update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / subst0 / tlt.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/subst0/tlt.ma b/matita/matita/contribs/lambdadelta/basic_1/subst0/tlt.ma
index c8e8420bb49b18b157d8b16a13bc85683e0256d2..2d32fcad4449ac5136b3ea649e419676a7b8c186 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/subst0/tlt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/subst0/tlt.ma
@@ -14,13 +14,11 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/subst0/defs.ma".
+include "basic_1/subst0/fwd.ma".
 
-include "Basic-1/lift/props.ma".
+include "basic_1/lift/tlt.ma".
 
-include "Basic-1/lift/tlt.ma".
-
-theorem subst0_weight_le:
+lemma subst0_weight_le:
  \forall (u: T).(\forall (t: T).(\forall (z: T).(\forall (d: nat).((subst0 d 
 u t z) \to (\forall (f: ((nat \to nat))).(\forall (g: ((nat \to 
 nat))).(((\forall (m: nat).(le (f m) (g m)))) \to ((lt (weight_map f (lift (S 
@@ -34,8 +32,10 @@ n) O t0)) (g n)) \to (le (weight_map f t2) (weight_map g t1))))))))))
 (\lambda (v: T).(\lambda (i: nat).(\lambda (f: ((nat \to nat))).(\lambda (g: 
 ((nat \to nat))).(\lambda (_: ((\forall (m: nat).(le (f m) (g m))))).(\lambda 
 (H1: (lt (weight_map f (lift (S i) O v)) (g i))).(le_S_n (weight_map f (lift 
-(S i) O v)) (weight_map g (TLRef i)) (le_S (S (weight_map f (lift (S i) O 
-v))) (weight_map g (TLRef i)) H1)))))))) (\lambda (v: T).(\lambda (u2: 
+(S i) O v)) (weight_map g (TLRef i)) (le_S_n (S (weight_map f (lift (S i) O 
+v))) (S (weight_map g (TLRef i))) (le_S (S (S (weight_map f (lift (S i) O 
+v)))) (S (weight_map g (TLRef i))) (le_n_S (S (weight_map f (lift (S i) O 
+v))) (weight_map g (TLRef i)) H1)))))))))) (\lambda (v: T).(\lambda (u2: 
 T).(\lambda (u1: T).(\lambda (i: nat).(\lambda (_: (subst0 i v u1 
 u2)).(\lambda (H1: ((\forall (f: ((nat \to nat))).(\forall (g: ((nat \to 
 nat))).(((\forall (m: nat).(le (f m) (g m)))) \to ((lt (weight_map f (lift (S 
@@ -63,14 +63,14 @@ nat))).(\lambda (H2: ((\forall (m: nat).(le (f m) (g m))))).(\lambda (H3: (lt
 (weight_map (wadd f O) t0)) (plus (weight_map g u1) (weight_map (wadd g O) 
 t0)) (le_plus_plus (weight_map f u2) (weight_map g u1) (weight_map (wadd f O) 
 t0) (weight_map (wadd g O) t0) (H1 f g H2 H3) (weight_le t0 (wadd f O) (wadd 
-g O) (\lambda (n: nat).(wadd_le f g H2 O O (le_n O) n))))))))) (\lambda (f: 
+g O) (\lambda (n: nat).(wadd_le f g H2 O O (le_O_n O) n))))))))) (\lambda (f: 
 ((nat \to nat))).(\lambda (g: ((nat \to nat))).(\lambda (H2: ((\forall (m: 
 nat).(le (f m) (g m))))).(\lambda (H3: (lt (weight_map f (lift (S i) O v)) (g 
 i))).(le_n_S (plus (weight_map f u2) (weight_map (wadd f O) t0)) (plus 
 (weight_map g u1) (weight_map (wadd g O) t0)) (le_plus_plus (weight_map f u2) 
 (weight_map g u1) (weight_map (wadd f O) t0) (weight_map (wadd g O) t0) (H1 f 
 g H2 H3) (weight_le t0 (wadd f O) (wadd g O) (\lambda (n: nat).(wadd_le f g 
-H2 O O (le_n O) n))))))))) b)) (\lambda (_: F).(\lambda (f0: ((nat \to 
+H2 O O (le_O_n O) n))))))))) b)) (\lambda (_: F).(\lambda (f0: ((nat \to 
 nat))).(\lambda (g: ((nat \to nat))).(\lambda (H2: ((\forall (m: nat).(le (f0 
 m) (g m))))).(\lambda (H3: (lt (weight_map f0 (lift (S i) O v)) (g 
 i))).(le_n_S (plus (weight_map f0 u2) (weight_map f0 t0)) (plus (weight_map g 
@@ -121,7 +121,7 @@ i))).(le_n_S (plus (weight_map f u0) (weight_map (wadd f O) t2)) (plus
 (weight_map g u0) (weight_map (wadd g O) t1)) (le_plus_plus (weight_map f u0) 
 (weight_map g u0) (weight_map (wadd f O) t2) (weight_map (wadd g O) t1) 
 (weight_le u0 f g H2) (H1 (wadd f O) (wadd g O) (\lambda (m: nat).(wadd_le f 
-g H2 O O (le_n O) m)) (eq_ind nat (weight_map f (lift (S i) O v)) (\lambda 
+g H2 O O (le_O_n O) m)) (eq_ind nat (weight_map f (lift (S i) O v)) (\lambda 
 (n: nat).(lt n (g i))) H3 (weight_map (wadd f O) (lift (S (S i)) O v)) 
 (lift_weight_add_O O v (S i) f)))))))))))))))) (\lambda (v: T).(\lambda (t2: 
 T).(\lambda (t1: T).(\lambda (i: nat).(\lambda (_: (subst0 (S i) v t1 
@@ -134,38 +134,39 @@ t1)))))))).(\lambda (u0: T).(\lambda (f: ((nat \to nat))).(\lambda (g: ((nat
 (weight_map (wadd f O) t2)) (plus (weight_map g u0) (weight_map (wadd g O) 
 t1)) (le_plus_plus (weight_map f u0) (weight_map g u0) (weight_map (wadd f O) 
 t2) (weight_map (wadd g O) t1) (weight_le u0 f g H2) (H1 (wadd f O) (wadd g 
-O) (\lambda (m: nat).(wadd_le f g H2 O O (le_n O) m)) (eq_ind nat (weight_map 
-f (lift (S i) O v)) (\lambda (n: nat).(lt n (g i))) H3 (weight_map (wadd f O) 
-(lift (S (S i)) O v)) (lift_weight_add_O O v (S i) f)))))))))))))))) b)) 
-(\lambda (_: F).(\lambda (v: T).(\lambda (t2: T).(\lambda (t1: T).(\lambda 
-(i: nat).(\lambda (_: (subst0 i v t1 t2)).(\lambda (H1: ((\forall (f0: ((nat 
-\to nat))).(\forall (g: ((nat \to nat))).(((\forall (m: nat).(le (f0 m) (g 
-m)))) \to ((lt (weight_map f0 (lift (S i) O v)) (g i)) \to (le (weight_map f0 
-t2) (weight_map g t1)))))))).(\lambda (u0: T).(\lambda (f0: ((nat \to 
-nat))).(\lambda (g: ((nat \to nat))).(\lambda (H2: ((\forall (m: nat).(le (f0 
-m) (g m))))).(\lambda (H3: (lt (weight_map f0 (lift (S i) O v)) (g 
-i))).(le_n_S (plus (weight_map f0 u0) (weight_map f0 t2)) (plus (weight_map g 
-u0) (weight_map g t1)) (le_plus_plus (weight_map f0 u0) (weight_map g u0) 
-(weight_map f0 t2) (weight_map g t1) (weight_le u0 f0 g H2) (H1 f0 g H2 
-H3))))))))))))))) k)) (\lambda (v: T).(\lambda (u1: T).(\lambda (u2: 
-T).(\lambda (i: nat).(\lambda (_: (subst0 i v u1 u2)).(\lambda (H1: ((\forall 
-(f: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall (m: nat).(le (f 
-m) (g m)))) \to ((lt (weight_map f (lift (S i) O v)) (g i)) \to (le 
-(weight_map f u2) (weight_map g u1)))))))).(\lambda (k: K).(K_ind (\lambda 
-(k0: K).(\forall (t1: T).(\forall (t2: T).((subst0 (s k0 i) v t1 t2) \to 
-(((\forall (f: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall (m: 
-nat).(le (f m) (g m)))) \to ((lt (weight_map f (lift (S (s k0 i)) O v)) (g (s 
-k0 i))) \to (le (weight_map f t2) (weight_map g t1))))))) \to (\forall (f: 
-((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall (m: nat).(le (f m) 
-(g m)))) \to ((lt (weight_map f (lift (S i) O v)) (g i)) \to (le (weight_map 
-f (THead k0 u2 t2)) (weight_map g (THead k0 u1 t1)))))))))))) (\lambda (b: 
-B).(B_ind (\lambda (b0: B).(\forall (t1: T).(\forall (t2: T).((subst0 (s 
-(Bind b0) i) v t1 t2) \to (((\forall (f: ((nat \to nat))).(\forall (g: ((nat 
+O) (\lambda (m: nat).(wadd_le f g H2 O O (le_O_n O) m)) (eq_ind nat 
+(weight_map f (lift (S i) O v)) (\lambda (n: nat).(lt n (g i))) H3 
+(weight_map (wadd f O) (lift (S (S i)) O v)) (lift_weight_add_O O v (S i) 
+f)))))))))))))))) b)) (\lambda (_: F).(\lambda (v: T).(\lambda (t2: 
+T).(\lambda (t1: T).(\lambda (i: nat).(\lambda (_: (subst0 i v t1 
+t2)).(\lambda (H1: ((\forall (f0: ((nat \to nat))).(\forall (g: ((nat \to 
+nat))).(((\forall (m: nat).(le (f0 m) (g m)))) \to ((lt (weight_map f0 (lift 
+(S i) O v)) (g i)) \to (le (weight_map f0 t2) (weight_map g 
+t1)))))))).(\lambda (u0: T).(\lambda (f0: ((nat \to nat))).(\lambda (g: ((nat 
+\to nat))).(\lambda (H2: ((\forall (m: nat).(le (f0 m) (g m))))).(\lambda 
+(H3: (lt (weight_map f0 (lift (S i) O v)) (g i))).(le_n_S (plus (weight_map 
+f0 u0) (weight_map f0 t2)) (plus (weight_map g u0) (weight_map g t1)) 
+(le_plus_plus (weight_map f0 u0) (weight_map g u0) (weight_map f0 t2) 
+(weight_map g t1) (weight_le u0 f0 g H2) (H1 f0 g H2 H3))))))))))))))) k)) 
+(\lambda (v: T).(\lambda (u1: T).(\lambda (u2: T).(\lambda (i: nat).(\lambda 
+(_: (subst0 i v u1 u2)).(\lambda (H1: ((\forall (f: ((nat \to nat))).(\forall 
+(g: ((nat \to nat))).(((\forall (m: nat).(le (f m) (g m)))) \to ((lt 
+(weight_map f (lift (S i) O v)) (g i)) \to (le (weight_map f u2) (weight_map 
+g u1)))))))).(\lambda (k: K).(K_ind (\lambda (k0: K).(\forall (t1: 
+T).(\forall (t2: T).((subst0 (s k0 i) v t1 t2) \to (((\forall (f: ((nat \to 
+nat))).(\forall (g: ((nat \to nat))).(((\forall (m: nat).(le (f m) (g m)))) 
+\to ((lt (weight_map f (lift (S (s k0 i)) O v)) (g (s k0 i))) \to (le 
+(weight_map f t2) (weight_map g t1))))))) \to (\forall (f: ((nat \to 
+nat))).(\forall (g: ((nat \to nat))).(((\forall (m: nat).(le (f m) (g m)))) 
+\to ((lt (weight_map f (lift (S i) O v)) (g i)) \to (le (weight_map f (THead 
+k0 u2 t2)) (weight_map g (THead k0 u1 t1)))))))))))) (\lambda (b: B).(B_ind 
+(\lambda (b0: B).(\forall (t1: T).(\forall (t2: T).((subst0 (s (Bind b0) i) v 
+t1 t2) \to (((\forall (f: ((nat \to nat))).(\forall (g: ((nat \to 
+nat))).(((\forall (m: nat).(le (f m) (g m)))) \to ((lt (weight_map f (lift (S 
+(s (Bind b0) i)) O v)) (g (s (Bind b0) i))) \to (le (weight_map f t2) 
+(weight_map g t1))))))) \to (\forall (f: ((nat \to nat))).(\forall (g: ((nat 
 \to nat))).(((\forall (m: nat).(le (f m) (g m)))) \to ((lt (weight_map f 
-(lift (S (s (Bind b0) i)) O v)) (g (s (Bind b0) i))) \to (le (weight_map f 
-t2) (weight_map g t1))))))) \to (\forall (f: ((nat \to nat))).(\forall (g: 
-((nat \to nat))).(((\forall (m: nat).(le (f m) (g m)))) \to ((lt (weight_map 
-f (lift (S i) O v)) (g i)) \to (le (weight_map f (THead (Bind b0) u2 t2)) 
+(lift (S i) O v)) (g i)) \to (le (weight_map f (THead (Bind b0) u2 t2)) 
 (weight_map g (THead (Bind b0) u1 t1)))))))))))) (\lambda (t1: T).(\lambda 
 (t2: T).(\lambda (_: (subst0 (S i) v t1 t2)).(\lambda (H3: ((\forall (f: 
 ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall (m: nat).(le (f m) 
@@ -193,7 +194,7 @@ i))).(le_n_S (plus (weight_map f u2) (weight_map (wadd f O) t2)) (plus
 (weight_map g u1) (weight_map (wadd g O) t1)) (le_plus_plus (weight_map f u2) 
 (weight_map g u1) (weight_map (wadd f O) t2) (weight_map (wadd g O) t1) (H1 f 
 g H4 H5) (H3 (wadd f O) (wadd g O) (\lambda (m: nat).(wadd_le f g H4 O O 
-(le_n O) m)) (eq_ind nat (weight_map f (lift (S i) O v)) (\lambda (n: 
+(le_O_n O) m)) (eq_ind nat (weight_map f (lift (S i) O v)) (\lambda (n: 
 nat).(lt n (g i))) H5 (weight_map (wadd f O) (lift (S (S i)) O v)) 
 (lift_weight_add_O O v (S i) f))))))))))))) (\lambda (t1: T).(\lambda (t2: 
 T).(\lambda (_: (subst0 (S i) v t1 t2)).(\lambda (H3: ((\forall (f: ((nat \to 
@@ -205,8 +206,8 @@ t2) (weight_map g t1)))))))).(\lambda (f: ((nat \to nat))).(\lambda (g: ((nat
 (weight_map (wadd f O) t2)) (plus (weight_map g u1) (weight_map (wadd g O) 
 t1)) (le_plus_plus (weight_map f u2) (weight_map g u1) (weight_map (wadd f O) 
 t2) (weight_map (wadd g O) t1) (H1 f g H4 H5) (H3 (wadd f O) (wadd g O) 
-(\lambda (m: nat).(wadd_le f g H4 O O (le_n O) m)) (eq_ind nat (weight_map f 
-(lift (S i) O v)) (\lambda (n: nat).(lt n (g i))) H5 (weight_map (wadd f O) 
+(\lambda (m: nat).(wadd_le f g H4 O O (le_O_n O) m)) (eq_ind nat (weight_map 
+f (lift (S i) O v)) (\lambda (n: nat).(lt n (g i))) H5 (weight_map (wadd f O) 
 (lift (S (S i)) O v)) (lift_weight_add_O O v (S i) f))))))))))))) b)) 
 (\lambda (_: F).(\lambda (t1: T).(\lambda (t2: T).(\lambda (_: (subst0 i v t1 
 t2)).(\lambda (H3: ((\forall (f0: ((nat \to nat))).(\forall (g: ((nat \to 
@@ -218,11 +219,8 @@ nat))).(\lambda (H4: ((\forall (m: nat).(le (f0 m) (g m))))).(\lambda (H5:
 (weight_map f0 t2)) (plus (weight_map g u1) (weight_map g t1)) (le_plus_plus 
 (weight_map f0 u2) (weight_map g u1) (weight_map f0 t2) (weight_map g t1) (H1 
 f0 g H4 H5) (H3 f0 g H4 H5)))))))))))) k)))))))) d u t z H))))).
-(* COMMENTS
-Initial nodes: 4101
-END *)
 
-theorem subst0_weight_lt:
+lemma subst0_weight_lt:
  \forall (u: T).(\forall (t: T).(\forall (z: T).(\forall (d: nat).((subst0 d 
 u t z) \to (\forall (f: ((nat \to nat))).(\forall (g: ((nat \to 
 nat))).(((\forall (m: nat).(le (f m) (g m)))) \to ((lt (weight_map f (lift (S 
@@ -264,7 +262,7 @@ nat))).(\lambda (H2: ((\forall (m: nat).(le (f m) (g m))))).(\lambda (H3: (lt
 t0)) (lt_le_plus_plus (weight_map f u2) (weight_map g u1) (weight_map (wadd f 
 O) t0) (weight_map (wadd g O) t0) (H1 f g H2 H3) (weight_le t0 (wadd f O) 
 (wadd g O) (\lambda (n: nat).(le_S_n (wadd f O n) (wadd g O n) (le_n_S (wadd 
-f O n) (wadd g O n) (wadd_le f g H2 O O (le_n O) n))))))))))) (\lambda (f: 
+f O n) (wadd g O n) (wadd_le f g H2 O O (le_O_n O) n))))))))))) (\lambda (f: 
 ((nat \to nat))).(\lambda (g: ((nat \to nat))).(\lambda (H2: ((\forall (m: 
 nat).(le (f m) (g m))))).(\lambda (H3: (lt (weight_map f (lift (S i) O v)) (g 
 i))).(lt_n_S (plus (weight_map f u2) (weight_map (wadd f O) t0)) (plus 
@@ -272,7 +270,7 @@ i))).(lt_n_S (plus (weight_map f u2) (weight_map (wadd f O) t0)) (plus
 u2) (weight_map g u1) (weight_map (wadd f O) t0) (weight_map (wadd g O) t0) 
 (H1 f g H2 H3) (weight_le t0 (wadd f O) (wadd g O) (\lambda (n: nat).(le_S_n 
 (wadd f O n) (wadd g O n) (le_n_S (wadd f O n) (wadd g O n) (wadd_le f g H2 O 
-O (le_n O) n))))))))))) b)) (\lambda (_: F).(\lambda (f0: ((nat \to 
+O (le_O_n O) n))))))))))) b)) (\lambda (_: F).(\lambda (f0: ((nat \to 
 nat))).(\lambda (g: ((nat \to nat))).(\lambda (H2: ((\forall (m: nat).(le (f0 
 m) (g m))))).(\lambda (H3: (lt (weight_map f0 (lift (S i) O v)) (g 
 i))).(lt_n_S (plus (weight_map f0 u2) (weight_map f0 t0)) (plus (weight_map g 
@@ -323,7 +321,7 @@ i))).(lt_n_S (plus (weight_map f u0) (weight_map (wadd f O) t2)) (plus
 (weight_map g u0) (weight_map (wadd g O) t1)) (le_lt_plus_plus (weight_map f 
 u0) (weight_map g u0) (weight_map (wadd f O) t2) (weight_map (wadd g O) t1) 
 (weight_le u0 f g H2) (H1 (wadd f O) (wadd g O) (\lambda (m: nat).(wadd_le f 
-g H2 O O (le_n O) m)) (eq_ind nat (weight_map f (lift (S i) O v)) (\lambda 
+g H2 O O (le_O_n O) m)) (eq_ind nat (weight_map f (lift (S i) O v)) (\lambda 
 (n: nat).(lt n (g i))) H3 (weight_map (wadd f O) (lift (S (S i)) O v)) 
 (lift_weight_add_O O v (S i) f)))))))))))))))) (\lambda (v: T).(\lambda (t2: 
 T).(\lambda (t1: T).(\lambda (i: nat).(\lambda (_: (subst0 (S i) v t1 
@@ -336,7 +334,7 @@ t1)))))))).(\lambda (u0: T).(\lambda (f: ((nat \to nat))).(\lambda (g: ((nat
 (weight_map (wadd f O) t2)) (plus (weight_map g u0) (weight_map (wadd g O) 
 t1)) (le_lt_plus_plus (weight_map f u0) (weight_map g u0) (weight_map (wadd f 
 O) t2) (weight_map (wadd g O) t1) (weight_le u0 f g H2) (H1 (wadd f O) (wadd 
-g O) (\lambda (m: nat).(wadd_le f g H2 O O (le_n O) m)) (eq_ind nat 
+g O) (\lambda (m: nat).(wadd_le f g H2 O O (le_O_n O) m)) (eq_ind nat 
 (weight_map f (lift (S i) O v)) (\lambda (n: nat).(lt n (g i))) H3 
 (weight_map (wadd f O) (lift (S (S i)) O v)) (lift_weight_add_O O v (S i) 
 f)))))))))))))))) b)) (\lambda (_: F).(\lambda (v: T).(\lambda (t2: 
@@ -397,7 +395,7 @@ nat))).(\lambda (H4: ((\forall (m: nat).(le (f m) (g m))))).(\lambda (H5: (lt
 t1)) (lt_plus_plus (weight_map f u2) (weight_map g u1) (weight_map (wadd f O) 
 t2) (weight_map (wadd g O) t1) (H1 f g H4 H5) (H3 (wadd f O) (wadd g O) 
 (\lambda (m: nat).(le_S_n (wadd f O m) (wadd g O m) (le_n_S (wadd f O m) 
-(wadd g O m) (wadd_le f g H4 O O (le_n O) m)))) (eq_ind nat (weight_map f 
+(wadd g O m) (wadd_le f g H4 O O (le_O_n O) m)))) (eq_ind nat (weight_map f 
 (lift (S i) O v)) (\lambda (n: nat).(lt n (g i))) H5 (weight_map (wadd f O) 
 (lift (S (S i)) O v)) (lift_weight_add_O O v (S i) f))))))))))))) (\lambda 
 (t1: T).(\lambda (t2: T).(\lambda (_: (subst0 (S i) v t1 t2)).(\lambda (H3: 
@@ -410,7 +408,7 @@ i))).(lt_n_S (plus (weight_map f u2) (weight_map (wadd f O) t2)) (plus
 (weight_map g u1) (weight_map (wadd g O) t1)) (lt_plus_plus (weight_map f u2) 
 (weight_map g u1) (weight_map (wadd f O) t2) (weight_map (wadd g O) t1) (H1 f 
 g H4 H5) (H3 (wadd f O) (wadd g O) (\lambda (m: nat).(le_S_n (wadd f O m) 
-(wadd g O m) (le_n_S (wadd f O m) (wadd g O m) (wadd_le f g H4 O O (le_n O) 
+(wadd g O m) (le_n_S (wadd f O m) (wadd g O m) (wadd_le f g H4 O O (le_O_n O) 
 m)))) (eq_ind nat (weight_map f (lift (S i) O v)) (\lambda (n: nat).(lt n (g 
 i))) H5 (weight_map (wadd f O) (lift (S (S i)) O v)) (lift_weight_add_O O v 
 (S i) f))))))))))))) b)) (\lambda (_: F).(\lambda (t1: T).(\lambda (t2: 
@@ -424,11 +422,8 @@ f0 u2) (weight_map f0 t2)) (plus (weight_map g u1) (weight_map g t1))
 (lt_plus_plus (weight_map f0 u2) (weight_map g u1) (weight_map f0 t2) 
 (weight_map g t1) (H1 f0 g H4 H5) (H3 f0 g H4 H5)))))))))))) k)))))))) d u t 
 z H))))).
-(* COMMENTS
-Initial nodes: 4207
-END *)
 
-theorem subst0_tlt_head:
+lemma subst0_tlt_head:
  \forall (u: T).(\forall (t: T).(\forall (z: T).((subst0 O u t z) \to (tlt 
 (THead (Bind Abbr) u z) (THead (Bind Abbr) u t)))))
 \def
@@ -451,18 +446,12 @@ nat).O) u)))) (le_n (S (weight_map (\lambda (_: nat).O) u))) (lift O O u)
 (lift_r u O)) (weight_map (wadd (\lambda (_: nat).O) (S (weight_map (\lambda 
 (_: nat).O) u))) (lift (S O) O u)) (lift_weight_add_O (S (weight_map (\lambda 
 (_: nat).O) u)) u O (\lambda (_: nat).O))))))))).
-(* COMMENTS
-Initial nodes: 347
-END *)
 
-theorem subst0_tlt:
+lemma subst0_tlt:
  \forall (u: T).(\forall (t: T).(\forall (z: T).((subst0 O u t z) \to (tlt z 
 (THead (Bind Abbr) u t)))))
 \def
  \lambda (u: T).(\lambda (t: T).(\lambda (z: T).(\lambda (H: (subst0 O u t 
 z)).(tlt_trans (THead (Bind Abbr) u z) z (THead (Bind Abbr) u t) (tlt_head_dx 
 (Bind Abbr) u z) (subst0_tlt_head u t z H))))).
-(* COMMENTS
-Initial nodes: 59
-END *)