- matitac: now directories are allowed as command line arguments

           all .ma files inside these directories are compiled
- basic_1: commit os sections tlt iso

diff --git a/matita/matita/contribs/lambdadelta/basic_1/iso/defs.ma b/matita/matita/contribs/lambdadelta/basic_1/iso/defs.ma
index 202b8a30022ab36133a6b4dc9ca696cdb13d7f7c..54a5e01fc20a05e080a0f6c29d55b8310b8e2f93 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/iso/defs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/iso/defs.ma
@@ -14,7 +14,7 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/T/defs.ma".
+include "basic_1/T/defs.ma".
 
 inductive iso: T \to (T \to Prop) \def
 | iso_sort: \forall (n1: nat).(\forall (n2: nat).(iso (TSort n1) (TSort n2)))

diff --git a/matita/matita/contribs/lambdadelta/basic_1/iso/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1/iso/fwd.ma
index 761e982f7c40dd43a1534c3fd26b18113ead60a4..40917f7b90f7f11284419fa42247b9fd0ca4836f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/iso/fwd.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/iso/fwd.ma
@@ -14,67 +14,100 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/iso/defs.ma".
+include "basic_1/iso/defs.ma".
 
-include "Basic-1/tlist/defs.ma".
+include "basic_1/tlist/defs.ma".
+
+theorem 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: 
+T).(\forall (t1: T).(\forall (t2: T).(\forall (k: K).(P (THead k v1 t1) 
+(THead k v2 t2)))))))) \to (\forall (t: T).(\forall (t0: T).((iso t t0) \to 
+(P t t0)))))))
+\def
+ \lambda (P: ((T \to (T \to Prop)))).(\lambda (f: ((\forall (n1: 
+nat).(\forall (n2: nat).(P (TSort n1) (TSort n2)))))).(\lambda (f0: ((\forall 
+(i1: nat).(\forall (i2: nat).(P (TLRef i1) (TLRef i2)))))).(\lambda (f1: 
+((\forall (v1: T).(\forall (v2: T).(\forall (t1: T).(\forall (t2: T).(\forall 
+(k: K).(P (THead k v1 t1) (THead k v2 t2))))))))).(\lambda (t: T).(\lambda 
+(t0: T).(\lambda (i: (iso t t0)).(match i with [(iso_sort x x0) \Rightarrow 
+(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:
  \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)).(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 in T return (\lambda (_: T).nat) 
-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 in T return (\lambda 
-(_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow 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 in T return (\lambda (_: T).Prop) 
-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))).
-(* COMMENTS
-Initial nodes: 321
-END *)
+ \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 
+(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))))))).
 
 theorem 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)).(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 in T return (\lambda (_: 
-T).Prop) 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 in T return (\lambda (_: T).nat) 
-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 in T return (\lambda (_: T).Prop) 
-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))).
-(* COMMENTS
-Initial nodes: 321
-END *)
+ \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))))))).
 
 theorem iso_gen_head:
  \forall (k: K).(\forall (v1: T).(\forall (t1: T).(\forall (u2: T).((iso 
@@ -82,41 +115,53 @@ theorem iso_gen_head:
 (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)).(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 in T 
-return (\lambda (_: T).Prop) 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 in T return (\lambda (_: T).Prop) 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 H2 \def 
-(f_equal T K (\lambda (e: T).(match e in T return (\lambda (_: T).K) 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 in T return (\lambda (_: T).T) with 
+(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 
+(\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 
 [(TSort _) \Rightarrow v0 | (TLRef _) \Rightarrow v0 | (THead _ t _) 
-\Rightarrow t])) (THead k0 v0 t0) (THead k v1 t1) H1) in ((let H4 \def 
-(f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) 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))))).
-(* COMMENTS
-Initial nodes: 545
-END *)
+\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))))))))).
 
 theorem iso_flats_lref_bind_false:
  \forall (f: F).(\forall (b: B).(\forall (i: nat).(\forall (v: T).(\forall 
@@ -124,32 +169,39 @@ theorem iso_flats_lref_bind_false:
 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).(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 in T return 
-(\lambda (_: T).Prop) 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 in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | 
-(TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow (match k in K return 
-(\lambda (_: K).Prop) with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow 
-False])])) I (THead (Flat f) x0 x1) H2) in (False_ind P H3))))) H1)))))))) 
-vs)))))).
-(* COMMENTS
-Initial nodes: 391
-END *)
+(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))))))))).
 
 theorem iso_flats_flat_bind_false:
  \forall (f1: F).(\forall (f2: F).(\forall (b: B).(\forall (v: T).(\forall 
@@ -158,34 +210,41 @@ theorem iso_flats_flat_bind_false:
 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).(TList_ind 
+(v2: T).(\lambda (t: T).(\lambda (t2: T).(\lambda (vs: TList).(let TMP_1 \def 
 (\lambda (t0: TList).((iso (THeads (Flat f1) t0 (THead (Flat f2) v2 t2)) 
-(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 in T return (\lambda (_: 
-T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | 
-(THead k _ _) \Rightarrow (match k in K return (\lambda (_: K).Prop) 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 in T return 
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) 
-\Rightarrow False | (THead k _ _) \Rightarrow (match k in K return (\lambda 
-(_: K).Prop) with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow 
-False])])) I (THead (Flat f1) x0 x1) H2) in (False_ind P H3))))) H1)))))))) 
-vs)))))))).
-(* COMMENTS
-Initial nodes: 461
-END *)
+(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))))))))))).
 

diff --git a/matita/matita/contribs/lambdadelta/basic_1/iso/props.ma b/matita/matita/contribs/lambdadelta/basic_1/iso/props.ma
index af521d0739bc2bd5bd950111e83096404c679f8d..3a1c86826391697d5ce2ab45ab6c48c6051a3300 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/iso/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/iso/props.ma
@@ -14,43 +14,51 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/iso/fwd.ma".
+include "basic_1/T/fwd.ma".
+
+include "basic_1/iso/fwd.ma".
 
 theorem iso_refl:
  \forall (t: T).(iso t t)
 \def
- \lambda (t: T).(T_ind (\lambda (t0: T).(iso t0 t0)) (\lambda (n: 
-nat).(iso_sort n n)) (\lambda (n: nat).(iso_lref n n)) (\lambda (k: 
-K).(\lambda (t0: T).(\lambda (_: (iso t0 t0)).(\lambda (t1: T).(\lambda (_: 
-(iso t1 t1)).(iso_head t0 t0 t1 t1 k)))))) t).
-(* COMMENTS
-Initial nodes: 59
-END *)
+ \lambda (t: T).(let TMP_1 \def (\lambda (t0: T).(iso t0 t0)) in (let TMP_2 
+\def (\lambda (n: nat).(iso_sort n n)) in (let TMP_3 \def (\lambda (n: 
+nat).(iso_lref n n)) in (let TMP_4 \def (\lambda (k: K).(\lambda (t0: 
+T).(\lambda (_: (iso t0 t0)).(\lambda (t1: T).(\lambda (_: (iso t1 
+t1)).(iso_head t0 t0 t1 t1 k)))))) in (T_ind TMP_1 TMP_2 TMP_3 TMP_4 t))))).
 
 theorem iso_trans:
  \forall (t1: T).(\forall (t2: T).((iso t1 t2) \to (\forall (t3: T).((iso t2 
 t3) \to (iso t1 t3)))))
 \def
- \lambda (t1: T).(\lambda (t2: T).(\lambda (H: (iso t1 t2)).(iso_ind (\lambda 
-(t: T).(\lambda (t0: T).(\forall (t3: T).((iso t0 t3) \to (iso t t3))))) 
-(\lambda (n1: nat).(\lambda (n2: nat).(\lambda (t3: T).(\lambda (H0: (iso 
-(TSort n2) t3)).(let H_x \def (iso_gen_sort t3 n2 H0) in (let H1 \def H_x in 
-(ex_ind nat (\lambda (n3: nat).(eq T t3 (TSort n3))) (iso (TSort n1) t3) 
-(\lambda (x: nat).(\lambda (H2: (eq T t3 (TSort x))).(eq_ind_r T (TSort x) 
-(\lambda (t: T).(iso (TSort n1) t)) (iso_sort n1 x) t3 H2))) H1))))))) 
-(\lambda (i1: nat).(\lambda (i2: nat).(\lambda (t3: T).(\lambda (H0: (iso 
-(TLRef i2) t3)).(let H_x \def (iso_gen_lref t3 i2 H0) in (let H1 \def H_x in 
-(ex_ind nat (\lambda (n2: nat).(eq T t3 (TLRef n2))) (iso (TLRef i1) t3) 
-(\lambda (x: nat).(\lambda (H2: (eq T t3 (TLRef x))).(eq_ind_r T (TLRef x) 
-(\lambda (t: T).(iso (TLRef i1) t)) (iso_lref i1 x) t3 H2))) H1))))))) 
-(\lambda (v1: T).(\lambda (v2: T).(\lambda (t3: T).(\lambda (t4: T).(\lambda 
-(k: K).(\lambda (t5: T).(\lambda (H0: (iso (THead k v2 t4) t5)).(let H_x \def 
-(iso_gen_head k v2 t4 t5 H0) in (let H1 \def H_x in (ex_2_ind T T (\lambda 
-(v3: T).(\lambda (t6: T).(eq T t5 (THead k v3 t6)))) (iso (THead k v1 t3) t5) 
-(\lambda (x0: T).(\lambda (x1: T).(\lambda (H2: (eq T t5 (THead k x0 
-x1))).(eq_ind_r T (THead k x0 x1) (\lambda (t: T).(iso (THead k v1 t3) t)) 
-(iso_head v1 x0 t3 x1 k) t5 H2)))) H1)))))))))) t1 t2 H))).
-(* COMMENTS
-Initial nodes: 351
-END *)
+ \lambda (t1: T).(\lambda (t2: T).(\lambda (H: (iso t1 t2)).(let TMP_1 \def 
+(\lambda (t: T).(\lambda (t0: T).(\forall (t3: T).((iso t0 t3) \to (iso t 
+t3))))) in (let TMP_11 \def (\lambda (n1: nat).(\lambda (n2: nat).(\lambda 
+(t3: T).(\lambda (H0: (iso (TSort n2) t3)).(let H_x \def (iso_gen_sort t3 n2 
+H0) in (let H1 \def H_x in (let TMP_3 \def (\lambda (n3: nat).(let TMP_2 \def 
+(TSort n3) in (eq T t3 TMP_2))) in (let TMP_4 \def (TSort n1) in (let TMP_5 
+\def (iso TMP_4 t3) in (let TMP_10 \def (\lambda (x: nat).(\lambda (H2: (eq T 
+t3 (TSort x))).(let TMP_6 \def (TSort x) in (let TMP_8 \def (\lambda (t: 
+T).(let TMP_7 \def (TSort n1) in (iso TMP_7 t))) in (let TMP_9 \def (iso_sort 
+n1 x) in (eq_ind_r T TMP_6 TMP_8 TMP_9 t3 H2)))))) in (ex_ind nat TMP_3 TMP_5 
+TMP_10 H1))))))))))) in (let TMP_21 \def (\lambda (i1: nat).(\lambda (i2: 
+nat).(\lambda (t3: T).(\lambda (H0: (iso (TLRef i2) t3)).(let H_x \def 
+(iso_gen_lref t3 i2 H0) in (let H1 \def H_x in (let TMP_13 \def (\lambda (n2: 
+nat).(let TMP_12 \def (TLRef n2) in (eq T t3 TMP_12))) in (let TMP_14 \def 
+(TLRef i1) in (let TMP_15 \def (iso TMP_14 t3) in (let TMP_20 \def (\lambda 
+(x: nat).(\lambda (H2: (eq T t3 (TLRef x))).(let TMP_16 \def (TLRef x) in 
+(let TMP_18 \def (\lambda (t: T).(let TMP_17 \def (TLRef i1) in (iso TMP_17 
+t))) in (let TMP_19 \def (iso_lref i1 x) in (eq_ind_r T TMP_16 TMP_18 TMP_19 
+t3 H2)))))) in (ex_ind nat TMP_13 TMP_15 TMP_20 H1))))))))))) in (let TMP_31 
+\def (\lambda (v1: T).(\lambda (v2: T).(\lambda (t3: T).(\lambda (t4: 
+T).(\lambda (k: K).(\lambda (t5: T).(\lambda (H0: (iso (THead k v2 t4) 
+t5)).(let H_x \def (iso_gen_head k v2 t4 t5 H0) in (let H1 \def H_x in (let 
+TMP_23 \def (\lambda (v3: T).(\lambda (t6: T).(let TMP_22 \def (THead k v3 
+t6) in (eq T t5 TMP_22)))) in (let TMP_24 \def (THead k v1 t3) in (let TMP_25 
+\def (iso TMP_24 t5) in (let TMP_30 \def (\lambda (x0: T).(\lambda (x1: 
+T).(\lambda (H2: (eq T t5 (THead k x0 x1))).(let TMP_26 \def (THead k x0 x1) 
+in (let TMP_28 \def (\lambda (t: T).(let TMP_27 \def (THead k v1 t3) in (iso 
+TMP_27 t))) in (let TMP_29 \def (iso_head v1 x0 t3 x1 k) in (eq_ind_r T 
+TMP_26 TMP_28 TMP_29 t5 H2))))))) in (ex_2_ind T T TMP_23 TMP_25 TMP_30 
+H1)))))))))))))) in (iso_ind TMP_1 TMP_11 TMP_21 TMP_31 t1 t2 H))))))).
 

diff --git a/matita/matita/contribs/lambdadelta/basic_1/tlt/defs.ma b/matita/matita/contribs/lambdadelta/basic_1/tlt/defs.ma
index 546bdb78d60b98b5b2d33747839bca62e5914738..a75af6bd21fa3e791eb900cfdf4e72b6e955a7b2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/tlt/defs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/tlt/defs.ma
@@ -14,7 +14,7 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/T/defs.ma".
+include "basic_1/T/defs.ma".
 
 definition wadd:
  ((nat \to nat)) \to (nat \to (nat \to nat))
@@ -22,25 +22,35 @@ definition wadd:
  \lambda (f: ((nat \to nat))).(\lambda (w: nat).(\lambda (n: nat).(match n 
 with [O \Rightarrow w | (S m) \Rightarrow (f m)]))).
 
-definition weight_map:
- ((nat \to nat)) \to (T \to nat)
-\def
- let rec weight_map (f: ((nat \to nat))) (t: T) on t: nat \def (match t with 
+let rec weight_map (f: (nat \to nat)) (t: T) on t: nat \def match t with 
 [(TSort _) \Rightarrow O | (TLRef n) \Rightarrow (f n) | (THead k u t0) 
 \Rightarrow (match k with [(Bind b) \Rightarrow (match b with [Abbr 
-\Rightarrow (S (plus (weight_map f u) (weight_map (wadd f (S (weight_map f 
-u))) t0))) | Abst \Rightarrow (S (plus (weight_map f u) (weight_map (wadd f 
-O) t0))) | Void \Rightarrow (S (plus (weight_map f u) (weight_map (wadd f O) 
-t0)))]) | (Flat _) \Rightarrow (S (plus (weight_map f u) (weight_map f 
-t0)))])]) in weight_map.
+\Rightarrow (let TMP_12 \def (weight_map f u) in (let TMP_13 \def (weight_map 
+f u) in (let TMP_14 \def (S TMP_13) in (let TMP_15 \def (wadd f TMP_14) in 
+(let TMP_16 \def (weight_map TMP_15 t0) in (let TMP_17 \def (plus TMP_12 
+TMP_16) in (S TMP_17))))))) | Abst \Rightarrow (let TMP_8 \def (weight_map f 
+u) in (let TMP_9 \def (wadd f O) in (let TMP_10 \def (weight_map TMP_9 t0) in 
+(let TMP_11 \def (plus TMP_8 TMP_10) in (S TMP_11))))) | Void \Rightarrow 
+(let TMP_4 \def (weight_map f u) in (let TMP_5 \def (wadd f O) in (let TMP_6 
+\def (weight_map TMP_5 t0) in (let TMP_7 \def (plus TMP_4 TMP_6) in (S 
+TMP_7)))))]) | (Flat _) \Rightarrow (let TMP_1 \def (weight_map f u) in (let 
+TMP_2 \def (weight_map f t0) in (let TMP_3 \def (plus TMP_1 TMP_2) in (S 
+TMP_3))))])].
 
 definition weight:
  T \to nat
 \def
- weight_map (\lambda (_: nat).O).
+ let TMP_1 \def (\lambda (_: nat).O) in (weight_map TMP_1).
 
 definition tlt:
  T \to (T \to Prop)
 \def
- \lambda (t1: T).(\lambda (t2: T).(lt (weight t1) (weight t2))).
+ \lambda (t1: T).(\lambda (t2: T).(let TMP_1 \def (weight t1) in (let TMP_2 
+\def (weight t2) in (lt TMP_1 TMP_2)))).
+
+definition tle:
+ T \to (T \to Prop)
+\def
+ \lambda (t1: T).(\lambda (t2: T).(let TMP_1 \def (tweight t1) in (let TMP_2 
+\def (tweight t2) in (le TMP_1 TMP_2)))).
 

diff --git a/matita/matita/contribs/lambdadelta/basic_1/tlt/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1/tlt/fwd.ma
new file mode 100644 (file)
index 0000000..f284327
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_1/tlt/fwd.ma
@@ -0,0 +1,51 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+include "basic_1/tlt/defs.ma".
+
+theorem tlt_wf__q_ind:
+ \forall (P: ((T \to Prop))).(((\forall (n: nat).((\lambda (P0: ((T \to 
+Prop))).(\lambda (n0: nat).(\forall (t: T).((eq nat (weight t) n0) \to (P0 
+t))))) P n))) \to (\forall (t: T).(P t)))
+\def
+ let Q \def (\lambda (P: ((T \to Prop))).(\lambda (n: nat).(\forall (t: 
+T).((eq nat (weight t) n) \to (P t))))) in (\lambda (P: ((T \to 
+Prop))).(\lambda (H: ((\forall (n: nat).(\forall (t: T).((eq nat (weight t) 
+n) \to (P t)))))).(\lambda (t: T).(let TMP_1 \def (weight t) in (let TMP_2 
+\def (weight t) in (let TMP_3 \def (refl_equal nat TMP_2) in (H TMP_1 t 
+TMP_3))))))).
+
+theorem tlt_wf_ind:
+ \forall (P: ((T \to Prop))).(((\forall (t: T).(((\forall (v: T).((tlt v t) 
+\to (P v)))) \to (P t)))) \to (\forall (t: T).(P t)))
+\def
+ let Q \def (\lambda (P: ((T \to Prop))).(\lambda (n: nat).(\forall (t: 
+T).((eq nat (weight t) n) \to (P t))))) in (\lambda (P: ((T \to 
+Prop))).(\lambda (H: ((\forall (t: T).(((\forall (v: T).((lt (weight v) 
+(weight t)) \to (P v)))) \to (P t))))).(\lambda (t: T).(let TMP_1 \def 
+(\lambda (t0: T).(P t0)) in (let TMP_11 \def (\lambda (n: nat).(let TMP_2 
+\def (\lambda (t0: T).(P t0)) in (let TMP_3 \def (Q TMP_2) in (let TMP_10 
+\def (\lambda (n0: nat).(\lambda (H0: ((\forall (m: nat).((lt m n0) \to (Q 
+(\lambda (t0: T).(P t0)) m))))).(\lambda (t0: T).(\lambda (H1: (eq nat 
+(weight t0) n0)).(let TMP_4 \def (\lambda (n1: nat).(\forall (m: nat).((lt m 
+n1) \to (\forall (t1: T).((eq nat (weight t1) m) \to (P t1)))))) in (let 
+TMP_5 \def (weight t0) in (let H2 \def (eq_ind_r nat n0 TMP_4 H0 TMP_5 H1) in 
+(let TMP_9 \def (\lambda (v: T).(\lambda (H3: (lt (weight v) (weight 
+t0))).(let TMP_6 \def (weight v) in (let TMP_7 \def (weight v) in (let TMP_8 
+\def (refl_equal nat TMP_7) in (H2 TMP_6 H3 v TMP_8)))))) in (H t0 
+TMP_9))))))))) in (lt_wf_ind n TMP_3 TMP_10))))) in (tlt_wf__q_ind TMP_1 
+TMP_11 t)))))).
+

diff --git a/matita/matita/contribs/lambdadelta/basic_1/tlt/props.ma b/matita/matita/contribs/lambdadelta/basic_1/tlt/props.ma
index 0b4f16d4181fe4d47b744395a33e8e2af01f9eb4..584fa7daf1c6d09a3798200afc5f2dfaf37ad424 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/tlt/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/tlt/props.ma
@@ -14,7 +14,9 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/tlt/defs.ma".
+include "basic_1/T/fwd.ma".
+
+include "basic_1/tlt/defs.ma".
 
 theorem wadd_le:
  \forall (f: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall (n: 
@@ -23,12 +25,10 @@ nat).(le (f n) (g n)))) \to (\forall (v: nat).(\forall (w: nat).((le v w) \to
 \def
  \lambda (f: ((nat \to nat))).(\lambda (g: ((nat \to nat))).(\lambda (H: 
 ((\forall (n: nat).(le (f n) (g n))))).(\lambda (v: nat).(\lambda (w: 
-nat).(\lambda (H0: (le v w)).(\lambda (n: nat).(nat_ind (\lambda (n0: 
-nat).(le (wadd f v n0) (wadd g w n0))) H0 (\lambda (n0: nat).(\lambda (_: (le 
-(wadd f v n0) (wadd g w n0))).(H n0))) n))))))).
-(* COMMENTS
-Initial nodes: 81
-END *)
+nat).(\lambda (H0: (le v w)).(\lambda (n: nat).(let TMP_3 \def (\lambda (n0: 
+nat).(let TMP_1 \def (wadd f v n0) in (let TMP_2 \def (wadd g w n0) in (le 
+TMP_1 TMP_2)))) in (let TMP_4 \def (\lambda (n0: nat).(\lambda (_: (le (wadd 
+f v n0) (wadd g w n0))).(H n0))) in (nat_ind TMP_3 H0 TMP_4 n))))))))).
 
 theorem wadd_lt:
  \forall (f: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall (n: 
@@ -37,105 +37,158 @@ nat).(le (f n) (g n)))) \to (\forall (v: nat).(\forall (w: nat).((lt v w) \to
 \def
  \lambda (f: ((nat \to nat))).(\lambda (g: ((nat \to nat))).(\lambda (H: 
 ((\forall (n: nat).(le (f n) (g n))))).(\lambda (v: nat).(\lambda (w: 
-nat).(\lambda (H0: (lt v w)).(\lambda (n: nat).(nat_ind (\lambda (n0: 
-nat).(le (wadd f v n0) (wadd g w n0))) (le_S_n v w (le_S (S v) w H0)) 
-(\lambda (n0: nat).(\lambda (_: (le (wadd f v n0) (wadd g w n0))).(H n0))) 
-n))))))).
-(* COMMENTS
-Initial nodes: 95
-END *)
+nat).(\lambda (H0: (lt v w)).(\lambda (n: nat).(let TMP_3 \def (\lambda (n0: 
+nat).(let TMP_1 \def (wadd f v n0) in (let TMP_2 \def (wadd g w n0) in (le 
+TMP_1 TMP_2)))) in (let TMP_4 \def (S v) in (let TMP_5 \def (S w) in (let 
+TMP_6 \def (S v) in (let TMP_7 \def (S TMP_6) in (let TMP_8 \def (S w) in 
+(let TMP_9 \def (S v) in (let TMP_10 \def (le_n_S TMP_9 w H0) in (let TMP_11 
+\def (le_S TMP_7 TMP_8 TMP_10) in (let TMP_12 \def (le_S_n TMP_4 TMP_5 
+TMP_11) in (let TMP_13 \def (le_S_n v w TMP_12) in (let TMP_14 \def (\lambda 
+(n0: nat).(\lambda (_: (le (wadd f v n0) (wadd g w n0))).(H n0))) in (nat_ind 
+TMP_3 TMP_13 TMP_14 n))))))))))))))))))).
 
 theorem wadd_O:
  \forall (n: nat).(eq nat (wadd (\lambda (_: nat).O) O n) O)
 \def
- \lambda (n: nat).(nat_ind (\lambda (n0: nat).(eq nat (wadd (\lambda (_: 
-nat).O) O n0) O)) (refl_equal nat O) (\lambda (n0: nat).(\lambda (_: (eq nat 
-(wadd (\lambda (_: nat).O) O n0) O)).(refl_equal nat O))) n).
-(* COMMENTS
-Initial nodes: 53
-END *)
+ \lambda (n: nat).(let TMP_3 \def (\lambda (n0: nat).(let TMP_1 \def (\lambda 
+(_: nat).O) in (let TMP_2 \def (wadd TMP_1 O n0) in (eq nat TMP_2 O)))) in 
+(let TMP_4 \def (refl_equal nat O) in (let TMP_5 \def (\lambda (n0: 
+nat).(\lambda (_: (eq nat (wadd (\lambda (_: nat).O) O n0) O)).(refl_equal 
+nat O))) in (nat_ind TMP_3 TMP_4 TMP_5 n)))).
 
 theorem weight_le:
  \forall (t: T).(\forall (f: ((nat \to nat))).(\forall (g: ((nat \to 
 nat))).(((\forall (n: nat).(le (f n) (g n)))) \to (le (weight_map f t) 
 (weight_map g t)))))
 \def
- \lambda (t: T).(T_ind (\lambda (t0: T).(\forall (f: ((nat \to 
-nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f n) (g n)))) 
-\to (le (weight_map f t0) (weight_map g t0)))))) (\lambda (n: nat).(\lambda 
-(f: ((nat \to nat))).(\lambda (g: ((nat \to nat))).(\lambda (_: ((\forall 
-(n0: nat).(le (f n0) (g n0))))).(le_n (weight_map g (TSort n))))))) (\lambda 
-(n: nat).(\lambda (f: ((nat \to nat))).(\lambda (g: ((nat \to nat))).(\lambda 
-(H: ((\forall (n0: nat).(le (f n0) (g n0))))).(H n))))) (\lambda (k: 
-K).(K_ind (\lambda (k0: K).(\forall (t0: T).(((\forall (f: ((nat \to 
-nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f n) (g n)))) 
-\to (le (weight_map f t0) (weight_map g t0)))))) \to (\forall (t1: 
-T).(((\forall (f: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall 
-(n: nat).(le (f n) (g n)))) \to (le (weight_map f t1) (weight_map g t1)))))) 
-\to (\forall (f: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall 
-(n: nat).(le (f n) (g n)))) \to (le (weight_map f (THead k0 t0 t1)) 
-(weight_map g (THead k0 t0 t1))))))))))) (\lambda (b: B).(B_ind (\lambda (b0: 
-B).(\forall (t0: T).(((\forall (f: ((nat \to nat))).(\forall (g: ((nat \to 
-nat))).(((\forall (n: nat).(le (f n) (g n)))) \to (le (weight_map f t0) 
-(weight_map g t0)))))) \to (\forall (t1: T).(((\forall (f: ((nat \to 
+ \lambda (t: T).(let TMP_3 \def (\lambda (t0: T).(\forall (f: ((nat \to 
 nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f n) (g n)))) 
-\to (le (weight_map f t1) (weight_map g t1)))))) \to (\forall (f: ((nat \to 
-nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f n) (g n)))) 
-\to (le (match b0 with [Abbr \Rightarrow (S (plus (weight_map f t0) 
-(weight_map (wadd f (S (weight_map f t0))) t1))) | Abst \Rightarrow (S (plus 
-(weight_map f t0) (weight_map (wadd f O) t1))) | Void \Rightarrow (S (plus 
-(weight_map f t0) (weight_map (wadd f O) t1)))]) (match b0 with [Abbr 
-\Rightarrow (S (plus (weight_map g t0) (weight_map (wadd g (S (weight_map g 
-t0))) t1))) | Abst \Rightarrow (S (plus (weight_map g t0) (weight_map (wadd g 
-O) t1))) | Void \Rightarrow (S (plus (weight_map g t0) (weight_map (wadd g O) 
-t1)))])))))))))) (\lambda (t0: T).(\lambda (H: ((\forall (f: ((nat \to 
-nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f n) (g n)))) 
-\to (le (weight_map f t0) (weight_map g t0))))))).(\lambda (t1: T).(\lambda 
-(H0: ((\forall (f: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall 
-(n: nat).(le (f n) (g n)))) \to (le (weight_map f t1) (weight_map g 
-t1))))))).(\lambda (f: ((nat \to nat))).(\lambda (g: ((nat \to 
-nat))).(\lambda (H1: ((\forall (n: nat).(le (f n) (g n))))).(le_n_S (plus 
-(weight_map f t0) (weight_map (wadd f (S (weight_map f t0))) t1)) (plus 
-(weight_map g t0) (weight_map (wadd g (S (weight_map g t0))) t1)) 
-(le_plus_plus (weight_map f t0) (weight_map g t0) (weight_map (wadd f (S 
-(weight_map f t0))) t1) (weight_map (wadd g (S (weight_map g t0))) t1) (H f g 
-H1) (H0 (wadd f (S (weight_map f t0))) (wadd g (S (weight_map g t0))) 
-(\lambda (n: nat).(wadd_le f g H1 (S (weight_map f t0)) (S (weight_map g t0)) 
-(le_n_S (weight_map f t0) (weight_map g t0) (H f g H1)) n)))))))))))) 
-(\lambda (t0: T).(\lambda (H: ((\forall (f: ((nat \to nat))).(\forall (g: 
-((nat \to nat))).(((\forall (n: nat).(le (f n) (g n)))) \to (le (weight_map f 
-t0) (weight_map g t0))))))).(\lambda (t1: T).(\lambda (H0: ((\forall (f: 
+\to (let TMP_1 \def (weight_map f t0) in (let TMP_2 \def (weight_map g t0) in 
+(le TMP_1 TMP_2))))))) in (let TMP_6 \def (\lambda (n: nat).(\lambda (f: 
+((nat \to nat))).(\lambda (g: ((nat \to nat))).(\lambda (_: ((\forall (n0: 
+nat).(le (f n0) (g n0))))).(let TMP_4 \def (TSort n) in (let TMP_5 \def 
+(weight_map g TMP_4) in (le_O_n TMP_5))))))) in (let TMP_7 \def (\lambda (n: 
+nat).(\lambda (f: ((nat \to nat))).(\lambda (g: ((nat \to nat))).(\lambda (H: 
+((\forall (n0: nat).(le (f n0) (g n0))))).(H n))))) in (let TMP_144 \def 
+(\lambda (k: K).(let TMP_12 \def (\lambda (k0: K).(\forall (t0: T).(((\forall 
+(f: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f 
+n) (g n)))) \to (le (weight_map f t0) (weight_map g t0)))))) \to (\forall 
+(t1: T).(((\forall (f: ((nat \to nat))).(\forall (g: ((nat \to 
+nat))).(((\forall (n: nat).(le (f n) (g n)))) \to (le (weight_map f t1) 
+(weight_map g t1)))))) \to (\forall (f: ((nat \to nat))).(\forall (g: ((nat 
+\to nat))).(((\forall (n: nat).(le (f n) (g n)))) \to (let TMP_8 \def (THead 
+k0 t0 t1) in (let TMP_9 \def (weight_map f TMP_8) in (let TMP_10 \def (THead 
+k0 t0 t1) in (let TMP_11 \def (weight_map g TMP_10) in (le TMP_9 
+TMP_11))))))))))))) in (let TMP_129 \def (\lambda (b: B).(let TMP_43 \def 
+(\lambda (b0: B).(\forall (t0: T).(((\forall (f: ((nat \to nat))).(\forall 
+(g: ((nat \to nat))).(((\forall (n: nat).(le (f n) (g n)))) \to (le 
+(weight_map f t0) (weight_map g t0)))))) \to (\forall (t1: T).(((\forall (f: 
 ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f n) 
-(g n)))) \to (le (weight_map f t1) (weight_map g t1))))))).(\lambda (f: ((nat 
+(g n)))) \to (le (weight_map f t1) (weight_map g t1)))))) \to (\forall (f: 
+((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f n) 
+(g n)))) \to (let TMP_27 \def (match b0 with [Abbr \Rightarrow (let TMP_21 
+\def (weight_map f t0) in (let TMP_22 \def (weight_map f t0) in (let TMP_23 
+\def (S TMP_22) in (let TMP_24 \def (wadd f TMP_23) in (let TMP_25 \def 
+(weight_map TMP_24 t1) in (let TMP_26 \def (plus TMP_21 TMP_25) in (S 
+TMP_26))))))) | Abst \Rightarrow (let TMP_17 \def (weight_map f t0) in (let 
+TMP_18 \def (wadd f O) in (let TMP_19 \def (weight_map TMP_18 t1) in (let 
+TMP_20 \def (plus TMP_17 TMP_19) in (S TMP_20))))) | Void \Rightarrow (let 
+TMP_13 \def (weight_map f t0) in (let TMP_14 \def (wadd f O) in (let TMP_15 
+\def (weight_map TMP_14 t1) in (let TMP_16 \def (plus TMP_13 TMP_15) in (S 
+TMP_16)))))]) in (let TMP_42 \def (match b0 with [Abbr \Rightarrow (let 
+TMP_36 \def (weight_map g t0) in (let TMP_37 \def (weight_map g t0) in (let 
+TMP_38 \def (S TMP_37) in (let TMP_39 \def (wadd g TMP_38) in (let TMP_40 
+\def (weight_map TMP_39 t1) in (let TMP_41 \def (plus TMP_36 TMP_40) in (S 
+TMP_41))))))) | Abst \Rightarrow (let TMP_32 \def (weight_map g t0) in (let 
+TMP_33 \def (wadd g O) in (let TMP_34 \def (weight_map TMP_33 t1) in (let 
+TMP_35 \def (plus TMP_32 TMP_34) in (S TMP_35))))) | Void \Rightarrow (let 
+TMP_28 \def (weight_map g t0) in (let TMP_29 \def (wadd g O) in (let TMP_30 
+\def (weight_map TMP_29 t1) in (let TMP_31 \def (plus TMP_28 TMP_30) in (S 
+TMP_31)))))]) in (le TMP_27 TMP_42))))))))))) in (let TMP_84 \def (\lambda 
+(t0: T).(\lambda (H: ((\forall (f: ((nat \to nat))).(\forall (g: ((nat \to 
+nat))).(((\forall (n: nat).(le (f n) (g n)))) \to (le (weight_map f t0) 
+(weight_map g t0))))))).(\lambda (t1: T).(\lambda (H0: ((\forall (f: ((nat 
+\to nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f n) (g 
+n)))) \to (le (weight_map f t1) (weight_map g t1))))))).(\lambda (f: ((nat 
 \to nat))).(\lambda (g: ((nat \to nat))).(\lambda (H1: ((\forall (n: nat).(le 
-(f n) (g n))))).(le_n_S (plus (weight_map f t0) (weight_map (wadd f O) t1)) 
-(plus (weight_map g t0) (weight_map (wadd g O) t1)) (le_plus_plus (weight_map 
-f t0) (weight_map g t0) (weight_map (wadd f O) t1) (weight_map (wadd g O) t1) 
-(H f g H1) (H0 (wadd f O) (wadd g O) (\lambda (n: nat).(wadd_le f g H1 O O 
-(le_n O) n)))))))))))) (\lambda (t0: T).(\lambda (H: ((\forall (f: ((nat \to 
-nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f n) (g n)))) 
-\to (le (weight_map f t0) (weight_map g t0))))))).(\lambda (t1: T).(\lambda 
-(H0: ((\forall (f: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall 
-(n: nat).(le (f n) (g n)))) \to (le (weight_map f t1) (weight_map g 
-t1))))))).(\lambda (f: ((nat \to nat))).(\lambda (g: ((nat \to 
-nat))).(\lambda (H1: ((\forall (n: nat).(le (f n) (g n))))).(le_n_S (plus 
-(weight_map f t0) (weight_map (wadd f O) t1)) (plus (weight_map g t0) 
-(weight_map (wadd g O) t1)) (le_plus_plus (weight_map f t0) (weight_map g t0) 
-(weight_map (wadd f O) t1) (weight_map (wadd g O) t1) (H f g H1) (H0 (wadd f 
-O) (wadd g O) (\lambda (n: nat).(wadd_le f g H1 O O (le_n O) n)))))))))))) 
-b)) (\lambda (_: F).(\lambda (t0: T).(\lambda (H: ((\forall (f0: ((nat \to 
-nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f0 n) (g n)))) 
-\to (le (weight_map f0 t0) (weight_map g t0))))))).(\lambda (t1: T).(\lambda 
-(H0: ((\forall (f0: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall 
-(n: nat).(le (f0 n) (g n)))) \to (le (weight_map f0 t1) (weight_map g 
-t1))))))).(\lambda (f0: ((nat \to nat))).(\lambda (g: ((nat \to 
-nat))).(\lambda (H1: ((\forall (n: nat).(le (f0 n) (g n))))).(le_n_S (plus 
-(weight_map f0 t0) (weight_map f0 t1)) (plus (weight_map g t0) (weight_map g 
-t1)) (le_plus_plus (weight_map f0 t0) (weight_map g t0) (weight_map f0 t1) 
-(weight_map g t1) (H f0 g H1) (H0 f0 g H1))))))))))) k)) t).
-(* COMMENTS
-Initial nodes: 1309
-END *)
+(f n) (g n))))).(let TMP_44 \def (weight_map f t0) in (let TMP_45 \def 
+(weight_map f t0) in (let TMP_46 \def (S TMP_45) in (let TMP_47 \def (wadd f 
+TMP_46) in (let TMP_48 \def (weight_map TMP_47 t1) in (let TMP_49 \def (plus 
+TMP_44 TMP_48) in (let TMP_50 \def (weight_map g t0) in (let TMP_51 \def 
+(weight_map g t0) in (let TMP_52 \def (S TMP_51) in (let TMP_53 \def (wadd g 
+TMP_52) in (let TMP_54 \def (weight_map TMP_53 t1) in (let TMP_55 \def (plus 
+TMP_50 TMP_54) in (let TMP_56 \def (weight_map f t0) in (let TMP_57 \def 
+(weight_map g t0) in (let TMP_58 \def (weight_map f t0) in (let TMP_59 \def 
+(S TMP_58) in (let TMP_60 \def (wadd f TMP_59) in (let TMP_61 \def 
+(weight_map TMP_60 t1) in (let TMP_62 \def (weight_map g t0) in (let TMP_63 
+\def (S TMP_62) in (let TMP_64 \def (wadd g TMP_63) in (let TMP_65 \def 
+(weight_map TMP_64 t1) in (let TMP_66 \def (H f g H1) in (let TMP_67 \def 
+(weight_map f t0) in (let TMP_68 \def (S TMP_67) in (let TMP_69 \def (wadd f 
+TMP_68) in (let TMP_70 \def (weight_map g t0) in (let TMP_71 \def (S TMP_70) 
+in (let TMP_72 \def (wadd g TMP_71) in (let TMP_81 \def (\lambda (n: 
+nat).(let TMP_73 \def (weight_map f t0) in (let TMP_74 \def (S TMP_73) in 
+(let TMP_75 \def (weight_map g t0) in (let TMP_76 \def (S TMP_75) in (let 
+TMP_77 \def (weight_map f t0) in (let TMP_78 \def (weight_map g t0) in (let 
+TMP_79 \def (H f g H1) in (let TMP_80 \def (le_n_S TMP_77 TMP_78 TMP_79) in 
+(wadd_le f g H1 TMP_74 TMP_76 TMP_80 n)))))))))) in (let TMP_82 \def (H0 
+TMP_69 TMP_72 TMP_81) in (let TMP_83 \def (le_plus_plus TMP_56 TMP_57 TMP_61 
+TMP_65 TMP_66 TMP_82) in (le_n_S TMP_49 TMP_55 
+TMP_83)))))))))))))))))))))))))))))))))))))))) in (let TMP_106 \def (\lambda 
+(t0: T).(\lambda (H: ((\forall (f: ((nat \to nat))).(\forall (g: ((nat \to 
+nat))).(((\forall (n: nat).(le (f n) (g n)))) \to (le (weight_map f t0) 
+(weight_map g t0))))))).(\lambda (t1: T).(\lambda (H0: ((\forall (f: ((nat 
+\to nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f n) (g 
+n)))) \to (le (weight_map f t1) (weight_map g t1))))))).(\lambda (f: ((nat 
+\to nat))).(\lambda (g: ((nat \to nat))).(\lambda (H1: ((\forall (n: nat).(le 
+(f n) (g n))))).(let TMP_85 \def (weight_map f t0) in (let TMP_86 \def (wadd 
+f O) in (let TMP_87 \def (weight_map TMP_86 t1) in (let TMP_88 \def (plus 
+TMP_85 TMP_87) in (let TMP_89 \def (weight_map g t0) in (let TMP_90 \def 
+(wadd g O) in (let TMP_91 \def (weight_map TMP_90 t1) in (let TMP_92 \def 
+(plus TMP_89 TMP_91) in (let TMP_93 \def (weight_map f t0) in (let TMP_94 
+\def (weight_map g t0) in (let TMP_95 \def (wadd f O) in (let TMP_96 \def 
+(weight_map TMP_95 t1) in (let TMP_97 \def (wadd g O) in (let TMP_98 \def 
+(weight_map TMP_97 t1) in (let TMP_99 \def (H f g H1) in (let TMP_100 \def 
+(wadd f O) in (let TMP_101 \def (wadd g O) in (let TMP_103 \def (\lambda (n: 
+nat).(let TMP_102 \def (le_O_n O) in (wadd_le f g H1 O O TMP_102 n))) in (let 
+TMP_104 \def (H0 TMP_100 TMP_101 TMP_103) in (let TMP_105 \def (le_plus_plus 
+TMP_93 TMP_94 TMP_96 TMP_98 TMP_99 TMP_104) in (le_n_S TMP_88 TMP_92 
+TMP_105)))))))))))))))))))))))))))) in (let TMP_128 \def (\lambda (t0: 
+T).(\lambda (H: ((\forall (f: ((nat \to nat))).(\forall (g: ((nat \to 
+nat))).(((\forall (n: nat).(le (f n) (g n)))) \to (le (weight_map f t0) 
+(weight_map g t0))))))).(\lambda (t1: T).(\lambda (H0: ((\forall (f: ((nat 
+\to nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f n) (g 
+n)))) \to (le (weight_map f t1) (weight_map g t1))))))).(\lambda (f: ((nat 
+\to nat))).(\lambda (g: ((nat \to nat))).(\lambda (H1: ((\forall (n: nat).(le 
+(f n) (g n))))).(let TMP_107 \def (weight_map f t0) in (let TMP_108 \def 
+(wadd f O) in (let TMP_109 \def (weight_map TMP_108 t1) in (let TMP_110 \def 
+(plus TMP_107 TMP_109) in (let TMP_111 \def (weight_map g t0) in (let TMP_112 
+\def (wadd g O) in (let TMP_113 \def (weight_map TMP_112 t1) in (let TMP_114 
+\def (plus TMP_111 TMP_113) in (let TMP_115 \def (weight_map f t0) in (let 
+TMP_116 \def (weight_map g t0) in (let TMP_117 \def (wadd f O) in (let 
+TMP_118 \def (weight_map TMP_117 t1) in (let TMP_119 \def (wadd g O) in (let 
+TMP_120 \def (weight_map TMP_119 t1) in (let TMP_121 \def (H f g H1) in (let 
+TMP_122 \def (wadd f O) in (let TMP_123 \def (wadd g O) in (let TMP_125 \def 
+(\lambda (n: nat).(let TMP_124 \def (le_O_n O) in (wadd_le f g H1 O O TMP_124 
+n))) in (let TMP_126 \def (H0 TMP_122 TMP_123 TMP_125) in (let TMP_127 \def 
+(le_plus_plus TMP_115 TMP_116 TMP_118 TMP_120 TMP_121 TMP_126) in (le_n_S 
+TMP_110 TMP_114 TMP_127)))))))))))))))))))))))))))) in (B_ind TMP_43 TMP_84 
+TMP_106 TMP_128 b)))))) in (let TMP_143 \def (\lambda (_: F).(\lambda (t0: 
+T).(\lambda (H: ((\forall (f0: ((nat \to nat))).(\forall (g: ((nat \to 
+nat))).(((\forall (n: nat).(le (f0 n) (g n)))) \to (le (weight_map f0 t0) 
+(weight_map g t0))))))).(\lambda (t1: T).(\lambda (H0: ((\forall (f0: ((nat 
+\to nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f0 n) (g 
+n)))) \to (le (weight_map f0 t1) (weight_map g t1))))))).(\lambda (f0: ((nat 
+\to nat))).(\lambda (g: ((nat \to nat))).(\lambda (H1: ((\forall (n: nat).(le 
+(f0 n) (g n))))).(let TMP_130 \def (weight_map f0 t0) in (let TMP_131 \def 
+(weight_map f0 t1) in (let TMP_132 \def (plus TMP_130 TMP_131) in (let 
+TMP_133 \def (weight_map g t0) in (let TMP_134 \def (weight_map g t1) in (let 
+TMP_135 \def (plus TMP_133 TMP_134) in (let TMP_136 \def (weight_map f0 t0) 
+in (let TMP_137 \def (weight_map g t0) in (let TMP_138 \def (weight_map f0 
+t1) in (let TMP_139 \def (weight_map g t1) in (let TMP_140 \def (H f0 g H1) 
+in (let TMP_141 \def (H0 f0 g H1) in (let TMP_142 \def (le_plus_plus TMP_136 
+TMP_137 TMP_138 TMP_139 TMP_140 TMP_141) in (le_n_S TMP_132 TMP_135 
+TMP_142)))))))))))))))))))))) in (K_ind TMP_12 TMP_129 TMP_143 k))))) in 
+(T_ind TMP_3 TMP_6 TMP_7 TMP_144 t))))).
 
 theorem weight_eq:
  \forall (t: T).(\forall (f: ((nat \to nat))).(\forall (g: ((nat \to 
@@ -143,158 +196,235 @@ nat))).(((\forall (n: nat).(eq nat (f n) (g n)))) \to (eq nat (weight_map f
 t) (weight_map g t)))))
 \def
  \lambda (t: T).(\lambda (f: ((nat \to nat))).(\lambda (g: ((nat \to 
-nat))).(\lambda (H: ((\forall (n: nat).(eq nat (f n) (g n))))).(le_antisym 
-(weight_map f t) (weight_map g t) (weight_le t f g (\lambda (n: 
-nat).(eq_ind_r nat (g n) (\lambda (n0: nat).(le n0 (g n))) (le_n (g n)) (f n) 
-(H n)))) (weight_le t g f (\lambda (n: nat).(eq_ind_r nat (g n) (\lambda (n0: 
-nat).(le (g n) n0)) (le_n (g n)) (f n) (H n)))))))).
-(* COMMENTS
-Initial nodes: 121
-END *)
+nat))).(\lambda (H: ((\forall (n: nat).(eq nat (f n) (g n))))).(let TMP_1 
+\def (weight_map f t) in (let TMP_2 \def (weight_map g t) in (let TMP_10 \def 
+(\lambda (n: nat).(let TMP_3 \def (g n) in (let TMP_5 \def (\lambda (n0: 
+nat).(let TMP_4 \def (g n) in (le n0 TMP_4))) in (let TMP_6 \def (g n) in 
+(let TMP_7 \def (le_n TMP_6) in (let TMP_8 \def (f n) in (let TMP_9 \def (H 
+n) in (eq_ind_r nat TMP_3 TMP_5 TMP_7 TMP_8 TMP_9)))))))) in (let TMP_11 \def 
+(weight_le t f g TMP_10) in (let TMP_19 \def (\lambda (n: nat).(let TMP_12 
+\def (g n) in (let TMP_14 \def (\lambda (n0: nat).(let TMP_13 \def (g n) in 
+(le TMP_13 n0))) in (let TMP_15 \def (g n) in (let TMP_16 \def (le_n TMP_15) 
+in (let TMP_17 \def (f n) in (let TMP_18 \def (H n) in (eq_ind_r nat TMP_12 
+TMP_14 TMP_16 TMP_17 TMP_18)))))))) in (let TMP_20 \def (weight_le t g f 
+TMP_19) in (le_antisym TMP_1 TMP_2 TMP_11 TMP_20)))))))))).
 
 theorem weight_add_O:
  \forall (t: T).(eq nat (weight_map (wadd (\lambda (_: nat).O) O) t) 
 (weight_map (\lambda (_: nat).O) t))
 \def
- \lambda (t: T).(weight_eq t (wadd (\lambda (_: nat).O) O) (\lambda (_: 
-nat).O) (\lambda (n: nat).(wadd_O n))).
-(* COMMENTS
-Initial nodes: 23
-END *)
+ \lambda (t: T).(let TMP_1 \def (\lambda (_: nat).O) in (let TMP_2 \def (wadd 
+TMP_1 O) in (let TMP_3 \def (\lambda (_: nat).O) in (let TMP_4 \def (\lambda 
+(n: nat).(wadd_O n)) in (weight_eq t TMP_2 TMP_3 TMP_4))))).
 
 theorem weight_add_S:
  \forall (t: T).(\forall (m: nat).(le (weight_map (wadd (\lambda (_: nat).O) 
 O) t) (weight_map (wadd (\lambda (_: nat).O) (S m)) t)))
 \def
- \lambda (t: T).(\lambda (m: nat).(weight_le t (wadd (\lambda (_: nat).O) O) 
-(wadd (\lambda (_: nat).O) (S m)) (\lambda (n: nat).(wadd_le (\lambda (_: 
-nat).O) (\lambda (_: nat).O) (\lambda (_: nat).(le_n O)) O (S m) (le_S O m 
-(le_O_n m)) n)))).
-(* COMMENTS
-Initial nodes: 61
-END *)
+ \lambda (t: T).(\lambda (m: nat).(let TMP_1 \def (\lambda (_: nat).O) in 
+(let TMP_2 \def (wadd TMP_1 O) in (let TMP_3 \def (\lambda (_: nat).O) in 
+(let TMP_4 \def (S m) in (let TMP_5 \def (wadd TMP_3 TMP_4) in (let TMP_12 
+\def (\lambda (n: nat).(let TMP_6 \def (\lambda (_: nat).O) in (let TMP_7 
+\def (\lambda (_: nat).O) in (let TMP_8 \def (\lambda (_: nat).(le_O_n O)) in 
+(let TMP_9 \def (S m) in (let TMP_10 \def (S m) in (let TMP_11 \def (le_O_n 
+TMP_10) in (wadd_le TMP_6 TMP_7 TMP_8 O TMP_9 TMP_11 n)))))))) in (weight_le 
+t TMP_2 TMP_5 TMP_12)))))))).
 
 theorem tlt_trans:
  \forall (v: T).(\forall (u: T).(\forall (t: T).((tlt u v) \to ((tlt v t) \to 
 (tlt u t)))))
 \def
  \lambda (v: T).(\lambda (u: T).(\lambda (t: T).(\lambda (H: (lt (weight u) 
-(weight v))).(\lambda (H0: (lt (weight v) (weight t))).(lt_trans (weight u) 
-(weight v) (weight t) H H0))))).
-(* COMMENTS
-Initial nodes: 43
-END *)
+(weight v))).(\lambda (H0: (lt (weight v) (weight t))).(let TMP_1 \def 
+(weight u) in (let TMP_2 \def (weight v) in (let TMP_3 \def (weight t) in 
+(lt_trans TMP_1 TMP_2 TMP_3 H H0)))))))).
 
 theorem tlt_head_sx:
  \forall (k: K).(\forall (u: T).(\forall (t: T).(tlt u (THead k u t))))
 \def
- \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (u: T).(\forall (t: T).(lt 
-(weight_map (\lambda (_: nat).O) u) (weight_map (\lambda (_: nat).O) (THead 
-k0 u t)))))) (\lambda (b: B).(B_ind (\lambda (b0: B).(\forall (u: T).(\forall 
-(t: T).(lt (weight_map (\lambda (_: nat).O) u) (match b0 with [Abbr 
-\Rightarrow (S (plus (weight_map (\lambda (_: nat).O) u) (weight_map (wadd 
-(\lambda (_: nat).O) (S (weight_map (\lambda (_: nat).O) u))) t))) | Abst 
-\Rightarrow (S (plus (weight_map (\lambda (_: nat).O) u) (weight_map (wadd 
-(\lambda (_: nat).O) O) t))) | Void \Rightarrow (S (plus (weight_map (\lambda 
-(_: nat).O) u) (weight_map (wadd (\lambda (_: nat).O) O) t)))]))))) (\lambda 
-(u: T).(\lambda (t: T).(le_n_S (weight_map (\lambda (_: nat).O) u) (plus 
-(weight_map (\lambda (_: nat).O) u) (weight_map (wadd (\lambda (_: nat).O) (S 
-(weight_map (\lambda (_: nat).O) u))) t)) (le_plus_l (weight_map (\lambda (_: 
-nat).O) u) (weight_map (wadd (\lambda (_: nat).O) (S (weight_map (\lambda (_: 
-nat).O) u))) t))))) (\lambda (u: T).(\lambda (t: T).(le_n_S (weight_map 
-(\lambda (_: nat).O) u) (plus (weight_map (\lambda (_: nat).O) u) (weight_map 
-(wadd (\lambda (_: nat).O) O) t)) (le_plus_l (weight_map (\lambda (_: nat).O) 
-u) (weight_map (wadd (\lambda (_: nat).O) O) t))))) (\lambda (u: T).(\lambda 
-(t: T).(le_n_S (weight_map (\lambda (_: nat).O) u) (plus (weight_map (\lambda 
-(_: nat).O) u) (weight_map (wadd (\lambda (_: nat).O) O) t)) (le_plus_l 
-(weight_map (\lambda (_: nat).O) u) (weight_map (wadd (\lambda (_: nat).O) O) 
-t))))) b)) (\lambda (_: F).(\lambda (u: T).(\lambda (t: T).(le_n_S 
-(weight_map (\lambda (_: nat).O) u) (plus (weight_map (\lambda (_: nat).O) u) 
-(weight_map (\lambda (_: nat).O) t)) (le_plus_l (weight_map (\lambda (_: 
-nat).O) u) (weight_map (\lambda (_: nat).O) t)))))) k).
-(* COMMENTS
-Initial nodes: 379
-END *)
+ \lambda (k: K).(let TMP_6 \def (\lambda (k0: K).(\forall (u: T).(\forall (t: 
+T).(let TMP_1 \def (\lambda (_: nat).O) in (let TMP_2 \def (weight_map TMP_1 
+u) in (let TMP_3 \def (\lambda (_: nat).O) in (let TMP_4 \def (THead k0 u t) 
+in (let TMP_5 \def (weight_map TMP_3 TMP_4) in (lt TMP_2 TMP_5))))))))) in 
+(let TMP_83 \def (\lambda (b: B).(let TMP_31 \def (\lambda (b0: B).(\forall 
+(u: T).(\forall (t: T).(let TMP_7 \def (\lambda (_: nat).O) in (let TMP_8 
+\def (weight_map TMP_7 u) in (let TMP_30 \def (match b0 with [Abbr 
+\Rightarrow (let TMP_21 \def (\lambda (_: nat).O) in (let TMP_22 \def 
+(weight_map TMP_21 u) in (let TMP_23 \def (\lambda (_: nat).O) in (let TMP_24 
+\def (\lambda (_: nat).O) in (let TMP_25 \def (weight_map TMP_24 u) in (let 
+TMP_26 \def (S TMP_25) in (let TMP_27 \def (wadd TMP_23 TMP_26) in (let 
+TMP_28 \def (weight_map TMP_27 t) in (let TMP_29 \def (plus TMP_22 TMP_28) in 
+(S TMP_29)))))))))) | Abst \Rightarrow (let TMP_15 \def (\lambda (_: nat).O) 
+in (let TMP_16 \def (weight_map TMP_15 u) in (let TMP_17 \def (\lambda (_: 
+nat).O) in (let TMP_18 \def (wadd TMP_17 O) in (let TMP_19 \def (weight_map 
+TMP_18 t) in (let TMP_20 \def (plus TMP_16 TMP_19) in (S TMP_20))))))) | Void 
+\Rightarrow (let TMP_9 \def (\lambda (_: nat).O) in (let TMP_10 \def 
+(weight_map TMP_9 u) in (let TMP_11 \def (\lambda (_: nat).O) in (let TMP_12 
+\def (wadd TMP_11 O) in (let TMP_13 \def (weight_map TMP_12 t) in (let TMP_14 
+\def (plus TMP_10 TMP_13) in (S TMP_14)))))))]) in (lt TMP_8 TMP_30))))))) in 
+(let TMP_52 \def (\lambda (u: T).(\lambda (t: T).(let TMP_32 \def (\lambda 
+(_: nat).O) in (let TMP_33 \def (weight_map TMP_32 u) in (let TMP_34 \def 
+(\lambda (_: nat).O) in (let TMP_35 \def (weight_map TMP_34 u) in (let TMP_36 
+\def (\lambda (_: nat).O) in (let TMP_37 \def (\lambda (_: nat).O) in (let 
+TMP_38 \def (weight_map TMP_37 u) in (let TMP_39 \def (S TMP_38) in (let 
+TMP_40 \def (wadd TMP_36 TMP_39) in (let TMP_41 \def (weight_map TMP_40 t) in 
+(let TMP_42 \def (plus TMP_35 TMP_41) in (let TMP_43 \def (\lambda (_: 
+nat).O) in (let TMP_44 \def (weight_map TMP_43 u) in (let TMP_45 \def 
+(\lambda (_: nat).O) in (let TMP_46 \def (\lambda (_: nat).O) in (let TMP_47 
+\def (weight_map TMP_46 u) in (let TMP_48 \def (S TMP_47) in (let TMP_49 \def 
+(wadd TMP_45 TMP_48) in (let TMP_50 \def (weight_map TMP_49 t) in (let TMP_51 
+\def (le_plus_l TMP_44 TMP_50) in (le_n_S TMP_33 TMP_42 
+TMP_51))))))))))))))))))))))) in (let TMP_67 \def (\lambda (u: T).(\lambda 
+(t: T).(let TMP_53 \def (\lambda (_: nat).O) in (let TMP_54 \def (weight_map 
+TMP_53 u) in (let TMP_55 \def (\lambda (_: nat).O) in (let TMP_56 \def 
+(weight_map TMP_55 u) in (let TMP_57 \def (\lambda (_: nat).O) in (let TMP_58 
+\def (wadd TMP_57 O) in (let TMP_59 \def (weight_map TMP_58 t) in (let TMP_60 
+\def (plus TMP_56 TMP_59) in (let TMP_61 \def (\lambda (_: nat).O) in (let 
+TMP_62 \def (weight_map TMP_61 u) in (let TMP_63 \def (\lambda (_: nat).O) in 
+(let TMP_64 \def (wadd TMP_63 O) in (let TMP_65 \def (weight_map TMP_64 t) in 
+(let TMP_66 \def (le_plus_l TMP_62 TMP_65) in (le_n_S TMP_54 TMP_60 
+TMP_66))))))))))))))))) in (let TMP_82 \def (\lambda (u: T).(\lambda (t: 
+T).(let TMP_68 \def (\lambda (_: nat).O) in (let TMP_69 \def (weight_map 
+TMP_68 u) in (let TMP_70 \def (\lambda (_: nat).O) in (let TMP_71 \def 
+(weight_map TMP_70 u) in (let TMP_72 \def (\lambda (_: nat).O) in (let TMP_73 
+\def (wadd TMP_72 O) in (let TMP_74 \def (weight_map TMP_73 t) in (let TMP_75 
+\def (plus TMP_71 TMP_74) in (let TMP_76 \def (\lambda (_: nat).O) in (let 
+TMP_77 \def (weight_map TMP_76 u) in (let TMP_78 \def (\lambda (_: nat).O) in 
+(let TMP_79 \def (wadd TMP_78 O) in (let TMP_80 \def (weight_map TMP_79 t) in 
+(let TMP_81 \def (le_plus_l TMP_77 TMP_80) in (le_n_S TMP_69 TMP_75 
+TMP_81))))))))))))))))) in (B_ind TMP_31 TMP_52 TMP_67 TMP_82 b)))))) in (let 
+TMP_96 \def (\lambda (_: F).(\lambda (u: T).(\lambda (t: T).(let TMP_84 \def 
+(\lambda (_: nat).O) in (let TMP_85 \def (weight_map TMP_84 u) in (let TMP_86 
+\def (\lambda (_: nat).O) in (let TMP_87 \def (weight_map TMP_86 u) in (let 
+TMP_88 \def (\lambda (_: nat).O) in (let TMP_89 \def (weight_map TMP_88 t) in 
+(let TMP_90 \def (plus TMP_87 TMP_89) in (let TMP_91 \def (\lambda (_: 
+nat).O) in (let TMP_92 \def (weight_map TMP_91 u) in (let TMP_93 \def 
+(\lambda (_: nat).O) in (let TMP_94 \def (weight_map TMP_93 t) in (let TMP_95 
+\def (le_plus_l TMP_92 TMP_94) in (le_n_S TMP_85 TMP_90 
+TMP_95)))))))))))))))) in (K_ind TMP_6 TMP_83 TMP_96 k)))).
 
 theorem tlt_head_dx:
  \forall (k: K).(\forall (u: T).(\forall (t: T).(tlt t (THead k u t))))
 \def
- \lambda (k: K).(K_ind (\lambda (k0: K).(\forall (u: T).(\forall (t: T).(lt 
-(weight_map (\lambda (_: nat).O) t) (weight_map (\lambda (_: nat).O) (THead 
-k0 u t)))))) (\lambda (b: B).(B_ind (\lambda (b0: B).(\forall (u: T).(\forall 
-(t: T).(lt (weight_map (\lambda (_: nat).O) t) (match b0 with [Abbr 
-\Rightarrow (S (plus (weight_map (\lambda (_: nat).O) u) (weight_map (wadd 
-(\lambda (_: nat).O) (S (weight_map (\lambda (_: nat).O) u))) t))) | Abst 
-\Rightarrow (S (plus (weight_map (\lambda (_: nat).O) u) (weight_map (wadd 
-(\lambda (_: nat).O) O) t))) | Void \Rightarrow (S (plus (weight_map (\lambda 
-(_: nat).O) u) (weight_map (wadd (\lambda (_: nat).O) O) t)))]))))) (\lambda 
-(u: T).(\lambda (t: T).(lt_le_trans (weight_map (\lambda (_: nat).O) t) (S 
-(weight_map (\lambda (_: nat).O) t)) (S (plus (weight_map (\lambda (_: 
-nat).O) u) (weight_map (wadd (\lambda (_: nat).O) (S (weight_map (\lambda (_: 
-nat).O) u))) t))) (lt_n_Sn (weight_map (\lambda (_: nat).O) t)) (le_n_S 
-(weight_map (\lambda (_: nat).O) t) (plus (weight_map (\lambda (_: nat).O) u) 
-(weight_map (wadd (\lambda (_: nat).O) (S (weight_map (\lambda (_: nat).O) 
-u))) t)) (le_trans (weight_map (\lambda (_: nat).O) t) (weight_map (wadd 
-(\lambda (_: nat).O) (S (weight_map (\lambda (_: nat).O) u))) t) (plus 
-(weight_map (\lambda (_: nat).O) u) (weight_map (wadd (\lambda (_: nat).O) (S 
-(weight_map (\lambda (_: nat).O) u))) t)) (eq_ind nat (weight_map (wadd 
-(\lambda (_: nat).O) O) t) (\lambda (n: nat).(le n (weight_map (wadd (\lambda 
-(_: nat).O) (S (weight_map (\lambda (_: nat).O) u))) t))) (weight_add_S t 
-(weight_map (\lambda (_: nat).O) u)) (weight_map (\lambda (_: nat).O) t) 
-(weight_add_O t)) (le_plus_r (weight_map (\lambda (_: nat).O) u) (weight_map 
-(wadd (\lambda (_: nat).O) (S (weight_map (\lambda (_: nat).O) u))) t))))))) 
-(\lambda (u: T).(\lambda (t: T).(eq_ind_r nat (weight_map (\lambda (_: 
-nat).O) t) (\lambda (n: nat).(lt (weight_map (\lambda (_: nat).O) t) (S (plus 
-(weight_map (\lambda (_: nat).O) u) n)))) (le_n_S (weight_map (\lambda (_: 
-nat).O) t) (plus (weight_map (\lambda (_: nat).O) u) (weight_map (\lambda (_: 
-nat).O) t)) (le_plus_r (weight_map (\lambda (_: nat).O) u) (weight_map 
-(\lambda (_: nat).O) t))) (weight_map (wadd (\lambda (_: nat).O) O) t) 
-(weight_add_O t)))) (\lambda (u: T).(\lambda (t: T).(eq_ind_r nat (weight_map 
-(\lambda (_: nat).O) t) (\lambda (n: nat).(lt (weight_map (\lambda (_: 
-nat).O) t) (S (plus (weight_map (\lambda (_: nat).O) u) n)))) (le_n_S 
-(weight_map (\lambda (_: nat).O) t) (plus (weight_map (\lambda (_: nat).O) u) 
-(weight_map (\lambda (_: nat).O) t)) (le_plus_r (weight_map (\lambda (_: 
-nat).O) u) (weight_map (\lambda (_: nat).O) t))) (weight_map (wadd (\lambda 
-(_: nat).O) O) t) (weight_add_O t)))) b)) (\lambda (_: F).(\lambda (u: 
-T).(\lambda (t: T).(le_n_S (weight_map (\lambda (_: nat).O) t) (plus 
-(weight_map (\lambda (_: nat).O) u) (weight_map (\lambda (_: nat).O) t)) 
-(le_plus_r (weight_map (\lambda (_: nat).O) u) (weight_map (\lambda (_: 
-nat).O) t)))))) k).
-(* COMMENTS
-Initial nodes: 659
-END *)
-
-theorem tlt_wf__q_ind:
- \forall (P: ((T \to Prop))).(((\forall (n: nat).((\lambda (P0: ((T \to 
-Prop))).(\lambda (n0: nat).(\forall (t: T).((eq nat (weight t) n0) \to (P0 
-t))))) P n))) \to (\forall (t: T).(P t)))
-\def
- let Q \def (\lambda (P: ((T \to Prop))).(\lambda (n: nat).(\forall (t: 
-T).((eq nat (weight t) n) \to (P t))))) in (\lambda (P: ((T \to 
-Prop))).(\lambda (H: ((\forall (n: nat).(\forall (t: T).((eq nat (weight t) 
-n) \to (P t)))))).(\lambda (t: T).(H (weight t) t (refl_equal nat (weight 
-t)))))).
-(* COMMENTS
-Initial nodes: 61
-END *)
+ \lambda (k: K).(let TMP_6 \def (\lambda (k0: K).(\forall (u: T).(\forall (t: 
+T).(let TMP_1 \def (\lambda (_: nat).O) in (let TMP_2 \def (weight_map TMP_1 
+t) in (let TMP_3 \def (\lambda (_: nat).O) in (let TMP_4 \def (THead k0 u t) 
+in (let TMP_5 \def (weight_map TMP_3 TMP_4) in (lt TMP_2 TMP_5))))))))) in 
+(let TMP_161 \def (\lambda (b: B).(let TMP_31 \def (\lambda (b0: B).(\forall 
+(u: T).(\forall (t: T).(let TMP_7 \def (\lambda (_: nat).O) in (let TMP_8 
+\def (weight_map TMP_7 t) in (let TMP_30 \def (match b0 with [Abbr 
+\Rightarrow (let TMP_21 \def (\lambda (_: nat).O) in (let TMP_22 \def 
+(weight_map TMP_21 u) in (let TMP_23 \def (\lambda (_: nat).O) in (let TMP_24 
+\def (\lambda (_: nat).O) in (let TMP_25 \def (weight_map TMP_24 u) in (let 
+TMP_26 \def (S TMP_25) in (let TMP_27 \def (wadd TMP_23 TMP_26) in (let 
+TMP_28 \def (weight_map TMP_27 t) in (let TMP_29 \def (plus TMP_22 TMP_28) in 
+(S TMP_29)))))))))) | Abst \Rightarrow (let TMP_15 \def (\lambda (_: nat).O) 
+in (let TMP_16 \def (weight_map TMP_15 u) in (let TMP_17 \def (\lambda (_: 
+nat).O) in (let TMP_18 \def (wadd TMP_17 O) in (let TMP_19 \def (weight_map 
+TMP_18 t) in (let TMP_20 \def (plus TMP_16 TMP_19) in (S TMP_20))))))) | Void 
+\Rightarrow (let TMP_9 \def (\lambda (_: nat).O) in (let TMP_10 \def 
+(weight_map TMP_9 u) in (let TMP_11 \def (\lambda (_: nat).O) in (let TMP_12 
+\def (wadd TMP_11 O) in (let TMP_13 \def (weight_map TMP_12 t) in (let TMP_14 
+\def (plus TMP_10 TMP_13) in (S TMP_14)))))))]) in (lt TMP_8 TMP_30))))))) in 
+(let TMP_106 \def (\lambda (u: T).(\lambda (t: T).(let TMP_32 \def (\lambda 
+(_: nat).O) in (let TMP_33 \def (weight_map TMP_32 t) in (let TMP_34 \def 
+(\lambda (_: nat).O) in (let TMP_35 \def (weight_map TMP_34 t) in (let TMP_36 
+\def (S TMP_35) in (let TMP_37 \def (\lambda (_: nat).O) in (let TMP_38 \def 
+(weight_map TMP_37 u) in (let TMP_39 \def (\lambda (_: nat).O) in (let TMP_40 
+\def (\lambda (_: nat).O) in (let TMP_41 \def (weight_map TMP_40 u) in (let 
+TMP_42 \def (S TMP_41) in (let TMP_43 \def (wadd TMP_39 TMP_42) in (let 
+TMP_44 \def (weight_map TMP_43 t) in (let TMP_45 \def (plus TMP_38 TMP_44) in 
+(let TMP_46 \def (S TMP_45) in (let TMP_47 \def (\lambda (_: nat).O) in (let 
+TMP_48 \def (weight_map TMP_47 t) in (let TMP_49 \def (lt_n_Sn TMP_48) in 
+(let TMP_50 \def (\lambda (_: nat).O) in (let TMP_51 \def (weight_map TMP_50 
+t) in (let TMP_52 \def (\lambda (_: nat).O) in (let TMP_53 \def (weight_map 
+TMP_52 u) in (let TMP_54 \def (\lambda (_: nat).O) in (let TMP_55 \def 
+(\lambda (_: nat).O) in (let TMP_56 \def (weight_map TMP_55 u) in (let TMP_57 
+\def (S TMP_56) in (let TMP_58 \def (wadd TMP_54 TMP_57) in (let TMP_59 \def 
+(weight_map TMP_58 t) in (let TMP_60 \def (plus TMP_53 TMP_59) in (let TMP_61 
+\def (\lambda (_: nat).O) in (let TMP_62 \def (weight_map TMP_61 t) in (let 
+TMP_63 \def (\lambda (_: nat).O) in (let TMP_64 \def (\lambda (_: nat).O) in 
+(let TMP_65 \def (weight_map TMP_64 u) in (let TMP_66 \def (S TMP_65) in (let 
+TMP_67 \def (wadd TMP_63 TMP_66) in (let TMP_68 \def (weight_map TMP_67 t) in 
+(let TMP_69 \def (\lambda (_: nat).O) in (let TMP_70 \def (weight_map TMP_69 
+u) in (let TMP_71 \def (\lambda (_: nat).O) in (let TMP_72 \def (\lambda (_: 
+nat).O) in (let TMP_73 \def (weight_map TMP_72 u) in (let TMP_74 \def (S 
+TMP_73) in (let TMP_75 \def (wadd TMP_71 TMP_74) in (let TMP_76 \def 
+(weight_map TMP_75 t) in (let TMP_77 \def (plus TMP_70 TMP_76) in (let TMP_78 
+\def (\lambda (_: nat).O) in (let TMP_79 \def (wadd TMP_78 O) in (let TMP_80 
+\def (weight_map TMP_79 t) in (let TMP_87 \def (\lambda (n: nat).(let TMP_81 
+\def (\lambda (_: nat).O) in (let TMP_82 \def (\lambda (_: nat).O) in (let 
+TMP_83 \def (weight_map TMP_82 u) in (let TMP_84 \def (S TMP_83) in (let 
+TMP_85 \def (wadd TMP_81 TMP_84) in (let TMP_86 \def (weight_map TMP_85 t) in 
+(le n TMP_86)))))))) in (let TMP_88 \def (\lambda (_: nat).O) in (let TMP_89 
+\def (weight_map TMP_88 u) in (let TMP_90 \def (weight_add_S t TMP_89) in 
+(let TMP_91 \def (\lambda (_: nat).O) in (let TMP_92 \def (weight_map TMP_91 
+t) in (let TMP_93 \def (weight_add_O t) in (let TMP_94 \def (eq_ind nat 
+TMP_80 TMP_87 TMP_90 TMP_92 TMP_93) in (let TMP_95 \def (\lambda (_: nat).O) 
+in (let TMP_96 \def (weight_map TMP_95 u) in (let TMP_97 \def (\lambda (_: 
+nat).O) in (let TMP_98 \def (\lambda (_: nat).O) in (let TMP_99 \def 
+(weight_map TMP_98 u) in (let TMP_100 \def (S TMP_99) in (let TMP_101 \def 
+(wadd TMP_97 TMP_100) in (let TMP_102 \def (weight_map TMP_101 t) in (let 
+TMP_103 \def (le_plus_r TMP_96 TMP_102) in (let TMP_104 \def (le_trans TMP_62 
+TMP_68 TMP_77 TMP_94 TMP_103) in (let TMP_105 \def (le_n_S TMP_51 TMP_60 
+TMP_104) in (lt_le_trans TMP_33 TMP_36 TMP_46 TMP_49 
+TMP_105)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+ in (let TMP_133 \def (\lambda (u: T).(\lambda (t: T).(let TMP_107 \def 
+(\lambda (_: nat).O) in (let TMP_108 \def (weight_map TMP_107 t) in (let 
+TMP_115 \def (\lambda (n: nat).(let TMP_109 \def (\lambda (_: nat).O) in (let 
+TMP_110 \def (weight_map TMP_109 t) in (let TMP_111 \def (\lambda (_: nat).O) 
+in (let TMP_112 \def (weight_map TMP_111 u) in (let TMP_113 \def (plus 
+TMP_112 n) in (let TMP_114 \def (S TMP_113) in (lt TMP_110 TMP_114)))))))) in 
+(let TMP_116 \def (\lambda (_: nat).O) in (let TMP_117 \def (weight_map 
+TMP_116 t) in (let TMP_118 \def (\lambda (_: nat).O) in (let TMP_119 \def 
+(weight_map TMP_118 u) in (let TMP_120 \def (\lambda (_: nat).O) in (let 
+TMP_121 \def (weight_map TMP_120 t) in (let TMP_122 \def (plus TMP_119 
+TMP_121) in (let TMP_123 \def (\lambda (_: nat).O) in (let TMP_124 \def 
+(weight_map TMP_123 u) in (let TMP_125 \def (\lambda (_: nat).O) in (let 
+TMP_126 \def (weight_map TMP_125 t) in (let TMP_127 \def (le_plus_r TMP_124 
+TMP_126) in (let TMP_128 \def (le_n_S TMP_117 TMP_122 TMP_127) in (let 
+TMP_129 \def (\lambda (_: nat).O) in (let TMP_130 \def (wadd TMP_129 O) in 
+(let TMP_131 \def (weight_map TMP_130 t) in (let TMP_132 \def (weight_add_O 
+t) in (eq_ind_r nat TMP_108 TMP_115 TMP_128 TMP_131 
+TMP_132))))))))))))))))))))))) in (let TMP_160 \def (\lambda (u: T).(\lambda 
+(t: T).(let TMP_134 \def (\lambda (_: nat).O) in (let TMP_135 \def 
+(weight_map TMP_134 t) in (let TMP_142 \def (\lambda (n: nat).(let TMP_136 
+\def (\lambda (_: nat).O) in (let TMP_137 \def (weight_map TMP_136 t) in (let 
+TMP_138 \def (\lambda (_: nat).O) in (let TMP_139 \def (weight_map TMP_138 u) 
+in (let TMP_140 \def (plus TMP_139 n) in (let TMP_141 \def (S TMP_140) in (lt 
+TMP_137 TMP_141)))))))) in (let TMP_143 \def (\lambda (_: nat).O) in (let 
+TMP_144 \def (weight_map TMP_143 t) in (let TMP_145 \def (\lambda (_: nat).O) 
+in (let TMP_146 \def (weight_map TMP_145 u) in (let TMP_147 \def (\lambda (_: 
+nat).O) in (let TMP_148 \def (weight_map TMP_147 t) in (let TMP_149 \def 
+(plus TMP_146 TMP_148) in (let TMP_150 \def (\lambda (_: nat).O) in (let 
+TMP_151 \def (weight_map TMP_150 u) in (let TMP_152 \def (\lambda (_: nat).O) 
+in (let TMP_153 \def (weight_map TMP_152 t) in (let TMP_154 \def (le_plus_r 
+TMP_151 TMP_153) in (let TMP_155 \def (le_n_S TMP_144 TMP_149 TMP_154) in 
+(let TMP_156 \def (\lambda (_: nat).O) in (let TMP_157 \def (wadd TMP_156 O) 
+in (let TMP_158 \def (weight_map TMP_157 t) in (let TMP_159 \def 
+(weight_add_O t) in (eq_ind_r nat TMP_135 TMP_142 TMP_155 TMP_158 
+TMP_159))))))))))))))))))))))) in (B_ind TMP_31 TMP_106 TMP_133 TMP_160 
+b)))))) in (let TMP_174 \def (\lambda (_: F).(\lambda (u: T).(\lambda (t: 
+T).(let TMP_162 \def (\lambda (_: nat).O) in (let TMP_163 \def (weight_map 
+TMP_162 t) in (let TMP_164 \def (\lambda (_: nat).O) in (let TMP_165 \def 
+(weight_map TMP_164 u) in (let TMP_166 \def (\lambda (_: nat).O) in (let 
+TMP_167 \def (weight_map TMP_166 t) in (let TMP_168 \def (plus TMP_165 
+TMP_167) in (let TMP_169 \def (\lambda (_: nat).O) in (let TMP_170 \def 
+(weight_map TMP_169 u) in (let TMP_171 \def (\lambda (_: nat).O) in (let 
+TMP_172 \def (weight_map TMP_171 t) in (let TMP_173 \def (le_plus_r TMP_170 
+TMP_172) in (le_n_S TMP_163 TMP_168 TMP_173)))))))))))))))) in (K_ind TMP_6 
+TMP_161 TMP_174 k)))).
 
-theorem tlt_wf_ind:
- \forall (P: ((T \to Prop))).(((\forall (t: T).(((\forall (v: T).((tlt v t) 
-\to (P v)))) \to (P t)))) \to (\forall (t: T).(P t)))
+theorem tle_r:
+ \forall (t: T).(tle t t)
 \def
- let Q \def (\lambda (P: ((T \to Prop))).(\lambda (n: nat).(\forall (t: 
-T).((eq nat (weight t) n) \to (P t))))) in (\lambda (P: ((T \to 
-Prop))).(\lambda (H: ((\forall (t: T).(((\forall (v: T).((lt (weight v) 
-(weight t)) \to (P v)))) \to (P t))))).(\lambda (t: T).(tlt_wf__q_ind 
-(\lambda (t0: T).(P t0)) (\lambda (n: nat).(lt_wf_ind n (Q (\lambda (t0: 
-T).(P t0))) (\lambda (n0: nat).(\lambda (H0: ((\forall (m: nat).((lt m n0) 
-\to (Q (\lambda (t0: T).(P t0)) m))))).(\lambda (t0: T).(\lambda (H1: (eq nat 
-(weight t0) n0)).(let H2 \def (eq_ind_r nat n0 (\lambda (n1: nat).(\forall 
-(m: nat).((lt m n1) \to (\forall (t1: T).((eq nat (weight t1) m) \to (P 
-t1)))))) H0 (weight t0) H1) in (H t0 (\lambda (v: T).(\lambda (H3: (lt 
-(weight v) (weight t0))).(H2 (weight v) H3 v (refl_equal nat (weight 
-v))))))))))))) t)))).
-(* COMMENTS
-Initial nodes: 179
-END *)
+ \lambda (t: T).(let TMP_3 \def (\lambda (t0: T).(let TMP_1 \def (tweight t0) 
+in (let TMP_2 \def (tweight t0) in (le TMP_1 TMP_2)))) in (let TMP_5 \def 
+(\lambda (_: nat).(let TMP_4 \def (S O) in (le_n TMP_4))) in (let TMP_7 \def 
+(\lambda (_: nat).(let TMP_6 \def (S O) in (le_n TMP_6))) in (let TMP_12 \def 
+(\lambda (_: K).(\lambda (t0: T).(\lambda (_: (le (tweight t0) (tweight 
+t0))).(\lambda (t1: T).(\lambda (_: (le (tweight t1) (tweight t1))).(let 
+TMP_8 \def (tweight t0) in (let TMP_9 \def (tweight t1) in (let TMP_10 \def 
+(plus TMP_8 TMP_9) in (let TMP_11 \def (S TMP_10) in (le_n TMP_11)))))))))) 
+in (T_ind TMP_3 TMP_5 TMP_7 TMP_12 t))))).
 

diff --git a/matita/matita/matitac.ml b/matita/matita/matitac.ml
index a93d694dcc240a2e17646cc14c3194c0e58c5344..d0f5603e58a347655379f812d378fa34fb9483ee 100644 (file)
--- a/matita/matita/matitac.ml
+++ b/matita/matita/matitac.ml
@@ -44,7 +44,14 @@ let main_compiler () =
          prerr_endline ("Too many roots found:\n\t" ^ String.concat "\n\t" roots);
          prerr_endline ("\nEnter one of these directories and retry");
          exit 1);
-    | _ -> targets
+    | _ ->
+      let map targets file =
+          if HExtlib.is_dir file then
+             let files = HExtlib.find ~test:(fun path -> Filename.check_suffix path ".ma") file in
+             files @ targets
+          else file :: targets
+      in
+      List.fold_left map [] (List.rev targets)
   in
   (* must be called after init since args are set by cmdline parsing *)
   let system_mode =  Helm_registry.get_bool "matita.system" in