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 3b756e98d4bff5e1900e4e7e5e86e3c23b93026e..7b62a5a15ed03f87a33fd56e0968900bddbc60b8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/T/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/T/props.ma
@@ -16,62 +16,49 @@
 
 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 TMP_1 \def (\lambda (ee: B).(match ee 
-with [Abbr \Rightarrow True | Abst \Rightarrow False | Void \Rightarrow 
-False])) in (let H0 \def (eq_ind B Abbr TMP_1 I Abst H) in (False_ind False 
-H0))).
+ \lambda (H: (eq B Abbr Abst)).(let H0 \def (eq_ind B Abbr (\lambda (ee: 
+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 TMP_1 \def (\lambda (ee: B).(match ee 
-with [Abbr \Rightarrow False | Abst \Rightarrow False | Void \Rightarrow 
-True])) in (let H0 \def (eq_ind B Void TMP_1 I Abst H) in (False_ind False 
-H0))).
+ \lambda (H: (eq B Void Abst)).(let H0 \def (eq_ind B Void (\lambda (ee: 
+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 TMP_1 \def (\lambda (ee: B).(match ee 
-with [Abbr \Rightarrow True | Abst \Rightarrow False | Void \Rightarrow 
-False])) in (let H0 \def (eq_ind B Abbr TMP_1 I Void H) in (False_ind False 
-H0))).
+ \lambda (H: (eq B Abbr Void)).(let H0 \def (eq_ind B Abbr (\lambda (ee: 
+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 TMP_1 \def (\lambda (ee: B).(match ee 
-with [Abbr \Rightarrow False | Abst \Rightarrow True | Void \Rightarrow 
-False])) in (let H0 \def (eq_ind B Abst TMP_1 I Void H) in (False_ind False 
-H0))).
+ \lambda (H: (eq B Abst Void)).(let H0 \def (eq_ind B Abst (\lambda (ee: 
+B).(match ee with [Abbr \Rightarrow False | Abst \Rightarrow True | Void 
+\Rightarrow False])) I Void H) in (False_ind False H0)).
 
-theorem tweight_lt:
+lemma tweight_lt:
  \forall (t: T).(lt O (tweight t))
 \def
- \lambda (t: T).(let TMP_2 \def (\lambda (t0: T).(let TMP_1 \def (tweight t0) 
-in (lt O TMP_1))) in (let TMP_4 \def (\lambda (_: nat).(let TMP_3 \def (S O) 
-in (le_n TMP_3))) in (let TMP_6 \def (\lambda (_: nat).(let TMP_5 \def (S O) 
-in (le_n TMP_5))) in (let TMP_15 \def (\lambda (_: K).(\lambda (t0: 
-T).(\lambda (H: (lt O (tweight t0))).(\lambda (t1: T).(\lambda (_: (lt O 
-(tweight t1))).(let TMP_7 \def (S O) in (let TMP_8 \def (tweight t0) in (let 
-TMP_9 \def (tweight t1) in (let TMP_10 \def (plus TMP_8 TMP_9) in (let TMP_11 
-\def (S O) in (let TMP_12 \def (tweight t0) in (let TMP_13 \def (tweight t1) 
-in (let TMP_14 \def (le_plus_trans TMP_11 TMP_12 TMP_13 H) in (le_S TMP_7 
-TMP_10 TMP_14)))))))))))))) in (T_ind TMP_2 TMP_4 TMP_6 TMP_15 t))))).
+ \lambda (t: T).(T_ind (\lambda (t0: T).(lt O (tweight t0))) (\lambda (_: 
+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).
 
-theorem tle_r:
+lemma tle_r:
  \forall (t: T).(tle t t)
 \def
- \lambda (t: T).(let TMP_3 \def (\lambda (t0: T).(let TMP_1 \def (tweight t0) 
-in (let TMP_2 \def (tweight t0) in (le TMP_1 TMP_2)))) in (let TMP_5 \def 
-(\lambda (_: nat).(let TMP_4 \def (S O) in (le_n TMP_4))) in (let TMP_7 \def 
-(\lambda (_: nat).(let TMP_6 \def (S O) in (le_n TMP_6))) in (let TMP_12 \def 
-(\lambda (_: K).(\lambda (t0: T).(\lambda (_: (le (tweight t0) (tweight 
-t0))).(\lambda (t1: T).(\lambda (_: (le (tweight t1) (tweight t1))).(let 
-TMP_8 \def (tweight t0) in (let TMP_9 \def (tweight t1) in (let TMP_10 \def 
-(plus TMP_8 TMP_9) in (let TMP_11 \def (S TMP_10) in (le_n TMP_11)))))))))) 
-in (T_ind TMP_3 TMP_5 TMP_7 TMP_12 t))))).
+ \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).