update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / T / props.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/T/props.ma b/matita/matita/contribs/lambdadelta/basic_1/T/props.ma
index faa9ed95d7ec8092b848ae861ff3da8b52e2b7e3..7b62a5a15ed03f87a33fd56e0968900bddbc60b8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/T/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/T/props.ma
@@ -14,90 +14,37 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/T/defs.ma".
+include "basic_1/T/fwd.ma".
 
-theorem not_abbr_abst:
+lemma not_abbr_abst:
  not (eq B Abbr Abst)
 \def
  \lambda (H: (eq B Abbr Abst)).(let H0 \def (eq_ind B Abbr (\lambda (ee: 
-B).(match ee in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow True | 
-Abst \Rightarrow False | Void \Rightarrow False])) I Abst H) in (False_ind 
-False H0)).
-(* COMMENTS
-Initial nodes: 34
-END *)
+B).(match ee with [Abbr \Rightarrow True | Abst \Rightarrow False | Void 
+\Rightarrow False])) I Abst H) in (False_ind False H0)).
 
-theorem not_void_abst:
+lemma not_void_abst:
  not (eq B Void Abst)
 \def
  \lambda (H: (eq B Void Abst)).(let H0 \def (eq_ind B Void (\lambda (ee: 
-B).(match ee in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow False | 
-Abst \Rightarrow False | Void \Rightarrow True])) I Abst H) in (False_ind 
-False H0)).
-(* COMMENTS
-Initial nodes: 34
-END *)
+B).(match ee with [Abbr \Rightarrow False | Abst \Rightarrow False | Void 
+\Rightarrow True])) I Abst H) in (False_ind False H0)).
 
-theorem not_abbr_void:
+lemma not_abbr_void:
  not (eq B Abbr Void)
 \def
  \lambda (H: (eq B Abbr Void)).(let H0 \def (eq_ind B Abbr (\lambda (ee: 
-B).(match ee in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow True | 
-Abst \Rightarrow False | Void \Rightarrow False])) I Void H) in (False_ind 
-False H0)).
-(* COMMENTS
-Initial nodes: 34
-END *)
+B).(match ee with [Abbr \Rightarrow True | Abst \Rightarrow False | Void 
+\Rightarrow False])) I Void H) in (False_ind False H0)).
 
-theorem not_abst_void:
+lemma not_abst_void:
  not (eq B Abst Void)
 \def
  \lambda (H: (eq B Abst Void)).(let H0 \def (eq_ind B Abst (\lambda (ee: 
-B).(match ee in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow False | 
-Abst \Rightarrow True | Void \Rightarrow False])) I Void H) in (False_ind 
-False H0)).
-(* COMMENTS
-Initial nodes: 34
-END *)
+B).(match ee with [Abbr \Rightarrow False | Abst \Rightarrow True | Void 
+\Rightarrow False])) I Void H) in (False_ind False H0)).
 
-theorem thead_x_y_y:
- \forall (k: K).(\forall (v: T).(\forall (t: T).((eq T (THead k v t) t) \to 
-(\forall (P: Prop).P))))
-\def
- \lambda (k: K).(\lambda (v: T).(\lambda (t: T).(T_ind (\lambda (t0: T).((eq 
-T (THead k v t0) t0) \to (\forall (P: Prop).P))) (\lambda (n: nat).(\lambda 
-(H: (eq T (THead k v (TSort n)) (TSort n))).(\lambda (P: Prop).(let H0 \def 
-(eq_ind T (THead k v (TSort n)) (\lambda (ee: T).(match ee in T return 
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) 
-\Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TSort n) H) in 
-(False_ind P H0))))) (\lambda (n: nat).(\lambda (H: (eq T (THead k v (TLRef 
-n)) (TLRef n))).(\lambda (P: Prop).(let H0 \def (eq_ind T (THead k v (TLRef 
-n)) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort 
-_) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _) 
-\Rightarrow True])) I (TLRef n) H) in (False_ind P H0))))) (\lambda (k0: 
-K).(\lambda (t0: T).(\lambda (_: (((eq T (THead k v t0) t0) \to (\forall (P: 
-Prop).P)))).(\lambda (t1: T).(\lambda (H0: (((eq T (THead k v t1) t1) \to 
-(\forall (P: Prop).P)))).(\lambda (H1: (eq T (THead k v (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 k1 _ _) \Rightarrow k1])) (THead k v (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 _ t2 _) \Rightarrow t2])) (THead k v (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 t0 t1) | (TLRef _) \Rightarrow (THead k0 t0 t1) | (THead _ _ t2) 
-\Rightarrow t2])) (THead k v (THead k0 t0 t1)) (THead k0 t0 t1) H1) in 
-(\lambda (H5: (eq T v t0)).(\lambda (H6: (eq K k k0)).(let H7 \def (eq_ind T 
-v (\lambda (t2: T).((eq T (THead k t2 t1) t1) \to (\forall (P0: Prop).P0))) 
-H0 t0 H5) in (let H8 \def (eq_ind K k (\lambda (k1: K).((eq T (THead k1 t0 
-t1) t1) \to (\forall (P0: Prop).P0))) H7 k0 H6) in (H8 H4 P)))))) H3)) 
-H2))))))))) t))).
-(* COMMENTS
-Initial nodes: 461
-END *)
-
-theorem tweight_lt:
+lemma tweight_lt:
  \forall (t: T).(lt O (tweight t))
 \def
  \lambda (t: T).(T_ind (\lambda (t0: T).(lt O (tweight t0))) (\lambda (_: 
@@ -105,7 +52,13 @@ nat).(le_n (S O))) (\lambda (_: nat).(le_n (S O))) (\lambda (_: K).(\lambda
 (t0: T).(\lambda (H: (lt O (tweight t0))).(\lambda (t1: T).(\lambda (_: (lt O 
 (tweight t1))).(le_S (S O) (plus (tweight t0) (tweight t1)) (le_plus_trans (S 
 O) (tweight t0) (tweight t1) H))))))) t).
-(* COMMENTS
-Initial nodes: 85
-END *)
+
+lemma tle_r:
+ \forall (t: T).(tle t t)
+\def
+ \lambda (t: T).(T_ind (\lambda (t0: T).(le (tweight t0) (tweight t0))) 
+(\lambda (_: nat).(le_n (S O))) (\lambda (_: nat).(le_n (S O))) (\lambda (_: 
+K).(\lambda (t0: T).(\lambda (_: (le (tweight t0) (tweight t0))).(\lambda 
+(t1: T).(\lambda (_: (le (tweight t1) (tweight t1))).(le_n (S (plus (tweight 
+t0) (tweight t1))))))))) t).