X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2Fgetl%2Ffwd.ma;h=7390775d31d6dbec7e5c7406af4242b028aa649c;hb=57ae1762497a5f3ea75740e2908e04adb8642cc2;hp=f8b2ebaa828c22e28ee6634f3b08e6fc27e20ce0;hpb=d795687ffe924872a5e36122c2bd3069d6409454;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_1/getl/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1/getl/fwd.ma
index f8b2ebaa8..7390775d3 100644
--- a/matita/matita/contribs/lambdadelta/basic_1/getl/fwd.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/getl/fwd.ma
@@ -20,7 +20,7 @@ include "basic_1/drop/fwd.ma".
 
 include "basic_1/clear/fwd.ma".
 
-theorem getl_ind:
+implied lemma getl_ind:
  \forall (h: nat).(\forall (c1: C).(\forall (c2: C).(\forall (P: 
 Prop).(((\forall (e: C).((drop h O c1 e) \to ((clear e c2) \to P)))) \to 
 ((getl h c1 c2) \to P)))))
@@ -30,165 +30,110 @@ Prop).(\lambda (f: ((\forall (e: C).((drop h O c1 e) \to ((clear e c2) \to
 P))))).(\lambda (g: (getl h c1 c2)).(match g with [(getl_intro x x0 x1) 
 \Rightarrow (f x x0 x1)])))))).
 
-theorem getl_gen_all:
+lemma getl_gen_all:
  \forall (c1: C).(\forall (c2: C).(\forall (i: nat).((getl i c1 c2) \to (ex2 
 C (\lambda (e: C).(drop i O c1 e)) (\lambda (e: C).(clear e c2))))))
 \def
  \lambda (c1: C).(\lambda (c2: C).(\lambda (i: nat).(\lambda (H: (getl i c1 
-c2)).(let TMP_1 \def (\lambda (e: C).(drop i O c1 e)) in (let TMP_2 \def 
-(\lambda (e: C).(clear e c2)) in (let TMP_3 \def (ex2 C TMP_1 TMP_2) in (let 
-TMP_6 \def (\lambda (e: C).(\lambda (H0: (drop i O c1 e)).(\lambda (H1: 
-(clear e c2)).(let TMP_4 \def (\lambda (e0: C).(drop i O c1 e0)) in (let 
-TMP_5 \def (\lambda (e0: C).(clear e0 c2)) in (ex_intro2 C TMP_4 TMP_5 e H0 
-H1)))))) in (getl_ind i c1 c2 TMP_3 TMP_6 H)))))))).
+c2)).(getl_ind i c1 c2 (ex2 C (\lambda (e: C).(drop i O c1 e)) (\lambda (e: 
+C).(clear e c2))) (\lambda (e: C).(\lambda (H0: (drop i O c1 e)).(\lambda 
+(H1: (clear e c2)).(ex_intro2 C (\lambda (e0: C).(drop i O c1 e0)) (\lambda 
+(e0: C).(clear e0 c2)) e H0 H1)))) H)))).
 
-theorem getl_gen_sort:
+lemma getl_gen_sort:
  \forall (n: nat).(\forall (h: nat).(\forall (x: C).((getl h (CSort n) x) \to 
 (\forall (P: Prop).P))))
 \def
  \lambda (n: nat).(\lambda (h: nat).(\lambda (x: C).(\lambda (H: (getl h 
-(CSort n) x)).(\lambda (P: Prop).(let TMP_1 \def (CSort n) in (let H0 \def 
-(getl_gen_all TMP_1 x h H) in (let TMP_3 \def (\lambda (e: C).(let TMP_2 \def 
-(CSort n) in (drop h O TMP_2 e))) in (let TMP_4 \def (\lambda (e: C).(clear e 
-x)) in (let TMP_13 \def (\lambda (x0: C).(\lambda (H1: (drop h O (CSort n) 
-x0)).(\lambda (H2: (clear x0 x)).(let TMP_5 \def (CSort n) in (let TMP_6 \def 
-(eq C x0 TMP_5) in (let TMP_7 \def (eq nat h O) in (let TMP_8 \def (eq nat O 
-O) in (let TMP_11 \def (\lambda (H3: (eq C x0 (CSort n))).(\lambda (_: (eq 
-nat h O)).(\lambda (_: (eq nat O O)).(let TMP_9 \def (\lambda (c: C).(clear c 
-x)) in (let TMP_10 \def (CSort n) in (let H6 \def (eq_ind C x0 TMP_9 H2 
-TMP_10 H3) in (clear_gen_sort x n H6 P))))))) in (let TMP_12 \def 
-(drop_gen_sort n h O x0 H1) in (and3_ind TMP_6 TMP_7 TMP_8 P TMP_11 
-TMP_12)))))))))) in (ex2_ind C TMP_3 TMP_4 P TMP_13 H0)))))))))).
+(CSort n) x)).(\lambda (P: Prop).(let H0 \def (getl_gen_all (CSort n) x h H) 
+in (ex2_ind C (\lambda (e: C).(drop h O (CSort n) e)) (\lambda (e: C).(clear 
+e x)) P (\lambda (x0: C).(\lambda (H1: (drop h O (CSort n) x0)).(\lambda (H2: 
+(clear x0 x)).(and3_ind (eq C x0 (CSort n)) (eq nat h O) (eq nat O O) P 
+(\lambda (H3: (eq C x0 (CSort n))).(\lambda (_: (eq nat h O)).(\lambda (_: 
+(eq nat O O)).(let H6 \def (eq_ind C x0 (\lambda (c: C).(clear c x)) H2 
+(CSort n) H3) in (clear_gen_sort x n H6 P))))) (drop_gen_sort n h O x0 
+H1))))) H0)))))).
 
-theorem getl_gen_O:
+lemma getl_gen_O:
  \forall (e: C).(\forall (x: C).((getl O e x) \to (clear e x)))
 \def
  \lambda (e: C).(\lambda (x: C).(\lambda (H: (getl O e x)).(let H0 \def 
-(getl_gen_all e x O H) in (let TMP_1 \def (\lambda (e0: C).(drop O O e e0)) 
-in (let TMP_2 \def (\lambda (e0: C).(clear e0 x)) in (let TMP_3 \def (clear e 
-x) in (let TMP_6 \def (\lambda (x0: C).(\lambda (H1: (drop O O e 
-x0)).(\lambda (H2: (clear x0 x)).(let TMP_4 \def (\lambda (c: C).(clear c x)) 
-in (let TMP_5 \def (drop_gen_refl e x0 H1) in (let H3 \def (eq_ind_r C x0 
-TMP_4 H2 e TMP_5) in H3)))))) in (ex2_ind C TMP_1 TMP_2 TMP_3 TMP_6 
-H0)))))))).
+(getl_gen_all e x O H) in (ex2_ind C (\lambda (e0: C).(drop O O e e0)) 
+(\lambda (e0: C).(clear e0 x)) (clear e x) (\lambda (x0: C).(\lambda (H1: 
+(drop O O e x0)).(\lambda (H2: (clear x0 x)).(let H3 \def (eq_ind_r C x0 
+(\lambda (c: C).(clear c x)) H2 e (drop_gen_refl e x0 H1)) in H3)))) H0)))).
 
-theorem getl_gen_S:
+lemma getl_gen_S:
  \forall (k: K).(\forall (c: C).(\forall (x: C).(\forall (u: T).(\forall (h: 
 nat).((getl (S h) (CHead c k u) x) \to (getl (r k h) c x))))))
 \def
  \lambda (k: K).(\lambda (c: C).(\lambda (x: C).(\lambda (u: T).(\lambda (h: 
-nat).(\lambda (H: (getl (S h) (CHead c k u) x)).(let TMP_1 \def (CHead c k u) 
-in (let TMP_2 \def (S h) in (let H0 \def (getl_gen_all TMP_1 x TMP_2 H) in 
-(let TMP_5 \def (\lambda (e: C).(let TMP_3 \def (S h) in (let TMP_4 \def 
-(CHead c k u) in (drop TMP_3 O TMP_4 e)))) in (let TMP_6 \def (\lambda (e: 
-C).(clear e x)) in (let TMP_7 \def (r k h) in (let TMP_8 \def (getl TMP_7 c 
-x) in (let TMP_11 \def (\lambda (x0: C).(\lambda (H1: (drop (S h) O (CHead c 
-k u) x0)).(\lambda (H2: (clear x0 x)).(let TMP_9 \def (r k h) in (let TMP_10 
-\def (drop_gen_drop k c x0 u h H1) in (getl_intro TMP_9 c x x0 TMP_10 
-H2)))))) in (ex2_ind C TMP_5 TMP_6 TMP_8 TMP_11 H0)))))))))))))).
+nat).(\lambda (H: (getl (S h) (CHead c k u) x)).(let H0 \def (getl_gen_all 
+(CHead c k u) x (S h) H) in (ex2_ind C (\lambda (e: C).(drop (S h) O (CHead c 
+k u) e)) (\lambda (e: C).(clear e x)) (getl (r k h) c x) (\lambda (x0: 
+C).(\lambda (H1: (drop (S h) O (CHead c k u) x0)).(\lambda (H2: (clear x0 
+x)).(getl_intro (r k h) c x x0 (drop_gen_drop k c x0 u h H1) H2)))) H0))))))).
 
-theorem getl_gen_2:
+lemma getl_gen_2:
  \forall (c1: C).(\forall (c2: C).(\forall (i: nat).((getl i c1 c2) \to (ex_3 
 B C T (\lambda (b: B).(\lambda (c: C).(\lambda (v: T).(eq C c2 (CHead c (Bind 
 b) v)))))))))
 \def
  \lambda (c1: C).(\lambda (c2: C).(\lambda (i: nat).(\lambda (H: (getl i c1 
-c2)).(let H0 \def (getl_gen_all c1 c2 i H) in (let TMP_1 \def (\lambda (e: 
-C).(drop i O c1 e)) in (let TMP_2 \def (\lambda (e: C).(clear e c2)) in (let 
-TMP_5 \def (\lambda (b: B).(\lambda (c: C).(\lambda (v: T).(let TMP_3 \def 
-(Bind b) in (let TMP_4 \def (CHead c TMP_3 v) in (eq C c2 TMP_4)))))) in (let 
-TMP_6 \def (ex_3 B C T TMP_5) in (let TMP_33 \def (\lambda (x: C).(\lambda 
-(_: (drop i O c1 x)).(\lambda (H2: (clear x c2)).(let H3 \def (clear_gen_all 
-x c2 H2) in (let TMP_9 \def (\lambda (b: B).(\lambda (e: C).(\lambda (u: 
-T).(let TMP_7 \def (Bind b) in (let TMP_8 \def (CHead e TMP_7 u) in (eq C c2 
-TMP_8)))))) in (let TMP_12 \def (\lambda (b: B).(\lambda (c: C).(\lambda (v: 
-T).(let TMP_10 \def (Bind b) in (let TMP_11 \def (CHead c TMP_10 v) in (eq C 
-c2 TMP_11)))))) in (let TMP_13 \def (ex_3 B C T TMP_12) in (let TMP_32 \def 
-(\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H4: (eq C c2 
-(CHead x1 (Bind x0) x2))).(let TMP_14 \def (\lambda (c: C).(clear x c)) in 
-(let TMP_15 \def (Bind x0) in (let TMP_16 \def (CHead x1 TMP_15 x2) in (let 
-H5 \def (eq_ind C c2 TMP_14 H2 TMP_16 H4) in (let TMP_17 \def (Bind x0) in 
-(let TMP_18 \def (CHead x1 TMP_17 x2) in (let TMP_22 \def (\lambda (c: 
-C).(let TMP_21 \def (\lambda (b: B).(\lambda (c0: C).(\lambda (v: T).(let 
-TMP_19 \def (Bind b) in (let TMP_20 \def (CHead c0 TMP_19 v) in (eq C c 
-TMP_20)))))) in (ex_3 B C T TMP_21))) in (let TMP_27 \def (\lambda (b: 
-B).(\lambda (c: C).(\lambda (v: T).(let TMP_23 \def (Bind x0) in (let TMP_24 
-\def (CHead x1 TMP_23 x2) in (let TMP_25 \def (Bind b) in (let TMP_26 \def 
-(CHead c TMP_25 v) in (eq C TMP_24 TMP_26)))))))) in (let TMP_28 \def (Bind 
-x0) in (let TMP_29 \def (CHead x1 TMP_28 x2) in (let TMP_30 \def (refl_equal 
-C TMP_29) in (let TMP_31 \def (ex_3_intro B C T TMP_27 x0 x1 x2 TMP_30) in 
-(eq_ind_r C TMP_18 TMP_22 TMP_31 c2 H4))))))))))))))))) in (ex_3_ind B C T 
-TMP_9 TMP_13 TMP_32 H3))))))))) in (ex2_ind C TMP_1 TMP_2 TMP_6 TMP_33 
-H0)))))))))).
+c2)).(let H0 \def (getl_gen_all c1 c2 i H) in (ex2_ind C (\lambda (e: 
+C).(drop i O c1 e)) (\lambda (e: C).(clear e c2)) (ex_3 B C T (\lambda (b: 
+B).(\lambda (c: C).(\lambda (v: T).(eq C c2 (CHead c (Bind b) v)))))) 
+(\lambda (x: C).(\lambda (_: (drop i O c1 x)).(\lambda (H2: (clear x 
+c2)).(let H3 \def (clear_gen_all x c2 H2) in (ex_3_ind B C T (\lambda (b: 
+B).(\lambda (e: C).(\lambda (u: T).(eq C c2 (CHead e (Bind b) u))))) (ex_3 B 
+C T (\lambda (b: B).(\lambda (c: C).(\lambda (v: T).(eq C c2 (CHead c (Bind 
+b) v)))))) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H4: 
+(eq C c2 (CHead x1 (Bind x0) x2))).(let H5 \def (eq_ind C c2 (\lambda (c: 
+C).(clear x c)) H2 (CHead x1 (Bind x0) x2) H4) in (eq_ind_r C (CHead x1 (Bind 
+x0) x2) (\lambda (c: C).(ex_3 B C T (\lambda (b: B).(\lambda (c0: C).(\lambda 
+(v: T).(eq C c (CHead c0 (Bind b) v))))))) (ex_3_intro B C T (\lambda (b: 
+B).(\lambda (c: C).(\lambda (v: T).(eq C (CHead x1 (Bind x0) x2) (CHead c 
+(Bind b) v))))) x0 x1 x2 (refl_equal C (CHead x1 (Bind x0) x2))) c2 H4)))))) 
+H3))))) H0))))).
 
-theorem getl_gen_flat:
+lemma getl_gen_flat:
  \forall (f: F).(\forall (e: C).(\forall (d: C).(\forall (v: T).(\forall (i: 
 nat).((getl i (CHead e (Flat f) v) d) \to (getl i e d))))))
 \def
  \lambda (f: F).(\lambda (e: C).(\lambda (d: C).(\lambda (v: T).(\lambda (i: 
-nat).(let TMP_1 \def (\lambda (n: nat).((getl n (CHead e (Flat f) v) d) \to 
-(getl n e d))) in (let TMP_7 \def (\lambda (H: (getl O (CHead e (Flat f) v) 
-d)).(let TMP_2 \def (drop_refl e) in (let TMP_3 \def (Flat f) in (let TMP_4 
-\def (CHead e TMP_3 v) in (let TMP_5 \def (getl_gen_O TMP_4 d H) in (let 
-TMP_6 \def (clear_gen_flat f e d v TMP_5) in (getl_intro O e d e TMP_2 
-TMP_6))))))) in (let TMP_9 \def (\lambda (n: nat).(\lambda (_: (((getl n 
-(CHead e (Flat f) v) d) \to (getl n e d)))).(\lambda (H0: (getl (S n) (CHead 
-e (Flat f) v) d)).(let TMP_8 \def (Flat f) in (getl_gen_S TMP_8 e d v n 
-H0))))) in (nat_ind TMP_1 TMP_7 TMP_9 i)))))))).
+nat).(nat_ind (\lambda (n: nat).((getl n (CHead e (Flat f) v) d) \to (getl n 
+e d))) (\lambda (H: (getl O (CHead e (Flat f) v) d)).(getl_intro O e d e 
+(drop_refl e) (clear_gen_flat f e d v (getl_gen_O (CHead e (Flat f) v) d 
+H)))) (\lambda (n: nat).(\lambda (_: (((getl n (CHead e (Flat f) v) d) \to 
+(getl n e d)))).(\lambda (H0: (getl (S n) (CHead e (Flat f) v) 
+d)).(getl_gen_S (Flat f) e d v n H0)))) i))))).
 
-theorem getl_gen_bind:
+lemma getl_gen_bind:
  \forall (b: B).(\forall (e: C).(\forall (d: C).(\forall (v: T).(\forall (i: 
 nat).((getl i (CHead e (Bind b) v) d) \to (or (land (eq nat i O) (eq C d 
 (CHead e (Bind b) v))) (ex2 nat (\lambda (j: nat).(eq nat i (S j))) (\lambda 
 (j: nat).(getl j e d)))))))))
 \def
  \lambda (b: B).(\lambda (e: C).(\lambda (d: C).(\lambda (v: T).(\lambda (i: 
-nat).(let TMP_10 \def (\lambda (n: nat).((getl n (CHead e (Bind b) v) d) \to 
-(let TMP_1 \def (eq nat n O) in (let TMP_2 \def (Bind b) in (let TMP_3 \def 
-(CHead e TMP_2 v) in (let TMP_4 \def (eq C d TMP_3) in (let TMP_5 \def (land 
-TMP_1 TMP_4) in (let TMP_7 \def (\lambda (j: nat).(let TMP_6 \def (S j) in 
-(eq nat n TMP_6))) in (let TMP_8 \def (\lambda (j: nat).(getl j e d)) in (let 
-TMP_9 \def (ex2 nat TMP_7 TMP_8) in (or TMP_5 TMP_9))))))))))) in (let TMP_52 
-\def (\lambda (H: (getl O (CHead e (Bind b) v) d)).(let TMP_11 \def (Bind b) 
-in (let TMP_12 \def (CHead e TMP_11 v) in (let TMP_22 \def (\lambda (c: 
-C).(let TMP_13 \def (eq nat O O) in (let TMP_14 \def (Bind b) in (let TMP_15 
-\def (CHead e TMP_14 v) in (let TMP_16 \def (eq C c TMP_15) in (let TMP_17 
-\def (land TMP_13 TMP_16) in (let TMP_19 \def (\lambda (j: nat).(let TMP_18 
-\def (S j) in (eq nat O TMP_18))) in (let TMP_20 \def (\lambda (j: nat).(getl 
-j e c)) in (let TMP_21 \def (ex2 nat TMP_19 TMP_20) in (or TMP_17 
-TMP_21)))))))))) in (let TMP_23 \def (eq nat O O) in (let TMP_24 \def (Bind 
-b) in (let TMP_25 \def (CHead e TMP_24 v) in (let TMP_26 \def (Bind b) in 
-(let TMP_27 \def (CHead e TMP_26 v) in (let TMP_28 \def (eq C TMP_25 TMP_27) 
-in (let TMP_29 \def (land TMP_23 TMP_28) in (let TMP_31 \def (\lambda (j: 
-nat).(let TMP_30 \def (S j) in (eq nat O TMP_30))) in (let TMP_34 \def 
-(\lambda (j: nat).(let TMP_32 \def (Bind b) in (let TMP_33 \def (CHead e 
-TMP_32 v) in (getl j e TMP_33)))) in (let TMP_35 \def (ex2 nat TMP_31 TMP_34) 
-in (let TMP_36 \def (eq nat O O) in (let TMP_37 \def (Bind b) in (let TMP_38 
-\def (CHead e TMP_37 v) in (let TMP_39 \def (Bind b) in (let TMP_40 \def 
-(CHead e TMP_39 v) in (let TMP_41 \def (eq C TMP_38 TMP_40) in (let TMP_42 
-\def (refl_equal nat O) in (let TMP_43 \def (Bind b) in (let TMP_44 \def 
-(CHead e TMP_43 v) in (let TMP_45 \def (refl_equal C TMP_44) in (let TMP_46 
-\def (conj TMP_36 TMP_41 TMP_42 TMP_45) in (let TMP_47 \def (or_introl TMP_29 
-TMP_35 TMP_46) in (let TMP_48 \def (Bind b) in (let TMP_49 \def (CHead e 
-TMP_48 v) in (let TMP_50 \def (getl_gen_O TMP_49 d H) in (let TMP_51 \def 
-(clear_gen_bind b e d v TMP_50) in (eq_ind_r C TMP_12 TMP_22 TMP_47 d 
-TMP_51))))))))))))))))))))))))))))))) in (let TMP_73 \def (\lambda (n: 
+nat).(nat_ind (\lambda (n: nat).((getl n (CHead e (Bind b) v) d) \to (or 
+(land (eq nat n O) (eq C d (CHead e (Bind b) v))) (ex2 nat (\lambda (j: 
+nat).(eq nat n (S j))) (\lambda (j: nat).(getl j e d)))))) (\lambda (H: (getl 
+O (CHead e (Bind b) v) d)).(eq_ind_r C (CHead e (Bind b) v) (\lambda (c: 
+C).(or (land (eq nat O O) (eq C c (CHead e (Bind b) v))) (ex2 nat (\lambda 
+(j: nat).(eq nat O (S j))) (\lambda (j: nat).(getl j e c))))) (or_introl 
+(land (eq nat O O) (eq C (CHead e (Bind b) v) (CHead e (Bind b) v))) (ex2 nat 
+(\lambda (j: nat).(eq nat O (S j))) (\lambda (j: nat).(getl j e (CHead e 
+(Bind b) v)))) (conj (eq nat O O) (eq C (CHead e (Bind b) v) (CHead e (Bind 
+b) v)) (refl_equal nat O) (refl_equal C (CHead e (Bind b) v)))) d 
+(clear_gen_bind b e d v (getl_gen_O (CHead e (Bind b) v) d H)))) (\lambda (n: 
 nat).(\lambda (_: (((getl n (CHead e (Bind b) v) d) \to (or (land (eq nat n 
 O) (eq C d (CHead e (Bind b) v))) (ex2 nat (\lambda (j: nat).(eq nat n (S 
 j))) (\lambda (j: nat).(getl j e d))))))).(\lambda (H0: (getl (S n) (CHead e 
-(Bind b) v) d)).(let TMP_53 \def (S n) in (let TMP_54 \def (eq nat TMP_53 O) 
-in (let TMP_55 \def (Bind b) in (let TMP_56 \def (CHead e TMP_55 v) in (let 
-TMP_57 \def (eq C d TMP_56) in (let TMP_58 \def (land TMP_54 TMP_57) in (let 
-TMP_61 \def (\lambda (j: nat).(let TMP_59 \def (S n) in (let TMP_60 \def (S 
-j) in (eq nat TMP_59 TMP_60)))) in (let TMP_62 \def (\lambda (j: nat).(getl j 
-e d)) in (let TMP_63 \def (ex2 nat TMP_61 TMP_62) in (let TMP_66 \def 
-(\lambda (j: nat).(let TMP_64 \def (S n) in (let TMP_65 \def (S j) in (eq nat 
-TMP_64 TMP_65)))) in (let TMP_67 \def (\lambda (j: nat).(getl j e d)) in (let 
-TMP_68 \def (S n) in (let TMP_69 \def (refl_equal nat TMP_68) in (let TMP_70 
-\def (Bind b) in (let TMP_71 \def (getl_gen_S TMP_70 e d v n H0) in (let 
-TMP_72 \def (ex_intro2 nat TMP_66 TMP_67 n TMP_69 TMP_71) in (or_intror 
-TMP_58 TMP_63 TMP_72)))))))))))))))))))) in (nat_ind TMP_10 TMP_52 TMP_73 
-i)))))))).
+(Bind b) v) d)).(or_intror (land (eq nat (S n) O) (eq C d (CHead e (Bind b) 
+v))) (ex2 nat (\lambda (j: nat).(eq nat (S n) (S j))) (\lambda (j: nat).(getl 
+j e d))) (ex_intro2 nat (\lambda (j: nat).(eq nat (S n) (S j))) (\lambda (j: 
+nat).(getl j e d)) n (refl_equal nat (S n)) (getl_gen_S (Bind b) e d v n 
+H0)))))) i))))).
 
 theorem getl_mono:
  \forall (c: C).(\forall (x1: C).(\forall (h: nat).((getl h c x1) \to 
@@ -196,19 +141,14 @@ theorem getl_mono:
 \def
  \lambda (c: C).(\lambda (x1: C).(\lambda (h: nat).(\lambda (H: (getl h c 
 x1)).(\lambda (x2: C).(\lambda (H0: (getl h c x2)).(let H1 \def (getl_gen_all 
-c x2 h H0) in (let TMP_1 \def (\lambda (e: C).(drop h O c e)) in (let TMP_2 
-\def (\lambda (e: C).(clear e x2)) in (let TMP_3 \def (eq C x1 x2) in (let 
-TMP_14 \def (\lambda (x: C).(\lambda (H2: (drop h O c x)).(\lambda (H3: 
-(clear x x2)).(let H4 \def (getl_gen_all c x1 h H) in (let TMP_4 \def 
-(\lambda (e: C).(drop h O c e)) in (let TMP_5 \def (\lambda (e: C).(clear e 
-x1)) in (let TMP_6 \def (eq C x1 x2) in (let TMP_13 \def (\lambda (x0: 
-C).(\lambda (H5: (drop h O c x0)).(\lambda (H6: (clear x0 x1)).(let TMP_7 
-\def (\lambda (c0: C).(drop h O c c0)) in (let TMP_8 \def (drop_mono c x O h 
-H2 x0 H5) in (let H7 \def (eq_ind C x TMP_7 H2 x0 TMP_8) in (let TMP_9 \def 
-(\lambda (c0: C).(drop h O c c0)) in (let TMP_10 \def (drop_mono c x O h H2 
-x0 H5) in (let H8 \def (eq_ind_r C x0 TMP_9 H7 x TMP_10) in (let TMP_11 \def 
-(\lambda (c0: C).(clear c0 x1)) in (let TMP_12 \def (drop_mono c x O h H2 x0 
-H5) in (let H9 \def (eq_ind_r C x0 TMP_11 H6 x TMP_12) in (clear_mono x x1 H9 
-x2 H3))))))))))))) in (ex2_ind C TMP_4 TMP_5 TMP_6 TMP_13 H4))))))))) in 
-(ex2_ind C TMP_1 TMP_2 TMP_3 TMP_14 H1))))))))))).
+c x2 h H0) in (ex2_ind C (\lambda (e: C).(drop h O c e)) (\lambda (e: 
+C).(clear e x2)) (eq C x1 x2) (\lambda (x: C).(\lambda (H2: (drop h O c 
+x)).(\lambda (H3: (clear x x2)).(let H4 \def (getl_gen_all c x1 h H) in 
+(ex2_ind C (\lambda (e: C).(drop h O c e)) (\lambda (e: C).(clear e x1)) (eq 
+C x1 x2) (\lambda (x0: C).(\lambda (H5: (drop h O c x0)).(\lambda (H6: (clear 
+x0 x1)).(let H7 \def (eq_ind C x (\lambda (c0: C).(drop h O c c0)) H2 x0 
+(drop_mono c x O h H2 x0 H5)) in (let H8 \def (eq_ind_r C x0 (\lambda (c0: 
+C).(drop h O c c0)) H7 x (drop_mono c x O h H2 x0 H5)) in (let H9 \def 
+(eq_ind_r C x0 (\lambda (c0: C).(clear c0 x1)) H6 x (drop_mono c x O h H2 x0 
+H5)) in (clear_mono x x1 H9 x2 H3))))))) H4))))) H1))))))).