update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / iso / props.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/iso/props.ma b/matita/matita/contribs/lambdadelta/basic_1/iso/props.ma
index 3a1c86826391697d5ce2ab45ab6c48c6051a3300..baef0f83321523681438f4b088596fbead267dfe 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/iso/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/iso/props.ma
@@ -18,47 +18,35 @@ include "basic_1/T/fwd.ma".
 
 include "basic_1/iso/fwd.ma".
 
-theorem iso_refl:
+lemma iso_refl:
  \forall (t: T).(iso t t)
 \def
- \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))))).
+ \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).
 
 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)).(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))))))).
+ \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))).