update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_1/csubv/props.ma b/matita/matita/contribs/lambdadelta/basic_1/csubv/props.ma
index a7e04739a1ebe55375ba469ffdcb6e53ee933d05..eb8448a1a348cadeba6c5ca0ae1f3579c8a8c7da 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/csubv/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/csubv/props.ma
@@ -20,30 +20,24 @@ include "basic_1/C/fwd.ma".
 
 include "basic_1/T/props.ma".
 
-theorem csubv_bind_same:
+lemma csubv_bind_same:
  \forall (c1: C).(\forall (c2: C).((csubv c1 c2) \to (\forall (b: B).(\forall 
 (v1: T).(\forall (v2: T).(csubv (CHead c1 (Bind b) v1) (CHead c2 (Bind b) 
 v2)))))))
 \def
  \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csubv c1 c2)).(\lambda (b: 
-B).(let TMP_5 \def (\lambda (b0: B).(\forall (v1: T).(\forall (v2: T).(let 
-TMP_1 \def (Bind b0) in (let TMP_2 \def (CHead c1 TMP_1 v1) in (let TMP_3 
-\def (Bind b0) in (let TMP_4 \def (CHead c2 TMP_3 v2) in (csubv TMP_2 
-TMP_4)))))))) in (let TMP_6 \def (\lambda (v1: T).(\lambda (v2: 
-T).(csubv_bind c1 c2 H Abbr not_abbr_void Abbr v1 v2))) in (let TMP_7 \def 
-(\lambda (v1: T).(\lambda (v2: T).(csubv_bind c1 c2 H Abst not_abst_void Abst 
-v1 v2))) in (let TMP_8 \def (\lambda (v1: T).(\lambda (v2: T).(csubv_void c1 
-c2 H v1 v2))) in (B_ind TMP_5 TMP_6 TMP_7 TMP_8 b)))))))).
+B).(B_ind (\lambda (b0: B).(\forall (v1: T).(\forall (v2: T).(csubv (CHead c1 
+(Bind b0) v1) (CHead c2 (Bind b0) v2))))) (\lambda (v1: T).(\lambda (v2: 
+T).(csubv_bind c1 c2 H Abbr not_abbr_void Abbr v1 v2))) (\lambda (v1: 
+T).(\lambda (v2: T).(csubv_bind c1 c2 H Abst not_abst_void Abst v1 v2))) 
+(\lambda (v1: T).(\lambda (v2: T).(csubv_void c1 c2 H v1 v2))) b)))).
 
-theorem csubv_refl:
+lemma csubv_refl:
  \forall (c: C).(csubv c c)
 \def
- \lambda (c: C).(let TMP_1 \def (\lambda (c0: C).(csubv c0 c0)) in (let TMP_2 
-\def (\lambda (n: nat).(csubv_sort n)) in (let TMP_8 \def (\lambda (c0: 
-C).(\lambda (H: (csubv c0 c0)).(\lambda (k: K).(let TMP_5 \def (\lambda (k0: 
-K).(\forall (t: T).(let TMP_3 \def (CHead c0 k0 t) in (let TMP_4 \def (CHead 
-c0 k0 t) in (csubv TMP_3 TMP_4))))) in (let TMP_6 \def (\lambda (b: 
-B).(\lambda (t: T).(csubv_bind_same c0 c0 H b t t))) in (let TMP_7 \def 
-(\lambda (f: F).(\lambda (t: T).(csubv_flat c0 c0 H f f t t))) in (K_ind 
-TMP_5 TMP_6 TMP_7 k))))))) in (C_ind TMP_1 TMP_2 TMP_8 c)))).
+ \lambda (c: C).(C_ind (\lambda (c0: C).(csubv c0 c0)) (\lambda (n: 
+nat).(csubv_sort n)) (\lambda (c0: C).(\lambda (H: (csubv c0 c0)).(\lambda 
+(k: K).(K_ind (\lambda (k0: K).(\forall (t: T).(csubv (CHead c0 k0 t) (CHead 
+c0 k0 t)))) (\lambda (b: B).(\lambda (t: T).(csubv_bind_same c0 c0 H b t t))) 
+(\lambda (f: F).(\lambda (t: T).(csubv_flat c0 c0 H f f t t))) k)))) c).