3 n H19) x3 u
-(pc3_pr2_x d x3 u (pr2_delta d e u0 (r (Bind Abst) (minus i (S n)))
-(getl_gen_S (Bind Abst) d (CHead e (Bind Abbr) u0) x3 (minus i (S n)) H20) u
-u (pr0_refl u) x3 H17))))))))))) H13)) H12))))))))) H8)) (\lambda (H8: (ex3_4
-B C C T (\lambda (b: B).(\lambda (e1: C).(\lambda (_: C).(\lambda (u1: T).(eq
-C (CHead d (Bind Abst) u) (CHead e1 (Bind b) u1)))))) (\lambda (b:
-B).(\lambda (_: C).(\lambda (e2: C).(\lambda (u1: T).(getl n c3 (CHead e2
-(Bind b) u1)))))) (\lambda (_: B).(\lambda (e1: C).(\lambda (e2: C).(\lambda
-(_: T).(csubst0 (minus i (S n)) u0 e1 e2))))))).(ex3_4_ind B C C T (\lambda
-(b: B).(\lambda (e1: C).(\lambda (_: C).(\lambda (u1: T).(eq C (CHead d (Bind
-Abst) u) (CHead e1 (Bind b) u1)))))) (\lambda (b: B).(\lambda (_: C).(\lambda
-(e2: C).(\lambda (u1: T).(getl n c3 (CHead e2 (Bind b) u1)))))) (\lambda (_:
-B).(\lambda (e1: C).(\lambda (e2: C).(\lambda (_: T).(csubst0 (minus i (S n))
-u0 e1 e2))))) (ty3 g c3 (TLRef n) (lift (S n) O u)) (\lambda (x0: B).(\lambda
-(x1: C).(\lambda (x2: C).(\lambda (x3: T).(\lambda (H9: (eq C (CHead d (Bind
-Abst) u) (CHead x1 (Bind x0) x3))).(\lambda (H10: (getl n c3 (CHead x2 (Bind
-x0) x3))).(\lambda (H11: (csubst0 (minus i (S n)) u0 x1 x2)).(let H12 \def
-(f_equal C C (\lambda (e0: C).(match e0 in C return (\lambda (_: C).C) with
-[(CSort _) \Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind
-Abst) u) (CHead x1 (Bind x0) x3) H9) in ((let H13 \def (f_equal C B (\lambda
-(e0: C).(match e0 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 d (Bind Abst)
-u) (CHead x1 (Bind x0) x3) H9) in ((let H14 \def (f_equal C T (\lambda (e0:
-C).(match e0 in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u |
-(CHead _ _ t3) \Rightarrow t3])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0)
-x3) H9) in (\lambda (H15: (eq B Abst x0)).(\lambda (H16: (eq C d x1)).(let
-H17 \def (eq_ind_r T x3 (\lambda (t3: T).(getl n c3 (CHead x2 (Bind x0) t3)))
-H10 u H14) in (let H18 \def (eq_ind_r C x1 (\lambda (c0: C).(csubst0 (minus i
-(S n)) u0 c0 x2)) H11 d H16) in (let H19 \def (eq_ind_r B x0 (\lambda (b:
-B).(getl n c3 (CHead x2 (Bind b) u))) H17 Abst H15) in (let H20 \def (eq_ind
-nat (minus i n) (\lambda (n0: nat).(getl n0 (CHead x2 (Bind Abst) u) (CHead e
-(Bind Abbr) u0))) (getl_conf_le i (CHead e (Bind Abbr) u0) c3
-(csubst0_getl_ge i i (le_n i) c c3 u0 H4 (CHead e (Bind Abbr) u0) H5) (CHead
-x2 (Bind Abst) u) n H19 (le_S_n n i (le_S (S n) i H6))) (S (minus i (S n)))
-(minus_x_Sy i n H6)) in (ty3_abst g n c3 x2 u H19 t0 (H2 (minus i (S n)) u0
-x2 u (fsubst0_fst (minus i (S n)) u0 d u x2 H18) e (csubst0_getl_ge_back
-(minus i (S n)) (minus i (S n)) (le_n (minus i (S n))) d x2 u0 H18 (CHead e
-(Bind Abbr) u0) (getl_gen_S (Bind Abst) x2 (CHead e (Bind Abbr) u0) u (minus
-i (S n)) H20))))))))))) H13)) H12))))))))) H8)) (\lambda (H8: (ex4_5 B C C T
-T (\lambda (b: B).(\lambda (e1: C).(\lambda (_: C).(\lambda (u1: T).(\lambda
-(_: T).(eq C (CHead d (Bind Abst) u) (CHead e1 (Bind b) u1))))))) (\lambda
-(b: B).(\lambda (_: C).(\lambda (e2: C).(\lambda (_: T).(\lambda (w: T).(getl
-n c3 (CHead e2 (Bind b) w))))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_:
-C).(\lambda (u1: T).(\lambda (w: T).(subst0 (minus i (S n)) u0 u1 w))))))
-(\lambda (_: B).(\lambda (e1: C).(\lambda (e2: C).(\lambda (_: T).(\lambda
-(_: T).(csubst0 (minus i (S n)) u0 e1 e2)))))))).(ex4_5_ind B C C T T
-(\lambda (b: B).(\lambda (e1: C).(\lambda (_: C).(\lambda (u1: T).(\lambda
-(_: T).(eq C (CHead d (Bind Abst) u) (CHead e1 (Bind b) u1))))))) (\lambda
-(b: B).(\lambda (_: C).(\lambda (e2: C).(\lambda (_: T).(\lambda (w: T).(getl
-n c3 (CHead e2 (Bind b) w))))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_:
-C).(\lambda (u1: T).(\lambda (w: T).(subst0 (minus i (S n)) u0 u1 w))))))
-(\lambda (_: B).(\lambda (e1: C).(\lambda (e2: C).(\lambda (_: T).(\lambda
-(_: T).(csubst0 (minus i (S n)) u0 e1 e2)))))) (ty3 g c3 (TLRef n) (lift (S
-n) O u)) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: C).(\lambda (x3:
-T).(\lambda (x4: T).(\lambda (H9: (eq C (CHead d (Bind Abst) u) (CHead x1
-(Bind x0) x3))).(\lambda (H10: (getl n c3 (CHead x2 (Bind x0) x4))).(\lambda
-(H11: (subst0 (minus i (S n)) u0 x3 x4)).(\lambda (H12: (csubst0 (minus i (S
-n)) u0 x1 x2)).(let H13 \def (f_equal C C (\lambda (e0: C).(match e0 in C
-return (\lambda (_: C).C) with [(CSort _) \Rightarrow d | (CHead c0 _ _)
-\Rightarrow c0])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0) x3) H9) in
-((let H14 \def (f_equal C B (\lambda (e0: C).(match e0 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 _)
+x3))).(\lambda (H10: (getl n c3 (CHead x2 (Bind x0) x3))).(\lambda (H11:
+(csubst0 (minus i (S n)) u0 x1 x2)).(let H12 \def (f_equal C C (\lambda (e0:
+C).(match e0 with [(CSort _) \Rightarrow d | (CHead c0 _ _) \Rightarrow c0]))
+(CHead d (Bind Abst) u) (CHead x1 (Bind x0) x3) H9) in ((let H13 \def
+(f_equal C B (\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow Abst |
+(CHead _ k _) \Rightarrow (match k with [(Bind b) \Rightarrow b | (Flat _)
\Rightarrow Abst])])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0) x3) H9) in
-((let H15 \def (f_equal C T (\lambda (e0: C).(match e0 in C return (\lambda
-(_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t3) \Rightarrow t3]))
-(CHead d (Bind Abst) u) (CHead x1 (Bind x0) x3) H9) in (\lambda (H16: (eq B
-Abst x0)).(\lambda (H17: (eq C d x1)).(let H18 \def (eq_ind_r T x3 (\lambda
-(t3: T).(subst0 (minus i (S n)) u0 t3 x4)) H11 u H15) in (let H19 \def
-(eq_ind_r C x1 (\lambda (c0: C).(csubst0 (minus i (S n)) u0 c0 x2)) H12 d
-H17) in (let H20 \def (eq_ind_r B x0 (\lambda (b: B).(getl n c3 (CHead x2
-(Bind b) x4))) H10 Abst H16) in (let H21 \def (eq_ind nat (minus i n)
-(\lambda (n0: nat).(getl n0 (CHead x2 (Bind Abst) x4) (CHead e (Bind Abbr)
+((let H14 \def (f_equal C T (\lambda (e0: C).(match e0 with [(CSort _)
+\Rightarrow u | (CHead _ _ t3) \Rightarrow t3])) (CHead d (Bind Abst) u)
+(CHead x1 (Bind x0) x3) H9) in (\lambda (H15: (eq B Abst x0)).(\lambda (H16:
+(eq C d x1)).(let H17 \def (eq_ind_r T x3 (\lambda (t3: T).(getl n c3 (CHead
+x2 (Bind x0) t3))) H10 u H14) in (let H18 \def (eq_ind_r C x1 (\lambda (c0:
+C).(csubst0 (minus i (S n)) u0 c0 x2)) H11 d H16) in (let H19 \def (eq_ind_r
+B x0 (\lambda (b: B).(getl n c3 (CHead x2 (Bind b) u))) H17 Abst H15) in (let
+H20 \def (eq_ind nat (minus i n) (\lambda (n0: nat).(getl n0 (CHead x2 (Bind
+Abst) u) (CHead e (Bind Abbr) u0))) (getl_conf_le i (CHead e (Bind Abbr) u0)
+c3 (csubst0_getl_ge i i (le_n i) c c3 u0 H4 (CHead e (Bind Abbr) u0) H5)
+(CHead x2 (Bind Abst) u) n H19 (le_S_n n i (le_S_n (S n) (S i) (le_S (S (S
+n)) (S i) (le_n_S (S n) i H6))))) (S (minus i (S n))) (minus_x_Sy i n H6)) in
+(ty3_abst g n c3 x2 u H19 t0 (H2 (minus i (S n)) u0 x2 u (fsubst0_fst (minus
+i (S n)) u0 d u x2 H18) e (csubst0_getl_ge_back (minus i (S n)) (minus i (S
+n)) (le_n (minus i (S n))) d x2 u0 H18 (CHead e (Bind Abbr) u0) (getl_gen_S
+(Bind Abst) x2 (CHead e (Bind Abbr) u0) u (minus i (S n)) H20)))))))))))
+H13)) H12))))))))) H8)) (\lambda (H8: (ex4_5 B C C T T (\lambda (b:
+B).(\lambda (e1: C).(\lambda (_: C).(\lambda (u1: T).(\lambda (_: T).(eq C
+(CHead d (Bind Abst) u) (CHead e1 (Bind b) u1))))))) (\lambda (b: B).(\lambda
+(_: C).(\lambda (e2: C).(\lambda (_: T).(\lambda (w: T).(getl n c3 (CHead e2
+(Bind b) w))))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_: C).(\lambda
+(u1: T).(\lambda (w: T).(subst0 (minus i (S n)) u0 u1 w)))))) (\lambda (_:
+B).(\lambda (e1: C).(\lambda (e2: C).(\lambda (_: T).(\lambda (_: T).(csubst0
+(minus i (S n)) u0 e1 e2)))))))).(ex4_5_ind B C C T T (\lambda (b:
+B).(\lambda (e1: C).(\lambda (_: C).(\lambda (u1: T).(\lambda (_: T).(eq C
+(CHead d (Bind Abst) u) (CHead e1 (Bind b) u1))))))) (\lambda (b: B).(\lambda
+(_: C).(\lambda (e2: C).(\lambda (_: T).(\lambda (w: T).(getl n c3 (CHead e2
+(Bind b) w))))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_: C).(\lambda
+(u1: T).(\lambda (w: T).(subst0 (minus i (S n)) u0 u1 w)))))) (\lambda (_:
+B).(\lambda (e1: C).(\lambda (e2: C).(\lambda (_: T).(\lambda (_: T).(csubst0
+(minus i (S n)) u0 e1 e2)))))) (ty3 g c3 (TLRef n) (lift (S n) O u)) (\lambda
+(x0: B).(\lambda (x1: C).(\lambda (x2: C).(\lambda (x3: T).(\lambda (x4:
+T).(\lambda (H9: (eq C (CHead d (Bind Abst) u) (CHead x1 (Bind x0)
+x3))).(\lambda (H10: (getl n c3 (CHead x2 (Bind x0) x4))).(\lambda (H11:
+(subst0 (minus i (S n)) u0 x3 x4)).(\lambda (H12: (csubst0 (minus i (S n)) u0
+x1 x2)).(let H13 \def (f_equal C C (\lambda (e0: C).(match e0 with [(CSort _)
+\Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind Abst) u)
+(CHead x1 (Bind x0) x3) H9) in ((let H14 \def (f_equal C B (\lambda (e0:
+C).(match e0 with [(CSort _) \Rightarrow Abst | (CHead _ k _) \Rightarrow
+(match k with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow Abst])])) (CHead
+d (Bind Abst) u) (CHead x1 (Bind x0) x3) H9) in ((let H15 \def (f_equal C T
+(\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow u | (CHead _ _ t3)
+\Rightarrow t3])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0) x3) H9) in
+(\lambda (H16: (eq B Abst x0)).(\lambda (H17: (eq C d x1)).(let H18 \def
+(eq_ind_r T x3 (\lambda (t3: T).(subst0 (minus i (S n)) u0 t3 x4)) H11 u H15)
+in (let H19 \def (eq_ind_r C x1 (\lambda (c0: C).(csubst0 (minus i (S n)) u0
+c0 x2)) H12 d H17) in (let H20 \def (eq_ind_r B x0 (\lambda (b: B).(getl n c3
+(CHead x2 (Bind b) x4))) H10 Abst H16) in (let H21 \def (eq_ind nat (minus i
+n) (\lambda (n0: nat).(getl n0 (CHead x2 (Bind Abst) x4) (CHead e (Bind Abbr)
u0))) (getl_conf_le i (CHead e (Bind Abbr) u0) c3 (csubst0_getl_ge i i (le_n
i) c c3 u0 H4 (CHead e (Bind Abbr) u0) H5) (CHead x2 (Bind Abst) x4) n H20
-(le_S_n n i (le_S (S n) i H6))) (S (minus i (S n))) (minus_x_Sy i n H6)) in
-(ty3_conv g c3 (lift (S n) O u) (lift (S n) O t0) (ty3_lift g x2 u t0 (H2
-(minus i (S n)) u0 x2 u (fsubst0_fst (minus i (S n)) u0 d u x2 H19) e
-(csubst0_getl_ge_back (minus i (S n)) (minus i (S n)) (le_n (minus i (S n)))
-d x2 u0 H19 (CHead e (Bind Abbr) u0) (getl_gen_S (Bind Abst) x2 (CHead e
-(Bind Abbr) u0) x4 (minus i (S n)) H21))) c3 O (S n) (getl_drop Abst c3 x2 x4
-n H20)) (TLRef n) (lift (S n) O x4) (ty3_abst g n c3 x2 x4 H20 t0 (H2 (minus
-i (S n)) u0 x2 x4 (fsubst0_both (minus i (S n)) u0 d u x4 H18 x2 H19) e
-(csubst0_getl_ge_back (minus i (S n)) (minus i (S n)) (le_n (minus i (S n)))
-d x2 u0 H19 (CHead e (Bind Abbr) u0) (getl_gen_S (Bind Abst) x2 (CHead e
-(Bind Abbr) u0) x4 (minus i (S n)) H21)))) (pc3_lift c3 x2 (S n) O (getl_drop
-Abst c3 x2 x4 n H20) x4 u (pc3_fsubst0 d u u (pc3_refl d u) (minus i (S n))
-u0 x2 x4 (fsubst0_both (minus i (S n)) u0 d u x4 H18 x2 H19) e
-(csubst0_getl_ge_back (minus i (S n)) (minus i (S n)) (le_n (minus i (S n)))
-d x2 u0 H19 (CHead e (Bind Abbr) u0) (getl_gen_S (Bind Abst) x2 (CHead e
-(Bind Abbr) u0) x4 (minus i (S n)) H21)))))))))))) H14)) H13))))))))))) H8))
-H7))) (\lambda (H6: (le i n)).(ty3_abst g n c3 d u (csubst0_getl_ge i n H6 c
-c3 u0 H4 (CHead d (Bind Abst) u) H0) t0 H1))))))) (\lambda (t3: T).(\lambda
-(H4: (subst0 i u0 (TLRef n) t3)).(\lambda (c3: C).(\lambda (H5: (csubst0 i u0
-c c3)).(\lambda (e: C).(\lambda (H6: (getl i c (CHead e (Bind Abbr)
-u0))).(land_ind (eq nat n i) (eq T t3 (lift (S n) O u0)) (ty3 g c3 t3 (lift
-(S n) O u)) (\lambda (H7: (eq nat n i)).(\lambda (H8: (eq T t3 (lift (S n) O
-u0))).(eq_ind_r T (lift (S n) O u0) (\lambda (t4: T).(ty3 g c3 t4 (lift (S n)
-O u))) (let H9 \def (eq_ind_r nat i (\lambda (n0: nat).(getl n0 c (CHead e
-(Bind Abbr) u0))) H6 n H7) in (let H10 \def (eq_ind_r nat i (\lambda (n0:
-nat).(csubst0 n0 u0 c c3)) H5 n H7) in (let H11 \def (eq_ind C (CHead d (Bind
-Abst) u) (\lambda (c0: C).(getl n c c0)) H0 (CHead e (Bind Abbr) u0)
-(getl_mono c (CHead d (Bind Abst) u) n H0 (CHead e (Bind Abbr) u0) H9)) in
-(let H12 \def (eq_ind C (CHead d (Bind Abst) 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 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 e (Bind Abbr) u0) (getl_mono c (CHead d (Bind
-Abst) u) n H0 (CHead e (Bind Abbr) u0) H9)) in (False_ind (ty3 g c3 (lift (S
-n) O u0) (lift (S n) O u)) H12))))) t3 H8))) (subst0_gen_lref u0 t3 i n
-H4)))))))) c2 t2 H3)))))))))))))) (\lambda (c: C).(\lambda (u: T).(\lambda
-(t0: T).(\lambda (H0: (ty3 g c u t0)).(\lambda (H1: ((\forall (i:
+(le_S_n n i (le_S_n (S n) (S i) (le_S (S (S n)) (S i) (le_n_S (S n) i H6)))))
+(S (minus i (S n))) (minus_x_Sy i n H6)) in (ty3_conv g c3 (lift (S n) O u)
+(lift (S n) O t0) (ty3_lift g x2 u t0 (H2 (minus i (S n)) u0 x2 u
+(fsubst0_fst (minus i (S n)) u0 d u x2 H19) e (csubst0_getl_ge_back (minus i
+(S n)) (minus i (S n)) (le_n (minus i (S n))) d x2 u0 H19 (CHead e (Bind
+Abbr) u0) (getl_gen_S (Bind Abst) x2 (CHead e (Bind Abbr) u0) x4 (minus i (S
+n)) H21))) c3 O (S n) (getl_drop Abst c3 x2 x4 n H20)) (TLRef n) (lift (S n)
+O x4) (ty3_abst g n c3 x2 x4 H20 t0 (H2 (minus i (S n)) u0 x2 x4
+(fsubst0_both (minus i (S n)) u0 d u x4 H18 x2 H19) e (csubst0_getl_ge_back
+(minus i (S n)) (minus i (S n)) (le_n (minus i (S n))) d x2 u0 H19 (CHead e
+(Bind Abbr) u0) (getl_gen_S (Bind Abst) x2 (CHead e (Bind Abbr) u0) x4 (minus
+i (S n)) H21)))) (pc3_lift c3 x2 (S n) O (getl_drop Abst c3 x2 x4 n H20) x4 u
+(pc3_fsubst0 d u u (pc3_refl d u) (minus i (S n)) u0 x2 x4 (fsubst0_both
+(minus i (S n)) u0 d u x4 H18 x2 H19) e (csubst0_getl_ge_back (minus i (S n))
+(minus i (S n)) (le_n (minus i (S n))) d x2 u0 H19 (CHead e (Bind Abbr) u0)
+(getl_gen_S (Bind Abst) x2 (CHead e (Bind Abbr) u0) x4 (minus i (S n))
+H21)))))))))))) H14)) H13))))))))))) H8)) H7))) (\lambda (H6: (le i
+n)).(ty3_abst g n c3 d u (csubst0_getl_ge i n H6 c c3 u0 H4 (CHead d (Bind
+Abst) u) H0) t0 H1))))))) (\lambda (t3: T).(\lambda (H4: (subst0 i u0 (TLRef
+n) t3)).(\lambda (c3: C).(\lambda (H5: (csubst0 i u0 c c3)).(\lambda (e:
+C).(\lambda (H6: (getl i c (CHead e (Bind Abbr) u0))).(land_ind (eq nat n i)
+(eq T t3 (lift (S n) O u0)) (ty3 g c3 t3 (lift (S n) O u)) (\lambda (H7: (eq
+nat n i)).(\lambda (H8: (eq T t3 (lift (S n) O u0))).(eq_ind_r T (lift (S n)
+O u0) (\lambda (t4: T).(ty3 g c3 t4 (lift (S n) O u))) (let H9 \def (eq_ind_r
+nat i (\lambda (n0: nat).(getl n0 c (CHead e (Bind Abbr) u0))) H6 n H7) in
+(let H10 \def (eq_ind_r nat i (\lambda (n0: nat).(csubst0 n0 u0 c c3)) H5 n
+H7) in (let H11 \def (eq_ind C (CHead d (Bind Abst) u) (\lambda (c0: C).(getl
+n c c0)) H0 (CHead e (Bind Abbr) u0) (getl_mono c (CHead d (Bind Abst) u) n
+H0 (CHead e (Bind Abbr) u0) H9)) in (let H12 \def (eq_ind C (CHead d (Bind
+Abst) u) (\lambda (ee: C).(match ee with [(CSort _) \Rightarrow False |
+(CHead _ k _) \Rightarrow (match k with [(Bind b) \Rightarrow (match b with
+[Abbr \Rightarrow False | Abst \Rightarrow True | Void \Rightarrow False]) |
+(Flat _) \Rightarrow False])])) I (CHead e (Bind Abbr) u0) (getl_mono c
+(CHead d (Bind Abst) u) n H0 (CHead e (Bind Abbr) u0) H9)) in (False_ind (ty3
+g c3 (lift (S n) O u0) (lift (S n) O u)) H12))))) t3 H8))) (subst0_gen_lref
+u0 t3 i n H4)))))))) c2 t2 H3)))))))))))))) (\lambda (c: C).(\lambda (u:
+T).(\lambda (t0: T).(\lambda (H0: (ty3 g c u t0)).(\lambda (H1: ((\forall (i:
nat).(\forall (u0: T).(\forall (c2: C).(\forall (t2: T).((fsubst0 i u0 c u c2
t2) \to (\forall (e: C).((getl i c (CHead e (Bind Abbr) u0)) \to (ty3 g c2 t2
t0)))))))))).(\lambda (b: B).(\lambda (t2: T).(\lambda (t3: T).(\lambda (H2:
i H10 t0) c3 H6) e H7)))) (ty3_correct g c3 t3 t0 (H3 i u c3 t3 (fsubst0_fst
i u c t3 c3 H6) e H7))) t5 H9)))))) H8)) (subst0_gen_head (Flat Cast) u t3 t2
t5 i H5)))))))) c2 t4 H4)))))))))))))) c1 t1 t H))))).
-(* COMMENTS
-Initial nodes: 23439
-END *)
-theorem ty3_csubst0:
+lemma ty3_csubst0:
\forall (g: G).(\forall (c1: C).(\forall (t1: T).(\forall (t2: T).((ty3 g c1
t1 t2) \to (\forall (e: C).(\forall (u: T).(\forall (i: nat).((getl i c1
(CHead e (Bind Abbr) u)) \to (\forall (c2: C).((csubst0 i u c1 c2) \to (ty3 g
nat).(\lambda (H0: (getl i c1 (CHead e (Bind Abbr) u))).(\lambda (c2:
C).(\lambda (H1: (csubst0 i u c1 c2)).(ty3_fsubst0 g c1 t1 t2 H i u c2 t1
(fsubst0_fst i u c1 t1 c2 H1) e H0))))))))))).
-(* COMMENTS
-Initial nodes: 89
-END *)
-theorem ty3_subst0:
+lemma ty3_subst0:
\forall (g: G).(\forall (c: C).(\forall (t1: T).(\forall (t: T).((ty3 g c t1
t) \to (\forall (e: C).(\forall (u: T).(\forall (i: nat).((getl i c (CHead e
(Bind Abbr) u)) \to (\forall (t2: T).((subst0 i u t1 t2) \to (ty3 g c t2
(H0: (getl i c (CHead e (Bind Abbr) u))).(\lambda (t2: T).(\lambda (H1:
(subst0 i u t1 t2)).(ty3_fsubst0 g c t1 t H i u c t2 (fsubst0_snd i u c t1 t2
H1) e H0))))))))))).
-(* COMMENTS
-Initial nodes: 89
-END *)
projects / helm.git / blobdiff