X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2Fiso%2Ffwd.ma;h=fc3550a4cfd3602cfb9eedb6ada3e94556b425d6;hb=57ae1762497a5f3ea75740e2908e04adb8642cc2;hp=40917f7b90f7f11284419fa42247b9fd0ca4836f;hpb=538c5526a6b3c3af44f92c9cc67d82f28995da96;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_1/iso/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1/iso/fwd.ma
index 40917f7b9..fc3550a4c 100644
--- a/matita/matita/contribs/lambdadelta/basic_1/iso/fwd.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/iso/fwd.ma
@@ -18,7 +18,7 @@ include "basic_1/iso/defs.ma".
 
 include "basic_1/tlist/defs.ma".
 
-theorem iso_ind:
+implied lemma iso_ind:
  \forall (P: ((T \to (T \to Prop)))).(((\forall (n1: nat).(\forall (n2: 
 nat).(P (TSort n1) (TSort n2))))) \to (((\forall (i1: nat).(\forall (i2: 
 nat).(P (TLRef i1) (TLRef i2))))) \to (((\forall (v1: T).(\forall (v2: 
@@ -35,216 +35,150 @@ nat).(\forall (n2: nat).(P (TSort n1) (TSort n2)))))).(\lambda (f0: ((\forall
 (f x x0) | (iso_lref x x0) \Rightarrow (f0 x x0) | (iso_head x x0 x1 x2 x3) 
 \Rightarrow (f1 x x0 x1 x2 x3)]))))))).
 
-theorem iso_gen_sort:
+lemma iso_gen_sort:
  \forall (u2: T).(\forall (n1: nat).((iso (TSort n1) u2) \to (ex nat (\lambda 
 (n2: nat).(eq T u2 (TSort n2))))))
 \def
- \lambda (u2: T).(\lambda (n1: nat).(\lambda (H: (iso (TSort n1) u2)).(let 
-TMP_1 \def (TSort n1) in (let TMP_2 \def (\lambda (t: T).(iso t u2)) in (let 
-TMP_5 \def (\lambda (_: T).(let TMP_4 \def (\lambda (n2: nat).(let TMP_3 \def 
-(TSort n2) in (eq T u2 TMP_3))) in (ex nat TMP_4))) in (let TMP_34 \def 
-(\lambda (y: T).(\lambda (H0: (iso y u2)).(let TMP_8 \def (\lambda (t: 
-T).(\lambda (t0: T).((eq T t (TSort n1)) \to (let TMP_7 \def (\lambda (n2: 
-nat).(let TMP_6 \def (TSort n2) in (eq T t0 TMP_6))) in (ex nat TMP_7))))) in 
-(let TMP_17 \def (\lambda (n0: nat).(\lambda (n2: nat).(\lambda (H1: (eq T 
-(TSort n0) (TSort n1))).(let TMP_9 \def (\lambda (e: T).(match e with [(TSort 
-n) \Rightarrow n | (TLRef _) \Rightarrow n0 | (THead _ _ _) \Rightarrow n0])) 
-in (let TMP_10 \def (TSort n0) in (let TMP_11 \def (TSort n1) in (let H2 \def 
-(f_equal T nat TMP_9 TMP_10 TMP_11 H1) in (let TMP_14 \def (\lambda (n3: 
-nat).(let TMP_12 \def (TSort n2) in (let TMP_13 \def (TSort n3) in (eq T 
-TMP_12 TMP_13)))) in (let TMP_15 \def (TSort n2) in (let TMP_16 \def 
-(refl_equal T TMP_15) in (ex_intro nat TMP_14 n2 TMP_16))))))))))) in (let 
-TMP_25 \def (\lambda (i1: nat).(\lambda (i2: nat).(\lambda (H1: (eq T (TLRef 
-i1) (TSort n1))).(let TMP_18 \def (TLRef i1) in (let TMP_19 \def (\lambda 
+ \lambda (u2: T).(\lambda (n1: nat).(\lambda (H: (iso (TSort n1) 
+u2)).(insert_eq T (TSort n1) (\lambda (t: T).(iso t u2)) (\lambda (_: T).(ex 
+nat (\lambda (n2: nat).(eq T u2 (TSort n2))))) (\lambda (y: T).(\lambda (H0: 
+(iso y u2)).(iso_ind (\lambda (t: T).(\lambda (t0: T).((eq T t (TSort n1)) 
+\to (ex nat (\lambda (n2: nat).(eq T t0 (TSort n2))))))) (\lambda (n0: 
+nat).(\lambda (n2: nat).(\lambda (H1: (eq T (TSort n0) (TSort n1))).(let H2 
+\def (f_equal T nat (\lambda (e: T).(match e with [(TSort n) \Rightarrow n | 
+(TLRef _) \Rightarrow n0 | (THead _ _ _) \Rightarrow n0])) (TSort n0) (TSort 
+n1) H1) in (ex_intro nat (\lambda (n3: nat).(eq T (TSort n2) (TSort n3))) n2 
+(refl_equal T (TSort n2))))))) (\lambda (i1: nat).(\lambda (i2: nat).(\lambda 
+(H1: (eq T (TLRef i1) (TSort n1))).(let H2 \def (eq_ind T (TLRef i1) (\lambda 
 (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow 
-True | (THead _ _ _) \Rightarrow False])) in (let TMP_20 \def (TSort n1) in 
-(let H2 \def (eq_ind T TMP_18 TMP_19 I TMP_20 H1) in (let TMP_23 \def 
-(\lambda (n2: nat).(let TMP_21 \def (TLRef i2) in (let TMP_22 \def (TSort n2) 
-in (eq T TMP_21 TMP_22)))) in (let TMP_24 \def (ex nat TMP_23) in (False_ind 
-TMP_24 H2)))))))))) in (let TMP_33 \def (\lambda (v1: T).(\lambda (v2: 
-T).(\lambda (t1: T).(\lambda (t2: T).(\lambda (k: K).(\lambda (H1: (eq T 
-(THead k v1 t1) (TSort n1))).(let TMP_26 \def (THead k v1 t1) in (let TMP_27 
-\def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) 
-\Rightarrow False | (THead _ _ _) \Rightarrow True])) in (let TMP_28 \def 
-(TSort n1) in (let H2 \def (eq_ind T TMP_26 TMP_27 I TMP_28 H1) in (let 
-TMP_31 \def (\lambda (n2: nat).(let TMP_29 \def (THead k v2 t2) in (let 
-TMP_30 \def (TSort n2) in (eq T TMP_29 TMP_30)))) in (let TMP_32 \def (ex nat 
-TMP_31) in (False_ind TMP_32 H2))))))))))))) in (iso_ind TMP_8 TMP_17 TMP_25 
-TMP_33 y u2 H0))))))) in (insert_eq T TMP_1 TMP_2 TMP_5 TMP_34 H))))))).
+True | (THead _ _ _) \Rightarrow False])) I (TSort n1) H1) in (False_ind (ex 
+nat (\lambda (n2: nat).(eq T (TLRef i2) (TSort n2)))) H2))))) (\lambda (v1: 
+T).(\lambda (v2: T).(\lambda (t1: T).(\lambda (t2: T).(\lambda (k: 
+K).(\lambda (H1: (eq T (THead k v1 t1) (TSort n1))).(let H2 \def (eq_ind T 
+(THead k v1 t1) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False 
+| (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TSort 
+n1) H1) in (False_ind (ex nat (\lambda (n2: nat).(eq T (THead k v2 t2) (TSort 
+n2)))) H2)))))))) y u2 H0))) H))).
 
-theorem iso_gen_lref:
+lemma iso_gen_lref:
  \forall (u2: T).(\forall (n1: nat).((iso (TLRef n1) u2) \to (ex nat (\lambda 
 (n2: nat).(eq T u2 (TLRef n2))))))
 \def
- \lambda (u2: T).(\lambda (n1: nat).(\lambda (H: (iso (TLRef n1) u2)).(let 
-TMP_1 \def (TLRef n1) in (let TMP_2 \def (\lambda (t: T).(iso t u2)) in (let 
-TMP_5 \def (\lambda (_: T).(let TMP_4 \def (\lambda (n2: nat).(let TMP_3 \def 
-(TLRef n2) in (eq T u2 TMP_3))) in (ex nat TMP_4))) in (let TMP_34 \def 
-(\lambda (y: T).(\lambda (H0: (iso y u2)).(let TMP_8 \def (\lambda (t: 
-T).(\lambda (t0: T).((eq T t (TLRef n1)) \to (let TMP_7 \def (\lambda (n2: 
-nat).(let TMP_6 \def (TLRef n2) in (eq T t0 TMP_6))) in (ex nat TMP_7))))) in 
-(let TMP_16 \def (\lambda (n0: nat).(\lambda (n2: nat).(\lambda (H1: (eq T 
-(TSort n0) (TLRef n1))).(let TMP_9 \def (TSort n0) in (let TMP_10 \def 
-(\lambda (ee: T).(match ee with [(TSort _) \Rightarrow True | (TLRef _) 
-\Rightarrow False | (THead _ _ _) \Rightarrow False])) in (let TMP_11 \def 
-(TLRef n1) in (let H2 \def (eq_ind T TMP_9 TMP_10 I TMP_11 H1) in (let TMP_14 
-\def (\lambda (n3: nat).(let TMP_12 \def (TSort n2) in (let TMP_13 \def 
-(TLRef n3) in (eq T TMP_12 TMP_13)))) in (let TMP_15 \def (ex nat TMP_14) in 
-(False_ind TMP_15 H2)))))))))) in (let TMP_25 \def (\lambda (i1: 
-nat).(\lambda (i2: nat).(\lambda (H1: (eq T (TLRef i1) (TLRef n1))).(let 
-TMP_17 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow i1 | (TLRef 
-n) \Rightarrow n | (THead _ _ _) \Rightarrow i1])) in (let TMP_18 \def (TLRef 
-i1) in (let TMP_19 \def (TLRef n1) in (let H2 \def (f_equal T nat TMP_17 
-TMP_18 TMP_19 H1) in (let TMP_22 \def (\lambda (n2: nat).(let TMP_20 \def 
-(TLRef i2) in (let TMP_21 \def (TLRef n2) in (eq T TMP_20 TMP_21)))) in (let 
-TMP_23 \def (TLRef i2) in (let TMP_24 \def (refl_equal T TMP_23) in (ex_intro 
-nat TMP_22 i2 TMP_24))))))))))) in (let TMP_33 \def (\lambda (v1: T).(\lambda 
-(v2: T).(\lambda (t1: T).(\lambda (t2: T).(\lambda (k: K).(\lambda (H1: (eq T 
-(THead k v1 t1) (TLRef n1))).(let TMP_26 \def (THead k v1 t1) in (let TMP_27 
-\def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) 
-\Rightarrow False | (THead _ _ _) \Rightarrow True])) in (let TMP_28 \def 
-(TLRef n1) in (let H2 \def (eq_ind T TMP_26 TMP_27 I TMP_28 H1) in (let 
-TMP_31 \def (\lambda (n2: nat).(let TMP_29 \def (THead k v2 t2) in (let 
-TMP_30 \def (TLRef n2) in (eq T TMP_29 TMP_30)))) in (let TMP_32 \def (ex nat 
-TMP_31) in (False_ind TMP_32 H2))))))))))))) in (iso_ind TMP_8 TMP_16 TMP_25 
-TMP_33 y u2 H0))))))) in (insert_eq T TMP_1 TMP_2 TMP_5 TMP_34 H))))))).
+ \lambda (u2: T).(\lambda (n1: nat).(\lambda (H: (iso (TLRef n1) 
+u2)).(insert_eq T (TLRef n1) (\lambda (t: T).(iso t u2)) (\lambda (_: T).(ex 
+nat (\lambda (n2: nat).(eq T u2 (TLRef n2))))) (\lambda (y: T).(\lambda (H0: 
+(iso y u2)).(iso_ind (\lambda (t: T).(\lambda (t0: T).((eq T t (TLRef n1)) 
+\to (ex nat (\lambda (n2: nat).(eq T t0 (TLRef n2))))))) (\lambda (n0: 
+nat).(\lambda (n2: nat).(\lambda (H1: (eq T (TSort n0) (TLRef n1))).(let H2 
+\def (eq_ind T (TSort n0) (\lambda (ee: T).(match ee with [(TSort _) 
+\Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow 
+False])) I (TLRef n1) H1) in (False_ind (ex nat (\lambda (n3: nat).(eq T 
+(TSort n2) (TLRef n3)))) H2))))) (\lambda (i1: nat).(\lambda (i2: 
+nat).(\lambda (H1: (eq T (TLRef i1) (TLRef n1))).(let H2 \def (f_equal T nat 
+(\lambda (e: T).(match e with [(TSort _) \Rightarrow i1 | (TLRef n) 
+\Rightarrow n | (THead _ _ _) \Rightarrow i1])) (TLRef i1) (TLRef n1) H1) in 
+(ex_intro nat (\lambda (n2: nat).(eq T (TLRef i2) (TLRef n2))) i2 (refl_equal 
+T (TLRef i2))))))) (\lambda (v1: T).(\lambda (v2: T).(\lambda (t1: 
+T).(\lambda (t2: T).(\lambda (k: K).(\lambda (H1: (eq T (THead k v1 t1) 
+(TLRef n1))).(let H2 \def (eq_ind T (THead k v1 t1) (\lambda (ee: T).(match 
+ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ 
+_ _) \Rightarrow True])) I (TLRef n1) H1) in (False_ind (ex nat (\lambda (n2: 
+nat).(eq T (THead k v2 t2) (TLRef n2)))) H2)))))))) y u2 H0))) H))).
 
-theorem iso_gen_head:
+lemma iso_gen_head:
  \forall (k: K).(\forall (v1: T).(\forall (t1: T).(\forall (u2: T).((iso 
 (THead k v1 t1) u2) \to (ex_2 T T (\lambda (v2: T).(\lambda (t2: T).(eq T u2 
 (THead k v2 t2)))))))))
 \def
  \lambda (k: K).(\lambda (v1: T).(\lambda (t1: T).(\lambda (u2: T).(\lambda 
-(H: (iso (THead k v1 t1) u2)).(let TMP_1 \def (THead k v1 t1) in (let TMP_2 
-\def (\lambda (t: T).(iso t u2)) in (let TMP_5 \def (\lambda (_: T).(let 
-TMP_4 \def (\lambda (v2: T).(\lambda (t2: T).(let TMP_3 \def (THead k v2 t2) 
-in (eq T u2 TMP_3)))) in (ex_2 T T TMP_4))) in (let TMP_47 \def (\lambda (y: 
-T).(\lambda (H0: (iso y u2)).(let TMP_8 \def (\lambda (t: T).(\lambda (t0: 
-T).((eq T t (THead k v1 t1)) \to (let TMP_7 \def (\lambda (v2: T).(\lambda 
-(t2: T).(let TMP_6 \def (THead k v2 t2) in (eq T t0 TMP_6)))) in (ex_2 T T 
-TMP_7))))) in (let TMP_16 \def (\lambda (n1: nat).(\lambda (n2: nat).(\lambda 
-(H1: (eq T (TSort n1) (THead k v1 t1))).(let TMP_9 \def (TSort n1) in (let 
-TMP_10 \def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow True | 
-(TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow False])) in (let 
-TMP_11 \def (THead k v1 t1) in (let H2 \def (eq_ind T TMP_9 TMP_10 I TMP_11 
-H1) in (let TMP_14 \def (\lambda (v2: T).(\lambda (t2: T).(let TMP_12 \def 
-(TSort n2) in (let TMP_13 \def (THead k v2 t2) in (eq T TMP_12 TMP_13))))) in 
-(let TMP_15 \def (ex_2 T T TMP_14) in (False_ind TMP_15 H2)))))))))) in (let 
-TMP_24 \def (\lambda (i1: nat).(\lambda (i2: nat).(\lambda (H1: (eq T (TLRef 
-i1) (THead k v1 t1))).(let TMP_17 \def (TLRef i1) in (let TMP_18 \def 
-(\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) 
-\Rightarrow True | (THead _ _ _) \Rightarrow False])) in (let TMP_19 \def 
-(THead k v1 t1) in (let H2 \def (eq_ind T TMP_17 TMP_18 I TMP_19 H1) in (let 
-TMP_22 \def (\lambda (v2: T).(\lambda (t2: T).(let TMP_20 \def (TLRef i2) in 
-(let TMP_21 \def (THead k v2 t2) in (eq T TMP_20 TMP_21))))) in (let TMP_23 
-\def (ex_2 T T TMP_22) in (False_ind TMP_23 H2)))))))))) in (let TMP_46 \def 
+(H: (iso (THead k v1 t1) u2)).(insert_eq T (THead k v1 t1) (\lambda (t: 
+T).(iso t u2)) (\lambda (_: T).(ex_2 T T (\lambda (v2: T).(\lambda (t2: 
+T).(eq T u2 (THead k v2 t2)))))) (\lambda (y: T).(\lambda (H0: (iso y 
+u2)).(iso_ind (\lambda (t: T).(\lambda (t0: T).((eq T t (THead k v1 t1)) \to 
+(ex_2 T T (\lambda (v2: T).(\lambda (t2: T).(eq T t0 (THead k v2 t2)))))))) 
+(\lambda (n1: nat).(\lambda (n2: nat).(\lambda (H1: (eq T (TSort n1) (THead k 
+v1 t1))).(let H2 \def (eq_ind T (TSort n1) (\lambda (ee: T).(match ee with 
+[(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) 
+\Rightarrow False])) I (THead k v1 t1) H1) in (False_ind (ex_2 T T (\lambda 
+(v2: T).(\lambda (t2: T).(eq T (TSort n2) (THead k v2 t2))))) H2))))) 
+(\lambda (i1: nat).(\lambda (i2: nat).(\lambda (H1: (eq T (TLRef i1) (THead k 
+v1 t1))).(let H2 \def (eq_ind T (TLRef i1) (\lambda (ee: T).(match ee with 
+[(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) 
+\Rightarrow False])) I (THead k v1 t1) H1) in (False_ind (ex_2 T T (\lambda 
+(v2: T).(\lambda (t2: T).(eq T (TLRef i2) (THead k v2 t2))))) H2))))) 
 (\lambda (v0: T).(\lambda (v2: T).(\lambda (t0: T).(\lambda (t2: T).(\lambda 
-(k0: K).(\lambda (H1: (eq T (THead k0 v0 t0) (THead k v1 t1))).(let TMP_25 
-\def (\lambda (e: T).(match e with [(TSort _) \Rightarrow k0 | (TLRef _) 
-\Rightarrow k0 | (THead k1 _ _) \Rightarrow k1])) in (let TMP_26 \def (THead 
-k0 v0 t0) in (let TMP_27 \def (THead k v1 t1) in (let H2 \def (f_equal T K 
-TMP_25 TMP_26 TMP_27 H1) in (let TMP_28 \def (\lambda (e: T).(match e with 
+(k0: K).(\lambda (H1: (eq T (THead k0 v0 t0) (THead k v1 t1))).(let H2 \def 
+(f_equal T K (\lambda (e: T).(match e with [(TSort _) \Rightarrow k0 | (TLRef 
+_) \Rightarrow k0 | (THead k1 _ _) \Rightarrow k1])) (THead k0 v0 t0) (THead 
+k v1 t1) H1) in ((let H3 \def (f_equal T T (\lambda (e: T).(match e with 
 [(TSort _) \Rightarrow v0 | (TLRef _) \Rightarrow v0 | (THead _ t _) 
-\Rightarrow t])) in (let TMP_29 \def (THead k0 v0 t0) in (let TMP_30 \def 
-(THead k v1 t1) in (let H3 \def (f_equal T T TMP_28 TMP_29 TMP_30 H1) in (let 
-TMP_31 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow t0 | (TLRef 
-_) \Rightarrow t0 | (THead _ _ t) \Rightarrow t])) in (let TMP_32 \def (THead 
-k0 v0 t0) in (let TMP_33 \def (THead k v1 t1) in (let H4 \def (f_equal T T 
-TMP_31 TMP_32 TMP_33 H1) in (let TMP_44 \def (\lambda (_: (eq T v0 
-v1)).(\lambda (H6: (eq K k0 k)).(let TMP_37 \def (\lambda (k1: K).(let TMP_36 
-\def (\lambda (v3: T).(\lambda (t3: T).(let TMP_34 \def (THead k1 v2 t2) in 
-(let TMP_35 \def (THead k v3 t3) in (eq T TMP_34 TMP_35))))) in (ex_2 T T 
-TMP_36))) in (let TMP_40 \def (\lambda (v3: T).(\lambda (t3: T).(let TMP_38 
-\def (THead k v2 t2) in (let TMP_39 \def (THead k v3 t3) in (eq T TMP_38 
-TMP_39))))) in (let TMP_41 \def (THead k v2 t2) in (let TMP_42 \def 
-(refl_equal T TMP_41) in (let TMP_43 \def (ex_2_intro T T TMP_40 v2 t2 
-TMP_42) in (eq_ind_r K k TMP_37 TMP_43 k0 H6)))))))) in (let TMP_45 \def 
-(TMP_44 H3) in (TMP_45 H2))))))))))))))))))))) in (iso_ind TMP_8 TMP_16 
-TMP_24 TMP_46 y u2 H0))))))) in (insert_eq T TMP_1 TMP_2 TMP_5 TMP_47 
-H))))))))).
+\Rightarrow t])) (THead k0 v0 t0) (THead k v1 t1) H1) in ((let H4 \def 
+(f_equal T T (\lambda (e: T).(match e with [(TSort _) \Rightarrow t0 | (TLRef 
+_) \Rightarrow t0 | (THead _ _ t) \Rightarrow t])) (THead k0 v0 t0) (THead k 
+v1 t1) H1) in (\lambda (_: (eq T v0 v1)).(\lambda (H6: (eq K k0 k)).(eq_ind_r 
+K k (\lambda (k1: K).(ex_2 T T (\lambda (v3: T).(\lambda (t3: T).(eq T (THead 
+k1 v2 t2) (THead k v3 t3)))))) (ex_2_intro T T (\lambda (v3: T).(\lambda (t3: 
+T).(eq T (THead k v2 t2) (THead k v3 t3)))) v2 t2 (refl_equal T (THead k v2 
+t2))) k0 H6)))) H3)) H2)))))))) y u2 H0))) H))))).
 
-theorem iso_flats_lref_bind_false:
+lemma iso_flats_lref_bind_false:
  \forall (f: F).(\forall (b: B).(\forall (i: nat).(\forall (v: T).(\forall 
 (t: T).(\forall (vs: TList).((iso (THeads (Flat f) vs (TLRef i)) (THead (Bind 
 b) v t)) \to (\forall (P: Prop).P)))))))
 \def
  \lambda (f: F).(\lambda (b: B).(\lambda (i: nat).(\lambda (v: T).(\lambda 
-(t: T).(\lambda (vs: TList).(let TMP_1 \def (\lambda (t0: TList).((iso 
-(THeads (Flat f) t0 (TLRef i)) (THead (Bind b) v t)) \to (\forall (P: 
-Prop).P))) in (let TMP_13 \def (\lambda (H: (iso (TLRef i) (THead (Bind b) v 
-t))).(\lambda (P: Prop).(let TMP_2 \def (Bind b) in (let TMP_3 \def (THead 
-TMP_2 v t) in (let H_x \def (iso_gen_lref TMP_3 i H) in (let H0 \def H_x in 
-(let TMP_7 \def (\lambda (n2: nat).(let TMP_4 \def (Bind b) in (let TMP_5 
-\def (THead TMP_4 v t) in (let TMP_6 \def (TLRef n2) in (eq T TMP_5 
-TMP_6))))) in (let TMP_12 \def (\lambda (x: nat).(\lambda (H1: (eq T (THead 
-(Bind b) v t) (TLRef x))).(let TMP_8 \def (Bind b) in (let TMP_9 \def (THead 
-TMP_8 v t) in (let TMP_10 \def (\lambda (ee: T).(match ee with [(TSort _) 
-\Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow 
-True])) in (let TMP_11 \def (TLRef x) in (let H2 \def (eq_ind T TMP_9 TMP_10 
-I TMP_11 H1) in (False_ind P H2)))))))) in (ex_ind nat TMP_7 P TMP_12 
-H0))))))))) in (let TMP_31 \def (\lambda (t0: T).(\lambda (t1: 
-TList).(\lambda (_: (((iso (THeads (Flat f) t1 (TLRef i)) (THead (Bind b) v 
-t)) \to (\forall (P: Prop).P)))).(\lambda (H0: (iso (THead (Flat f) t0 
-(THeads (Flat f) t1 (TLRef i))) (THead (Bind b) v t))).(\lambda (P: 
-Prop).(let TMP_14 \def (Flat f) in (let TMP_15 \def (Flat f) in (let TMP_16 
-\def (TLRef i) in (let TMP_17 \def (THeads TMP_15 t1 TMP_16) in (let TMP_18 
-\def (Bind b) in (let TMP_19 \def (THead TMP_18 v t) in (let H_x \def 
-(iso_gen_head TMP_14 t0 TMP_17 TMP_19 H0) in (let H1 \def H_x in (let TMP_24 
-\def (\lambda (v2: T).(\lambda (t2: T).(let TMP_20 \def (Bind b) in (let 
-TMP_21 \def (THead TMP_20 v t) in (let TMP_22 \def (Flat f) in (let TMP_23 
-\def (THead TMP_22 v2 t2) in (eq T TMP_21 TMP_23))))))) in (let TMP_30 \def 
-(\lambda (x0: T).(\lambda (x1: T).(\lambda (H2: (eq T (THead (Bind b) v t) 
-(THead (Flat f) x0 x1))).(let TMP_25 \def (Bind b) in (let TMP_26 \def (THead 
-TMP_25 v t) in (let TMP_27 \def (\lambda (ee: T).(match ee with [(TSort _) 
-\Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow 
-(match k with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) in 
-(let TMP_28 \def (Flat f) in (let TMP_29 \def (THead TMP_28 x0 x1) in (let H3 
-\def (eq_ind T TMP_26 TMP_27 I TMP_29 H2) in (False_ind P H3)))))))))) in 
-(ex_2_ind T T TMP_24 P TMP_30 H1)))))))))))))))) in (TList_ind TMP_1 TMP_13 
-TMP_31 vs))))))))).
+(t: T).(\lambda (vs: TList).(TList_ind (\lambda (t0: TList).((iso (THeads 
+(Flat f) t0 (TLRef i)) (THead (Bind b) v t)) \to (\forall (P: Prop).P))) 
+(\lambda (H: (iso (TLRef i) (THead (Bind b) v t))).(\lambda (P: Prop).(let 
+H_x \def (iso_gen_lref (THead (Bind b) v t) i H) in (let H0 \def H_x in 
+(ex_ind nat (\lambda (n2: nat).(eq T (THead (Bind b) v t) (TLRef n2))) P 
+(\lambda (x: nat).(\lambda (H1: (eq T (THead (Bind b) v t) (TLRef x))).(let 
+H2 \def (eq_ind T (THead (Bind b) v t) (\lambda (ee: T).(match ee with 
+[(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _) 
+\Rightarrow True])) I (TLRef x) H1) in (False_ind P H2)))) H0))))) (\lambda 
+(t0: T).(\lambda (t1: TList).(\lambda (_: (((iso (THeads (Flat f) t1 (TLRef 
+i)) (THead (Bind b) v t)) \to (\forall (P: Prop).P)))).(\lambda (H0: (iso 
+(THead (Flat f) t0 (THeads (Flat f) t1 (TLRef i))) (THead (Bind b) v 
+t))).(\lambda (P: Prop).(let H_x \def (iso_gen_head (Flat f) t0 (THeads (Flat 
+f) t1 (TLRef i)) (THead (Bind b) v t) H0) in (let H1 \def H_x in (ex_2_ind T 
+T (\lambda (v2: T).(\lambda (t2: T).(eq T (THead (Bind b) v t) (THead (Flat 
+f) v2 t2)))) P (\lambda (x0: T).(\lambda (x1: T).(\lambda (H2: (eq T (THead 
+(Bind b) v t) (THead (Flat f) x0 x1))).(let H3 \def (eq_ind T (THead (Bind b) 
+v t) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) 
+\Rightarrow False | (THead k _ _) \Rightarrow (match k with [(Bind _) 
+\Rightarrow True | (Flat _) \Rightarrow False])])) I (THead (Flat f) x0 x1) 
+H2) in (False_ind P H3))))) H1)))))))) vs)))))).
 
-theorem iso_flats_flat_bind_false:
+lemma iso_flats_flat_bind_false:
  \forall (f1: F).(\forall (f2: F).(\forall (b: B).(\forall (v: T).(\forall 
 (v2: T).(\forall (t: T).(\forall (t2: T).(\forall (vs: TList).((iso (THeads 
 (Flat f1) vs (THead (Flat f2) v2 t2)) (THead (Bind b) v t)) \to (\forall (P: 
 Prop).P)))))))))
 \def
  \lambda (f1: F).(\lambda (f2: F).(\lambda (b: B).(\lambda (v: T).(\lambda 
-(v2: T).(\lambda (t: T).(\lambda (t2: T).(\lambda (vs: TList).(let TMP_1 \def 
+(v2: T).(\lambda (t: T).(\lambda (t2: T).(\lambda (vs: TList).(TList_ind 
 (\lambda (t0: TList).((iso (THeads (Flat f1) t0 (THead (Flat f2) v2 t2)) 
-(THead (Bind b) v t)) \to (\forall (P: Prop).P))) in (let TMP_16 \def 
-(\lambda (H: (iso (THead (Flat f2) v2 t2) (THead (Bind b) v t))).(\lambda (P: 
-Prop).(let TMP_2 \def (Flat f2) in (let TMP_3 \def (Bind b) in (let TMP_4 
-\def (THead TMP_3 v t) in (let H_x \def (iso_gen_head TMP_2 v2 t2 TMP_4 H) in 
-(let H0 \def H_x in (let TMP_9 \def (\lambda (v3: T).(\lambda (t3: T).(let 
-TMP_5 \def (Bind b) in (let TMP_6 \def (THead TMP_5 v t) in (let TMP_7 \def 
-(Flat f2) in (let TMP_8 \def (THead TMP_7 v3 t3) in (eq T TMP_6 TMP_8))))))) 
-in (let TMP_15 \def (\lambda (x0: T).(\lambda (x1: T).(\lambda (H1: (eq T 
-(THead (Bind b) v t) (THead (Flat f2) x0 x1))).(let TMP_10 \def (Bind b) in 
-(let TMP_11 \def (THead TMP_10 v t) in (let TMP_12 \def (\lambda (ee: 
-T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False 
-| (THead k _ _) \Rightarrow (match k with [(Bind _) \Rightarrow True | (Flat 
-_) \Rightarrow False])])) in (let TMP_13 \def (Flat f2) in (let TMP_14 \def 
-(THead TMP_13 x0 x1) in (let H2 \def (eq_ind T TMP_11 TMP_12 I TMP_14 H1) in 
-(False_ind P H2)))))))))) in (ex_2_ind T T TMP_9 P TMP_15 H0)))))))))) in 
-(let TMP_35 \def (\lambda (t0: T).(\lambda (t1: TList).(\lambda (_: (((iso 
-(THeads (Flat f1) t1 (THead (Flat f2) v2 t2)) (THead (Bind b) v t)) \to 
-(\forall (P: Prop).P)))).(\lambda (H0: (iso (THead (Flat f1) t0 (THeads (Flat 
-f1) t1 (THead (Flat f2) v2 t2))) (THead (Bind b) v t))).(\lambda (P: 
-Prop).(let TMP_17 \def (Flat f1) in (let TMP_18 \def (Flat f1) in (let TMP_19 
-\def (Flat f2) in (let TMP_20 \def (THead TMP_19 v2 t2) in (let TMP_21 \def 
-(THeads TMP_18 t1 TMP_20) in (let TMP_22 \def (Bind b) in (let TMP_23 \def 
-(THead TMP_22 v t) in (let H_x \def (iso_gen_head TMP_17 t0 TMP_21 TMP_23 H0) 
-in (let H1 \def H_x in (let TMP_28 \def (\lambda (v3: T).(\lambda (t3: 
-T).(let TMP_24 \def (Bind b) in (let TMP_25 \def (THead TMP_24 v t) in (let 
-TMP_26 \def (Flat f1) in (let TMP_27 \def (THead TMP_26 v3 t3) in (eq T 
-TMP_25 TMP_27))))))) in (let TMP_34 \def (\lambda (x0: T).(\lambda (x1: 
-T).(\lambda (H2: (eq T (THead (Bind b) v t) (THead (Flat f1) x0 x1))).(let 
-TMP_29 \def (Bind b) in (let TMP_30 \def (THead TMP_29 v t) in (let TMP_31 
-\def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) 
-\Rightarrow False | (THead k _ _) \Rightarrow (match k with [(Bind _) 
-\Rightarrow True | (Flat _) \Rightarrow False])])) in (let TMP_32 \def (Flat 
-f1) in (let TMP_33 \def (THead TMP_32 x0 x1) in (let H3 \def (eq_ind T TMP_30 
-TMP_31 I TMP_33 H2) in (False_ind P H3)))))))))) in (ex_2_ind T T TMP_28 P 
-TMP_34 H1))))))))))))))))) in (TList_ind TMP_1 TMP_16 TMP_35 vs))))))))))).
+(THead (Bind b) v t)) \to (\forall (P: Prop).P))) (\lambda (H: (iso (THead 
+(Flat f2) v2 t2) (THead (Bind b) v t))).(\lambda (P: Prop).(let H_x \def 
+(iso_gen_head (Flat f2) v2 t2 (THead (Bind b) v t) H) in (let H0 \def H_x in 
+(ex_2_ind T T (\lambda (v3: T).(\lambda (t3: T).(eq T (THead (Bind b) v t) 
+(THead (Flat f2) v3 t3)))) P (\lambda (x0: T).(\lambda (x1: T).(\lambda (H1: 
+(eq T (THead (Bind b) v t) (THead (Flat f2) x0 x1))).(let H2 \def (eq_ind T 
+(THead (Bind b) v t) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow 
+False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow (match k with 
+[(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) I (THead (Flat 
+f2) x0 x1) H1) in (False_ind P H2))))) H0))))) (\lambda (t0: T).(\lambda (t1: 
+TList).(\lambda (_: (((iso (THeads (Flat f1) t1 (THead (Flat f2) v2 t2)) 
+(THead (Bind b) v t)) \to (\forall (P: Prop).P)))).(\lambda (H0: (iso (THead 
+(Flat f1) t0 (THeads (Flat f1) t1 (THead (Flat f2) v2 t2))) (THead (Bind b) v 
+t))).(\lambda (P: Prop).(let H_x \def (iso_gen_head (Flat f1) t0 (THeads 
+(Flat f1) t1 (THead (Flat f2) v2 t2)) (THead (Bind b) v t) H0) in (let H1 
+\def H_x in (ex_2_ind T T (\lambda (v3: T).(\lambda (t3: T).(eq T (THead 
+(Bind b) v t) (THead (Flat f1) v3 t3)))) P (\lambda (x0: T).(\lambda (x1: 
+T).(\lambda (H2: (eq T (THead (Bind b) v t) (THead (Flat f1) x0 x1))).(let H3 
+\def (eq_ind T (THead (Bind b) v t) (\lambda (ee: T).(match ee with [(TSort 
+_) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _) 
+\Rightarrow (match k with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow 
+False])])) I (THead (Flat f1) x0 x1) H2) in (False_ind P H3))))) H1)))))))) 
+vs)))))))).