update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_1/csubt/csuba.ma b/matita/matita/contribs/lambdadelta/basic_1/csubt/csuba.ma
index f465141ccc828d3451888f8a422fce596b32c18b..0de7f11cd1ac96a17720ee77ea6ab4892d9a421f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/csubt/csuba.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/csubt/csuba.ma
@@ -16,30 +16,24 @@
 
 include "basic_1/ty3/arity.ma".
 
-theorem csubt_csuba:
+lemma csubt_csuba:
  \forall (g: G).(\forall (c1: C).(\forall (c2: C).((csubt g c1 c2) \to (csuba 
 g c1 c2))))
 \def
  \lambda (g: G).(\lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csubt 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 (_: 
-(csubt g c3 c4)).(\lambda (H1: (csuba g c3 c4)).(\lambda (k: K).(\lambda (u: 
-T).(csuba_head g c3 c4 H1 k u))))))) in (let TMP_5 \def (\lambda (c3: 
-C).(\lambda (c4: C).(\lambda (_: (csubt 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_16 
-\def (\lambda (c3: C).(\lambda (c4: C).(\lambda (_: (csubt g c3 c4)).(\lambda 
-(H1: (csuba g c3 c4)).(\lambda (u: T).(\lambda (t: T).(\lambda (H2: (ty3 g c3 
-u t)).(\lambda (_: (ty3 g c4 u t)).(let H_x \def (ty3_arity g c3 u t H2) in 
-(let H4 \def H_x in (let TMP_6 \def (\lambda (a1: A).(arity g c3 u a1)) in 
-(let TMP_8 \def (\lambda (a1: A).(let TMP_7 \def (asucc g a1) in (arity g c3 
-t TMP_7))) in (let TMP_9 \def (Bind Abst) in (let TMP_10 \def (CHead c3 TMP_9 
-t) in (let TMP_11 \def (Bind Abbr) in (let TMP_12 \def (CHead c4 TMP_11 u) in 
-(let TMP_13 \def (csuba g TMP_10 TMP_12) in (let TMP_15 \def (\lambda (x: 
-A).(\lambda (H5: (arity g c3 u x)).(\lambda (H6: (arity g c3 t (asucc g 
-x))).(let TMP_14 \def (csuba_arity g c3 u x H5 c4 H1) in (csuba_abst g c3 c4 
-H1 t x H6 u TMP_14))))) in (ex2_ind A TMP_6 TMP_8 TMP_13 TMP_15 
-H4))))))))))))))))))) in (csubt_ind g TMP_1 TMP_3 TMP_4 TMP_5 TMP_16 c1 c2 
-H))))))))).
+c2)).(csubt_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 
+(_: (csubt g c3 c4)).(\lambda (H1: (csuba g c3 c4)).(\lambda (k: K).(\lambda 
+(u: T).(csuba_head g c3 c4 H1 k u))))))) (\lambda (c3: C).(\lambda (c4: 
+C).(\lambda (_: (csubt 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 (_: (csubt g c3 c4)).(\lambda (H1: (csuba g c3 c4)).(\lambda (u: 
+T).(\lambda (t: T).(\lambda (H2: (ty3 g c3 u t)).(\lambda (_: (ty3 g c4 u 
+t)).(let H_x \def (ty3_arity g c3 u t H2) in (let H4 \def H_x in (ex2_ind A 
+(\lambda (a1: A).(arity g c3 u a1)) (\lambda (a1: A).(arity g c3 t (asucc g 
+a1))) (csuba g (CHead c3 (Bind Abst) t) (CHead c4 (Bind Abbr) u)) (\lambda 
+(x: A).(\lambda (H5: (arity g c3 u x)).(\lambda (H6: (arity g c3 t (asucc g 
+x))).(csuba_abst g c3 c4 H1 t x H6 u (csuba_arity g c3 u x H5 c4 H1))))) 
+H4))))))))))) c1 c2 H)))).