nat).(\lambda (d: nat).(\lambda (H1: (eq T (THead k v (lift h d (THead k0 t0
t1))) (THead k0 t0 t1))).(\lambda (P: Prop).(let H2 \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 v (lift h d (THead k0 t0 t1))) (THead k0 t0 t1) H1) in ((let H3 \def
(f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with
-[(TSort _) \Rightarrow v | (TLRef _) \Rightarrow v | (THead _ t _)
-\Rightarrow t])) (THead k v (lift h d (THead k0 t0 t1))) (THead k0 t0 t1) H1)
-in ((let H4 \def (f_equal T T (\lambda (e: T).(match e in T return (\lambda
-(_: T).T) with [(TSort _) \Rightarrow (THead k0 ((let rec lref_map (f: ((nat
-\to nat))) (d: nat) (t: T) on t: T \def (match t with [(TSort n) \Rightarrow
-(TSort n) | (TLRef i) \Rightarrow (TLRef (match (blt i d) with [true
-\Rightarrow i | false \Rightarrow (f i)])) | (THead k u t0) \Rightarrow
-(THead k (lref_map f d u) (lref_map f (s k d) t0))]) in lref_map) (\lambda
-(x: nat).(plus x h)) d t0) ((let rec lref_map (f: ((nat \to nat))) (d: nat)
-(t: T) on t: T \def (match t with [(TSort n) \Rightarrow (TSort n) | (TLRef
-i) \Rightarrow (TLRef (match (blt i d) with [true \Rightarrow i | false
-\Rightarrow (f i)])) | (THead k u t0) \Rightarrow (THead k (lref_map f d u)
-(lref_map f (s k d) t0))]) in lref_map) (\lambda (x: nat).(plus x h)) (s k0
-d) t1)) | (TLRef _) \Rightarrow (THead k0 ((let rec lref_map (f: ((nat \to
-nat))) (d: nat) (t: T) on t: T \def (match t with [(TSort n) \Rightarrow
-(TSort n) | (TLRef i) \Rightarrow (TLRef (match (blt i d) with [true
-\Rightarrow i | false \Rightarrow (f i)])) | (THead k u t0) \Rightarrow
-(THead k (lref_map f d u) (lref_map f (s k d) t0))]) in lref_map) (\lambda
-(x: nat).(plus x h)) d t0) ((let rec lref_map (f: ((nat \to nat))) (d: nat)
-(t: T) on t: T \def (match t with [(TSort n) \Rightarrow (TSort n) | (TLRef
-i) \Rightarrow (TLRef (match (blt i d) with [true \Rightarrow i | false
-\Rightarrow (f i)])) | (THead k u t0) \Rightarrow (THead k (lref_map f d u)
-(lref_map f (s k d) t0))]) in lref_map) (\lambda (x: nat).(plus x h)) (s k0
-d) t1)) | (THead _ _ t) \Rightarrow t])) (THead k v (lift h d (THead k0 t0
-t1))) (THead k0 t0 t1) H1) in (\lambda (_: (eq T v t0)).(\lambda (H6: (eq K k
-k0)).(let H7 \def (eq_ind K k (\lambda (k: K).(\forall (v: T).(\forall (h:
-nat).(\forall (d: nat).((eq T (THead k v (lift h d t1)) t1) \to (\forall (P:
-Prop).P)))))) H0 k0 H6) in (let H8 \def (eq_ind T (lift h d (THead k0 t0 t1))
-(\lambda (t: T).(eq T t t1)) H4 (THead k0 (lift h d t0) (lift h (s k0 d) t1))
-(lift_head k0 t0 t1 h d)) in (H7 (lift h d t0) h (s k0 d) H8 P)))))) H3))
-H2)))))))))))) t)).
+[(TSort _) \Rightarrow v | (TLRef _) \Rightarrow v | (THead _ t2 _)
+\Rightarrow t2])) (THead k v (lift h d (THead k0 t0 t1))) (THead k0 t0 t1)
+H1) in ((let H4 \def (f_equal T T (\lambda (e: T).(match e in T return
+(\lambda (_: T).T) with [(TSort _) \Rightarrow (THead k0 ((let rec lref_map
+(f: ((nat \to nat))) (d0: nat) (t2: T) on t2: T \def (match t2 with [(TSort
+n) \Rightarrow (TSort n) | (TLRef i) \Rightarrow (TLRef (match (blt i d0)
+with [true \Rightarrow i | false \Rightarrow (f i)])) | (THead k1 u t3)
+\Rightarrow (THead k1 (lref_map f d0 u) (lref_map f (s k1 d0) t3))]) in
+lref_map) (\lambda (x: nat).(plus x h)) d t0) ((let rec lref_map (f: ((nat
+\to nat))) (d0: nat) (t2: T) on t2: T \def (match t2 with [(TSort n)
+\Rightarrow (TSort n) | (TLRef i) \Rightarrow (TLRef (match (blt i d0) with
+[true \Rightarrow i | false \Rightarrow (f i)])) | (THead k1 u t3)
+\Rightarrow (THead k1 (lref_map f d0 u) (lref_map f (s k1 d0) t3))]) in
+lref_map) (\lambda (x: nat).(plus x h)) (s k0 d) t1)) | (TLRef _) \Rightarrow
+(THead k0 ((let rec lref_map (f: ((nat \to nat))) (d0: nat) (t2: T) on t2: T
+\def (match t2 with [(TSort n) \Rightarrow (TSort n) | (TLRef i) \Rightarrow
+(TLRef (match (blt i d0) with [true \Rightarrow i | false \Rightarrow (f
+i)])) | (THead k1 u t3) \Rightarrow (THead k1 (lref_map f d0 u) (lref_map f
+(s k1 d0) t3))]) in lref_map) (\lambda (x: nat).(plus x h)) d t0) ((let rec
+lref_map (f: ((nat \to nat))) (d0: nat) (t2: T) on t2: T \def (match t2 with
+[(TSort n) \Rightarrow (TSort n) | (TLRef i) \Rightarrow (TLRef (match (blt i
+d0) with [true \Rightarrow i | false \Rightarrow (f i)])) | (THead k1 u t3)
+\Rightarrow (THead k1 (lref_map f d0 u) (lref_map f (s k1 d0) t3))]) in
+lref_map) (\lambda (x: nat).(plus x h)) (s k0 d) t1)) | (THead _ _ t2)
+\Rightarrow t2])) (THead k v (lift h d (THead k0 t0 t1))) (THead k0 t0 t1)
+H1) in (\lambda (_: (eq T v t0)).(\lambda (H6: (eq K k k0)).(let H7 \def
+(eq_ind K k (\lambda (k1: K).(\forall (v0: T).(\forall (h0: nat).(\forall
+(d0: nat).((eq T (THead k1 v0 (lift h0 d0 t1)) t1) \to (\forall (P0:
+Prop).P0)))))) H0 k0 H6) in (let H8 \def (eq_ind T (lift h d (THead k0 t0
+t1)) (\lambda (t2: T).(eq T t2 t1)) H4 (THead k0 (lift h d t0) (lift h (s k0
+d) t1)) (lift_head k0 t0 t1 h d)) in (H7 (lift h d t0) h (s k0 d) H8 P))))))
+H3)) H2)))))))))))) t)).
theorem lift_r:
\forall (t: T).(\forall (d: nat).(eq T (lift O d t) t))
K).(\lambda (t0: T).(\lambda (H: ((\forall (d: nat).(eq T (lift O d t0)
t0)))).(\lambda (t1: T).(\lambda (H0: ((\forall (d: nat).(eq T (lift O d t1)
t1)))).(\lambda (d: nat).(eq_ind_r T (THead k (lift O d t0) (lift O (s k d)
-t1)) (\lambda (t2: T).(eq T t2 (THead k t0 t1))) (sym_equal T (THead k t0 t1)
-(THead k (lift O d t0) (lift O (s k d) t1)) (sym_equal T (THead k (lift O d
-t0) (lift O (s k d) t1)) (THead k t0 t1) (sym_equal T (THead k t0 t1) (THead
-k (lift O d t0) (lift O (s k d) t1)) (f_equal3 K T T T THead k k t0 (lift O d
-t0) t1 (lift O (s k d) t1) (refl_equal K k) (sym_eq T (lift O d t0) t0 (H d))
+t1)) (\lambda (t2: T).(eq T t2 (THead k t0 t1))) (sym_eq T (THead k t0 t1)
+(THead k (lift O d t0) (lift O (s k d) t1)) (sym_eq T (THead k (lift O d t0)
+(lift O (s k d) t1)) (THead k t0 t1) (sym_eq T (THead k t0 t1) (THead k (lift
+O d t0) (lift O (s k d) t1)) (f_equal3 K T T T THead k k t0 (lift O d t0) t1
+(lift O (s k d) t1) (refl_equal K k) (sym_eq T (lift O d t0) t0 (H d))
(sym_eq T (lift O (s k d) t1) t1 (H0 (s k d))))))) (lift O d (THead k t0 t1))
(lift_head k t0 t1 O d)))))))) t).
(lift_lref_ge n h d H0)) in (sym_eq T t (TLRef n) (lift_gen_lref_ge h d n H0
t H1)))))))))) (\lambda (k: K).(K_ind (\lambda (k0: K).(\forall (t:
T).(((\forall (t0: T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d t)
-(lift h d t0)) \to (eq T t t0)))))) \to (\forall (t0: T).(((\forall (t:
-T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d t0) (lift h d t)) \to
-(eq T t0 t)))))) \to (\forall (t1: T).(\forall (h: nat).(\forall (d:
+(lift h d t0)) \to (eq T t t0)))))) \to (\forall (t0: T).(((\forall (t1:
+T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d t0) (lift h d t1))
+\to (eq T t0 t1)))))) \to (\forall (t1: T).(\forall (h: nat).(\forall (d:
nat).((eq T (lift h d (THead k0 t t0)) (lift h d t1)) \to (eq T (THead k0 t
t0) t1)))))))))) (\lambda (b: B).(\lambda (t: T).(\lambda (H: ((\forall (t0:
T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d t) (lift h d t0)) \to
-(eq T t t0))))))).(\lambda (t0: T).(\lambda (H0: ((\forall (t: T).(\forall
-(h: nat).(\forall (d: nat).((eq T (lift h d t0) (lift h d t)) \to (eq T t0
-t))))))).(\lambda (t1: T).(\lambda (h: nat).(\lambda (d: nat).(\lambda (H1:
+(eq T t t0))))))).(\lambda (t0: T).(\lambda (H0: ((\forall (t1: T).(\forall
+(h: nat).(\forall (d: nat).((eq T (lift h d t0) (lift h d t1)) \to (eq T t0
+t1))))))).(\lambda (t1: T).(\lambda (h: nat).(\lambda (d: nat).(\lambda (H1:
(eq T (lift h d (THead (Bind b) t t0)) (lift h d t1))).(let H2 \def (eq_ind T
-(lift h d (THead (Bind b) t t0)) (\lambda (t: T).(eq T t (lift h d t1))) H1
+(lift h d (THead (Bind b) t t0)) (\lambda (t2: T).(eq T t2 (lift h d t1))) H1
(THead (Bind b) (lift h d t) (lift h (S d) t0)) (lift_bind b t t0 h d)) in
(ex3_2_ind T T (\lambda (y: T).(\lambda (z: T).(eq T t1 (THead (Bind b) y
z)))) (\lambda (y: T).(\lambda (_: T).(eq T (lift h d t) (lift h d y))))
(H3: (eq T t1 (THead (Bind b) x0 x1))).(\lambda (H4: (eq T (lift h d t) (lift
h d x0))).(\lambda (H5: (eq T (lift h (S d) t0) (lift h (S d) x1))).(eq_ind_r
T (THead (Bind b) x0 x1) (\lambda (t2: T).(eq T (THead (Bind b) t t0) t2))
-(sym_equal T (THead (Bind b) x0 x1) (THead (Bind b) t t0) (sym_equal T (THead
-(Bind b) t t0) (THead (Bind b) x0 x1) (sym_equal T (THead (Bind b) x0 x1)
-(THead (Bind b) t t0) (f_equal3 K T T T THead (Bind b) (Bind b) x0 t x1 t0
-(refl_equal K (Bind b)) (sym_eq T t x0 (H x0 h d H4)) (sym_eq T t0 x1 (H0 x1
-h (S d) H5)))))) t1 H3)))))) (lift_gen_bind b (lift h d t) (lift h (S d) t0)
-t1 h d H2)))))))))))) (\lambda (f: F).(\lambda (t: T).(\lambda (H: ((\forall
-(t0: T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d t) (lift h d
-t0)) \to (eq T t t0))))))).(\lambda (t0: T).(\lambda (H0: ((\forall (t:
-T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d t0) (lift h d t)) \to
-(eq T t0 t))))))).(\lambda (t1: T).(\lambda (h: nat).(\lambda (d:
-nat).(\lambda (H1: (eq T (lift h d (THead (Flat f) t t0)) (lift h d
-t1))).(let H2 \def (eq_ind T (lift h d (THead (Flat f) t t0)) (\lambda (t:
-T).(eq T t (lift h d t1))) H1 (THead (Flat f) (lift h d t) (lift h d t0))
-(lift_flat f t t0 h d)) in (ex3_2_ind T T (\lambda (y: T).(\lambda (z: T).(eq
-T t1 (THead (Flat f) y z)))) (\lambda (y: T).(\lambda (_: T).(eq T (lift h d
-t) (lift h d y)))) (\lambda (_: T).(\lambda (z: T).(eq T (lift h d t0) (lift
-h d z)))) (eq T (THead (Flat f) t t0) t1) (\lambda (x0: T).(\lambda (x1:
-T).(\lambda (H3: (eq T t1 (THead (Flat f) x0 x1))).(\lambda (H4: (eq T (lift
-h d t) (lift h d x0))).(\lambda (H5: (eq T (lift h d t0) (lift h d
-x1))).(eq_ind_r T (THead (Flat f) x0 x1) (\lambda (t2: T).(eq T (THead (Flat
-f) t t0) t2)) (sym_equal T (THead (Flat f) x0 x1) (THead (Flat f) t t0)
-(sym_equal T (THead (Flat f) t t0) (THead (Flat f) x0 x1) (sym_equal T (THead
-(Flat f) x0 x1) (THead (Flat f) t t0) (f_equal3 K T T T THead (Flat f) (Flat
-f) x0 t x1 t0 (refl_equal K (Flat f)) (sym_eq T t x0 (H x0 h d H4)) (sym_eq T
-t0 x1 (H0 x1 h d H5)))))) t1 H3)))))) (lift_gen_flat f (lift h d t) (lift h d
-t0) t1 h d H2)))))))))))) k)) x).
+(sym_eq T (THead (Bind b) x0 x1) (THead (Bind b) t t0) (sym_eq T (THead (Bind
+b) t t0) (THead (Bind b) x0 x1) (sym_eq T (THead (Bind b) x0 x1) (THead (Bind
+b) t t0) (f_equal3 K T T T THead (Bind b) (Bind b) x0 t x1 t0 (refl_equal K
+(Bind b)) (sym_eq T t x0 (H x0 h d H4)) (sym_eq T t0 x1 (H0 x1 h (S d)
+H5)))))) t1 H3)))))) (lift_gen_bind b (lift h d t) (lift h (S d) t0) t1 h d
+H2)))))))))))) (\lambda (f: F).(\lambda (t: T).(\lambda (H: ((\forall (t0:
+T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d t) (lift h d t0)) \to
+(eq T t t0))))))).(\lambda (t0: T).(\lambda (H0: ((\forall (t1: T).(\forall
+(h: nat).(\forall (d: nat).((eq T (lift h d t0) (lift h d t1)) \to (eq T t0
+t1))))))).(\lambda (t1: T).(\lambda (h: nat).(\lambda (d: nat).(\lambda (H1:
+(eq T (lift h d (THead (Flat f) t t0)) (lift h d t1))).(let H2 \def (eq_ind T
+(lift h d (THead (Flat f) t t0)) (\lambda (t2: T).(eq T t2 (lift h d t1))) H1
+(THead (Flat f) (lift h d t) (lift h d t0)) (lift_flat f t t0 h d)) in
+(ex3_2_ind T T (\lambda (y: T).(\lambda (z: T).(eq T t1 (THead (Flat f) y
+z)))) (\lambda (y: T).(\lambda (_: T).(eq T (lift h d t) (lift h d y))))
+(\lambda (_: T).(\lambda (z: T).(eq T (lift h d t0) (lift h d z)))) (eq T
+(THead (Flat f) t t0) t1) (\lambda (x0: T).(\lambda (x1: T).(\lambda (H3: (eq
+T t1 (THead (Flat f) x0 x1))).(\lambda (H4: (eq T (lift h d t) (lift h d
+x0))).(\lambda (H5: (eq T (lift h d t0) (lift h d x1))).(eq_ind_r T (THead
+(Flat f) x0 x1) (\lambda (t2: T).(eq T (THead (Flat f) t t0) t2)) (sym_eq T
+(THead (Flat f) x0 x1) (THead (Flat f) t t0) (sym_eq T (THead (Flat f) t t0)
+(THead (Flat f) x0 x1) (sym_eq T (THead (Flat f) x0 x1) (THead (Flat f) t t0)
+(f_equal3 K T T T THead (Flat f) (Flat f) x0 t x1 t0 (refl_equal K (Flat f))
+(sym_eq T t x0 (H x0 h d H4)) (sym_eq T t0 x1 (H0 x1 h d H5)))))) t1 H3))))))
+(lift_gen_flat f (lift h d t) (lift h d t0) t1 h d H2)))))))))))) k)) x).
theorem lift_gen_lift:
\forall (t1: T).(\forall (x: T).(\forall (h1: nat).(\forall (h2:
(plus_lt_compat_r n (plus d2 h2) h1 H4)) (plus (plus d2 h1) h2)
(plus_permute_2_in_3 d2 h1 h2)) x H2 (ex2 T (\lambda (t2: T).(eq T x (lift h1
d1 t2))) (\lambda (t2: T).(eq T (TLRef n) (lift h2 d2 t2)))))) (\lambda (H4:
-(le (plus d2 h2) n)).(let H5 \def (eq_ind nat (plus n h1) (\lambda (n:
-nat).(eq T (TLRef n) (lift h2 (plus d2 h1) x))) H2 (plus (minus (plus n h1)
+(le (plus d2 h2) n)).(let H5 \def (eq_ind nat (plus n h1) (\lambda (n0:
+nat).(eq T (TLRef n0) (lift h2 (plus d2 h1) x))) H2 (plus (minus (plus n h1)
h2) h2) (le_plus_minus_sym h2 (plus n h1) (le_plus_trans h2 n h1
(le_trans_plus_r d2 h2 n H4)))) in (eq_ind_r T (TLRef (minus (plus n h1) h2))
(\lambda (t: T).(ex2 T (\lambda (t2: T).(eq T t (lift h1 d1 t2))) (\lambda
x (lift h1 d1 t2))) (\lambda (t2: T).(eq T (THead k0 t t0) (lift h2 d2
t2)))))) (\lambda (b: B).(\lambda (H3: (eq T (lift h1 d1 (THead (Bind b) t
t0)) (lift h2 (plus d2 h1) x))).(let H4 \def (eq_ind T (lift h1 d1 (THead
-(Bind b) t t0)) (\lambda (t: T).(eq T t (lift h2 (plus d2 h1) x))) H3 (THead
-(Bind b) (lift h1 d1 t) (lift h1 (S d1) t0)) (lift_bind b t t0 h1 d1)) in
-(ex3_2_ind T T (\lambda (y: T).(\lambda (z: T).(eq T x (THead (Bind b) y
+(Bind b) t t0)) (\lambda (t2: T).(eq T t2 (lift h2 (plus d2 h1) x))) H3
+(THead (Bind b) (lift h1 d1 t) (lift h1 (S d1) t0)) (lift_bind b t t0 h1 d1))
+in (ex3_2_ind T T (\lambda (y: T).(\lambda (z: T).(eq T x (THead (Bind b) y
z)))) (\lambda (y: T).(\lambda (_: T).(eq T (lift h1 d1 t) (lift h2 (plus d2
h1) y)))) (\lambda (_: T).(\lambda (z: T).(eq T (lift h1 (S d1) t0) (lift h2
(S (plus d2 h1)) z)))) (ex2 T (\lambda (t2: T).(eq T x (lift h1 d1 t2)))
x0 h1 h2 d1 d2 H1 H6)) x H5)))))) (lift_gen_bind b (lift h1 d1 t) (lift h1 (S
d1) t0) x h2 (plus d2 h1) H4))))) (\lambda (f: F).(\lambda (H3: (eq T (lift
h1 d1 (THead (Flat f) t t0)) (lift h2 (plus d2 h1) x))).(let H4 \def (eq_ind
-T (lift h1 d1 (THead (Flat f) t t0)) (\lambda (t: T).(eq T t (lift h2 (plus
+T (lift h1 d1 (THead (Flat f) t t0)) (\lambda (t2: T).(eq T t2 (lift h2 (plus
d2 h1) x))) H3 (THead (Flat f) (lift h1 d1 t) (lift h1 d1 t0)) (lift_flat f t
t0 h1 d1)) in (ex3_2_ind T T (\lambda (y: T).(\lambda (z: T).(eq T x (THead
(Flat f) y z)))) (\lambda (y: T).(\lambda (_: T).(eq T (lift h1 d1 t) (lift
(lift_lref_ge n (plus k h) d H1)) (lift k e (TLRef (plus n h))) (lift_lref_ge
(plus n h) k e (le_trans e (plus d h) (plus n h) H (plus_le_compat d n h h H1
(le_n h))))) (lift h d (TLRef n)) (lift_lref_ge n h d H1))))))))))) (\lambda
-(k: K).(\lambda (t0: T).(\lambda (H: ((\forall (h: nat).(\forall (k:
+(k: K).(\lambda (t0: T).(\lambda (H: ((\forall (h: nat).(\forall (k0:
nat).(\forall (d: nat).(\forall (e: nat).((le e (plus d h)) \to ((le d e) \to
-(eq T (lift k e (lift h d t0)) (lift (plus k h) d t0)))))))))).(\lambda (t1:
-T).(\lambda (H0: ((\forall (h: nat).(\forall (k: nat).(\forall (d:
-nat).(\forall (e: nat).((le e (plus d h)) \to ((le d e) \to (eq T (lift k e
-(lift h d t1)) (lift (plus k h) d t1)))))))))).(\lambda (h: nat).(\lambda
+(eq T (lift k0 e (lift h d t0)) (lift (plus k0 h) d t0)))))))))).(\lambda
+(t1: T).(\lambda (H0: ((\forall (h: nat).(\forall (k0: nat).(\forall (d:
+nat).(\forall (e: nat).((le e (plus d h)) \to ((le d e) \to (eq T (lift k0 e
+(lift h d t1)) (lift (plus k0 h) d t1)))))))))).(\lambda (h: nat).(\lambda
(k0: nat).(\lambda (d: nat).(\lambda (e: nat).(\lambda (H1: (le e (plus d
h))).(\lambda (H2: (le d e)).(eq_ind_r T (THead k (lift h d t0) (lift h (s k
d) t1)) (\lambda (t2: T).(eq T (lift k0 e t2) (lift (plus k0 h) d (THead k t0
(plus n k)) (le_lt_n_Sm (plus d k) (plus n k) (plus_le_compat d n k k H1
(le_n k))))))))) (plus k d) (plus_comm k d)) (lift k e (TLRef n))
(lift_lref_ge n k e H0)))))))))) (\lambda (k: K).(\lambda (t0: T).(\lambda
-(H: ((\forall (h: nat).(\forall (k: nat).(\forall (d: nat).(\forall (e:
-nat).((le e d) \to (eq T (lift h (plus k d) (lift k e t0)) (lift k e (lift h
-d t0)))))))))).(\lambda (t1: T).(\lambda (H0: ((\forall (h: nat).(\forall (k:
-nat).(\forall (d: nat).(\forall (e: nat).((le e d) \to (eq T (lift h (plus k
-d) (lift k e t1)) (lift k e (lift h d t1)))))))))).(\lambda (h: nat).(\lambda
-(k0: nat).(\lambda (d: nat).(\lambda (e: nat).(\lambda (H1: (le e
-d)).(eq_ind_r T (THead k (lift k0 e t0) (lift k0 (s k e) t1)) (\lambda (t2:
+(H: ((\forall (h: nat).(\forall (k0: nat).(\forall (d: nat).(\forall (e:
+nat).((le e d) \to (eq T (lift h (plus k0 d) (lift k0 e t0)) (lift k0 e (lift
+h d t0)))))))))).(\lambda (t1: T).(\lambda (H0: ((\forall (h: nat).(\forall
+(k0: nat).(\forall (d: nat).(\forall (e: nat).((le e d) \to (eq T (lift h
+(plus k0 d) (lift k0 e t1)) (lift k0 e (lift h d t1)))))))))).(\lambda (h:
+nat).(\lambda (k0: nat).(\lambda (d: nat).(\lambda (e: nat).(\lambda (H1: (le
+e d)).(eq_ind_r T (THead k (lift k0 e t0) (lift k0 (s k e) t1)) (\lambda (t2:
T).(eq T (lift h (plus k0 d) t2) (lift k0 e (lift h d (THead k t0 t1)))))
(eq_ind_r T (THead k (lift h (plus k0 d) (lift k0 e t0)) (lift h (s k (plus
k0 d)) (lift k0 (s k e) t1))) (\lambda (t2: T).(eq T t2 (lift k0 e (lift h d
projects / helm.git / blobdiff