update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / sn3 / lift1.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/sn3/lift1.ma b/matita/matita/contribs/lambdadelta/basic_1/sn3/lift1.ma
index 51bc3426ccade0be00a1761e4f518260b82a6828..71d9e93fe566cef9074b090726d46fea7b999b88 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/sn3/lift1.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/sn3/lift1.ma
@@ -20,34 +20,24 @@ include "basic_1/drop1/fwd.ma".
 
 include "basic_1/lift1/props.ma".
 
-theorem sns3_lifts1:
+lemma sns3_lifts1:
  \forall (e: C).(\forall (hds: PList).(\forall (c: C).((drop1 hds c e) \to 
 (\forall (ts: TList).((sns3 e ts) \to (sns3 c (lifts1 hds ts)))))))
 \def
- \lambda (e: C).(\lambda (hds: PList).(let TMP_2 \def (\lambda (p: 
-PList).(\forall (c: C).((drop1 p c e) \to (\forall (ts: TList).((sns3 e ts) 
-\to (let TMP_1 \def (lifts1 p ts) in (sns3 c TMP_1))))))) in (let TMP_9 \def 
-(\lambda (c: C).(\lambda (H: (drop1 PNil c e)).(\lambda (ts: TList).(\lambda 
-(H0: (sns3 e ts)).(let H_y \def (drop1_gen_pnil c e H) in (let TMP_4 \def 
-(\lambda (c0: C).(let TMP_3 \def (lifts1 PNil ts) in (sns3 c0 TMP_3))) in 
-(let TMP_5 \def (\lambda (t: TList).(sns3 e t)) in (let TMP_6 \def (lifts1 
-PNil ts) in (let TMP_7 \def (lifts1_nil ts) in (let TMP_8 \def (eq_ind_r 
-TList ts TMP_5 H0 TMP_6 TMP_7) in (eq_ind_r C e TMP_4 TMP_8 c H_y))))))))))) 
-in (let TMP_25 \def (\lambda (n: nat).(\lambda (n0: nat).(\lambda (p: 
-PList).(\lambda (H: ((\forall (c: C).((drop1 p c e) \to (\forall (ts: 
-TList).((sns3 e ts) \to (sns3 c (lifts1 p ts)))))))).(\lambda (c: C).(\lambda 
-(H0: (drop1 (PCons n n0 p) c e)).(\lambda (ts: TList).(\lambda (H1: (sns3 e 
-ts)).(let H_x \def (drop1_gen_pcons c e p n n0 H0) in (let H2 \def H_x in 
-(let TMP_10 \def (\lambda (c2: C).(drop n n0 c c2)) in (let TMP_11 \def 
-(\lambda (c2: C).(drop1 p c2 e)) in (let TMP_12 \def (PCons n n0 p) in (let 
-TMP_13 \def (lifts1 TMP_12 ts) in (let TMP_14 \def (sns3 c TMP_13) in (let 
-TMP_24 \def (\lambda (x: C).(\lambda (H3: (drop n n0 c x)).(\lambda (H4: 
-(drop1 p x e)).(let TMP_15 \def (lifts1 p ts) in (let TMP_16 \def (lifts n n0 
-TMP_15) in (let TMP_17 \def (\lambda (t: TList).(sns3 c t)) in (let TMP_18 
-\def (lifts1 p ts) in (let TMP_19 \def (H x H4 ts H1) in (let TMP_20 \def 
-(sns3_lifts c x n n0 H3 TMP_18 TMP_19) in (let TMP_21 \def (PCons n n0 p) in 
-(let TMP_22 \def (lifts1 TMP_21 ts) in (let TMP_23 \def (lifts1_cons n n0 p 
-ts) in (eq_ind_r TList TMP_16 TMP_17 TMP_20 TMP_22 TMP_23))))))))))))) in 
-(ex2_ind C TMP_10 TMP_11 TMP_14 TMP_24 H2))))))))))))))))) in (PList_ind 
-TMP_2 TMP_9 TMP_25 hds))))).
+ \lambda (e: C).(\lambda (hds: PList).(PList_ind (\lambda (p: PList).(\forall 
+(c: C).((drop1 p c e) \to (\forall (ts: TList).((sns3 e ts) \to (sns3 c 
+(lifts1 p ts))))))) (\lambda (c: C).(\lambda (H: (drop1 PNil c e)).(\lambda 
+(ts: TList).(\lambda (H0: (sns3 e ts)).(let H_y \def (drop1_gen_pnil c e H) 
+in (eq_ind_r C e (\lambda (c0: C).(sns3 c0 (lifts1 PNil ts))) (eq_ind_r TList 
+ts (\lambda (t: TList).(sns3 e t)) H0 (lifts1 PNil ts) (lifts1_nil ts)) c 
+H_y)))))) (\lambda (n: nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda 
+(H: ((\forall (c: C).((drop1 p c e) \to (\forall (ts: TList).((sns3 e ts) \to 
+(sns3 c (lifts1 p ts)))))))).(\lambda (c: C).(\lambda (H0: (drop1 (PCons n n0 
+p) c e)).(\lambda (ts: TList).(\lambda (H1: (sns3 e ts)).(let H_x \def 
+(drop1_gen_pcons c e p n n0 H0) in (let H2 \def H_x in (ex2_ind C (\lambda 
+(c2: C).(drop n n0 c c2)) (\lambda (c2: C).(drop1 p c2 e)) (sns3 c (lifts1 
+(PCons n n0 p) ts)) (\lambda (x: C).(\lambda (H3: (drop n n0 c x)).(\lambda 
+(H4: (drop1 p x e)).(eq_ind_r TList (lifts n n0 (lifts1 p ts)) (\lambda (t: 
+TList).(sns3 c t)) (sns3_lifts c x n n0 H3 (lifts1 p ts) (H x H4 ts H1)) 
+(lifts1 (PCons n n0 p) ts) (lifts1_cons n n0 p ts))))) H2))))))))))) hds)).