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 9b7a03f1dd104f7d44ba82b75bcc0ff345a74a78..7b62a5a15ed03f87a33fd56e0968900bddbc60b8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/T/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/T/props.ma
@@ -16,51 +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 in 
-B 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_2 \def (\lambda (ee: B).(match ee in 
-B with [Abbr \Rightarrow False | Abst \Rightarrow False | Void \Rightarrow 
-True])) in (let H0 \def (eq_ind B Void TMP_2 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_3 \def (\lambda (ee: B).(match ee in 
-B with [Abbr \Rightarrow True | Abst \Rightarrow False | Void \Rightarrow 
-False])) in (let H0 \def (eq_ind B Abbr TMP_3 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_4 \def (\lambda (ee: B).(match ee in 
-B with [Abbr \Rightarrow False | Abst \Rightarrow True | Void \Rightarrow 
-False])) in (let H0 \def (eq_ind B Abst TMP_4 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_1848 \def (\lambda (t0: T).(let TMP_1847 \def 
-(tweight t0) in (lt O TMP_1847))) in (let TMP_1846 \def (\lambda (_: 
-nat).(let TMP_1845 \def (S O) in (le_n TMP_1845))) in (let TMP_1844 \def 
-(\lambda (_: nat).(let TMP_1843 \def (S O) in (le_n TMP_1843))) in (let 
-TMP_1842 \def (\lambda (_: K).(\lambda (t0: T).(\lambda (H: (lt O (tweight 
-t0))).(\lambda (t1: T).(\lambda (_: (lt O (tweight t1))).(let TMP_1841 \def 
-(S O) in (let TMP_1839 \def (tweight t0) in (let TMP_1838 \def (tweight t1) 
-in (let TMP_1840 \def (plus TMP_1839 TMP_1838) in (let TMP_1836 \def (S O) in 
-(let TMP_1835 \def (tweight t0) in (let TMP_1834 \def (tweight t1) in (let 
-TMP_1837 \def (le_plus_trans TMP_1836 TMP_1835 TMP_1834 H) in (le_S TMP_1841 
-TMP_1840 TMP_1837)))))))))))))) in (T_ind TMP_1848 TMP_1846 TMP_1844 TMP_1842 
-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).
+
+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).