update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / csubc / csuba.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/csubc/csuba.ma b/matita/matita/contribs/lambdadelta/basic_1/csubc/csuba.ma
index b25cab8d4c60341acf574a50f110e9b08f735fb1..9e1d3014eafb585ea8f679b0ce20e20c2149a594 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/csubc/csuba.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/csubc/csuba.ma
@@ -18,24 +18,20 @@ include "basic_1/csubc/fwd.ma".
 
 include "basic_1/sc3/props.ma".
 
-theorem csubc_csuba:
+lemma csubc_csuba:
  \forall (g: G).(\forall (c1: C).(\forall (c2: C).((csubc g c1 c2) \to (csuba 
 g c1 c2))))
 \def
  \lambda (g: G).(\lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csubc g c1 
-c2)).(let TMP_1 \def (\lambda (c: C).(\lambda (c0: C).(csuba g c c0))) in 
-(let TMP_3 \def (\lambda (n: nat).(let TMP_2 \def (CSort n) in (csuba_refl g 
-TMP_2))) in (let TMP_4 \def (\lambda (c3: C).(\lambda (c4: C).(\lambda (_: 
-(csubc g c3 c4)).(\lambda (H1: (csuba g c3 c4)).(\lambda (k: K).(\lambda (v: 
-T).(csuba_head g c3 c4 H1 k v))))))) in (let TMP_5 \def (\lambda (c3: 
-C).(\lambda (c4: C).(\lambda (_: (csubc g c3 c4)).(\lambda (H1: (csuba g c3 
-c4)).(\lambda (b: B).(\lambda (H2: (not (eq B b Void))).(\lambda (u1: 
-T).(\lambda (u2: T).(csuba_void g c3 c4 H1 b H2 u1 u2))))))))) in (let TMP_9 
-\def (\lambda (c3: C).(\lambda (c4: C).(\lambda (_: (csubc g c3 c4)).(\lambda 
-(H1: (csuba g c3 c4)).(\lambda (v: T).(\lambda (a: A).(\lambda (H2: (sc3 g 
-(asucc g a) c3 v)).(\lambda (w: T).(\lambda (H3: (sc3 g a c4 w)).(let TMP_6 
-\def (asucc g a) in (let TMP_7 \def (sc3_arity_gen g c3 v TMP_6 H2) in (let 
-TMP_8 \def (sc3_arity_gen g c4 w a H3) in (csuba_abst g c3 c4 H1 v a TMP_7 w 
-TMP_8))))))))))))) in (csubc_ind g TMP_1 TMP_3 TMP_4 TMP_5 TMP_9 c1 c2 
-H))))))))).
+c2)).(csubc_ind g (\lambda (c: C).(\lambda (c0: C).(csuba g c c0))) (\lambda 
+(n: nat).(csuba_refl g (CSort n))) (\lambda (c3: C).(\lambda (c4: C).(\lambda 
+(_: (csubc g c3 c4)).(\lambda (H1: (csuba g c3 c4)).(\lambda (k: K).(\lambda 
+(v: T).(csuba_head g c3 c4 H1 k v))))))) (\lambda (c3: C).(\lambda (c4: 
+C).(\lambda (_: (csubc g c3 c4)).(\lambda (H1: (csuba g c3 c4)).(\lambda (b: 
+B).(\lambda (H2: (not (eq B b Void))).(\lambda (u1: T).(\lambda (u2: 
+T).(csuba_void g c3 c4 H1 b H2 u1 u2))))))))) (\lambda (c3: C).(\lambda (c4: 
+C).(\lambda (_: (csubc g c3 c4)).(\lambda (H1: (csuba g c3 c4)).(\lambda (v: 
+T).(\lambda (a: A).(\lambda (H2: (sc3 g (asucc g a) c3 v)).(\lambda (w: 
+T).(\lambda (H3: (sc3 g a c4 w)).(csuba_abst g c3 c4 H1 v a (sc3_arity_gen g 
+c3 v (asucc g a) H2) w (sc3_arity_gen g c4 w a H3))))))))))) c1 c2 H)))).