update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / arity / lift1.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/arity/lift1.ma b/matita/matita/contribs/lambdadelta/basic_1/arity/lift1.ma
index 5d668d2c2d650d2a6e48a497a631ff226e96348f..7267b7817b707c5655765ac06954c23fec683a61 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/arity/lift1.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/arity/lift1.ma
@@ -18,28 +18,24 @@ include "basic_1/arity/props.ma".
 
 include "basic_1/drop1/fwd.ma".
 
-theorem arity_lift1:
+lemma arity_lift1:
  \forall (g: G).(\forall (a: A).(\forall (c2: C).(\forall (hds: 
 PList).(\forall (c1: C).(\forall (t: T).((drop1 hds c1 c2) \to ((arity g c2 t 
 a) \to (arity g c1 (lift1 hds t) a))))))))
 \def
- \lambda (g: G).(\lambda (a: A).(\lambda (c2: C).(\lambda (hds: PList).(let 
-TMP_2 \def (\lambda (p: PList).(\forall (c1: C).(\forall (t: T).((drop1 p c1 
-c2) \to ((arity g c2 t a) \to (let TMP_1 \def (lift1 p t) in (arity g c1 
-TMP_1 a))))))) in (let TMP_4 \def (\lambda (c1: C).(\lambda (t: T).(\lambda 
-(H: (drop1 PNil c1 c2)).(\lambda (H0: (arity g c2 t a)).(let H_y \def 
-(drop1_gen_pnil c1 c2 H) in (let TMP_3 \def (\lambda (c: C).(arity g c t a)) 
-in (eq_ind_r C c2 TMP_3 H0 c1 H_y))))))) in (let TMP_13 \def (\lambda (n: 
+ \lambda (g: G).(\lambda (a: A).(\lambda (c2: C).(\lambda (hds: 
+PList).(PList_ind (\lambda (p: PList).(\forall (c1: C).(\forall (t: 
+T).((drop1 p c1 c2) \to ((arity g c2 t a) \to (arity g c1 (lift1 p t) a)))))) 
+(\lambda (c1: C).(\lambda (t: T).(\lambda (H: (drop1 PNil c1 c2)).(\lambda 
+(H0: (arity g c2 t a)).(let H_y \def (drop1_gen_pnil c1 c2 H) in (eq_ind_r C 
+c2 (\lambda (c: C).(arity g c t a)) H0 c1 H_y)))))) (\lambda (n: 
 nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda (H: ((\forall (c1: 
 C).(\forall (t: T).((drop1 p c1 c2) \to ((arity g c2 t a) \to (arity g c1 
 (lift1 p t) a))))))).(\lambda (c1: C).(\lambda (t: T).(\lambda (H0: (drop1 
 (PCons n n0 p) c1 c2)).(\lambda (H1: (arity g c2 t a)).(let H_x \def 
-(drop1_gen_pcons c1 c2 p n n0 H0) in (let H2 \def H_x in (let TMP_5 \def 
-(\lambda (c3: C).(drop n n0 c1 c3)) in (let TMP_6 \def (\lambda (c3: 
-C).(drop1 p c3 c2)) in (let TMP_7 \def (lift1 p t) in (let TMP_8 \def (lift n 
-n0 TMP_7) in (let TMP_9 \def (arity g c1 TMP_8 a) in (let TMP_12 \def 
-(\lambda (x: C).(\lambda (H3: (drop n n0 c1 x)).(\lambda (H4: (drop1 p x 
-c2)).(let TMP_10 \def (lift1 p t) in (let TMP_11 \def (H x t H4 H1) in 
-(arity_lift g x TMP_10 a TMP_11 c1 n n0 H3)))))) in (ex2_ind C TMP_5 TMP_6 
-TMP_9 TMP_12 H2))))))))))))))))) in (PList_ind TMP_2 TMP_4 TMP_13 hds))))))).
+(drop1_gen_pcons c1 c2 p n n0 H0) in (let H2 \def H_x in (ex2_ind C (\lambda 
+(c3: C).(drop n n0 c1 c3)) (\lambda (c3: C).(drop1 p c3 c2)) (arity g c1 
+(lift n n0 (lift1 p t)) a) (\lambda (x: C).(\lambda (H3: (drop n n0 c1 
+x)).(\lambda (H4: (drop1 p x c2)).(arity_lift g x (lift1 p t) a (H x t H4 H1) 
+c1 n n0 H3)))) H2))))))))))) hds)))).