update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / T / fwd.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/T/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1/T/fwd.ma
index 32ca6cbc8315d1bd6a5e2a51c7f10aac8f139c9b..5e1833cc17b0d50efe1271d388552cd15f3d86aa 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/T/fwd.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/T/fwd.ma
@@ -16,15 +16,14 @@
 
 include "basic_1/T/defs.ma".
 
-let rec T_rect (P: (T \to Type[0])) (f: (\forall (n: nat).(P (TSort n)))) 
-(f0: (\forall (n: nat).(P (TLRef n)))) (f1: (\forall (k: K).(\forall (t: 
-T).((P t) \to (\forall (t0: T).((P t0) \to (P (THead k t t0)))))))) (t: T) on 
-t: P t \def match t in T with [(TSort n) \Rightarrow (f n) | (TLRef n) 
-\Rightarrow (f0 n) | (THead k t0 t1) \Rightarrow (let TMP_2 \def ((T_rect P f 
-f0 f1) t0) in (let TMP_1 \def ((T_rect P f f0 f1) t1) in (f1 k t0 TMP_2 t1 
-TMP_1)))].
+implied rec lemma T_rect (P: (T \to Type[0])) (f: (\forall (n: nat).(P (TSort 
+n)))) (f0: (\forall (n: nat).(P (TLRef n)))) (f1: (\forall (k: K).(\forall 
+(t: T).((P t) \to (\forall (t0: T).((P t0) \to (P (THead k t t0)))))))) (t: 
+T) on t: P t \def match t with [(TSort n) \Rightarrow (f n) | (TLRef n) 
+\Rightarrow (f0 n) | (THead k t0 t1) \Rightarrow (f1 k t0 ((T_rect P f f0 f1) 
+t0) t1 ((T_rect P f f0 f1) t1))].
 
-theorem T_ind:
+implied lemma T_ind:
  \forall (P: ((T \to Prop))).(((\forall (n: nat).(P (TSort n)))) \to 
 (((\forall (n: nat).(P (TLRef n)))) \to (((\forall (k: K).(\forall (t: T).((P 
 t) \to (\forall (t0: T).((P t0) \to (P (THead k t t0)))))))) \to (\forall (t: 
@@ -32,46 +31,34 @@ T).(P t)))))
 \def
  \lambda (P: ((T \to Prop))).(T_rect P).
 
-theorem thead_x_y_y:
+lemma thead_x_y_y:
  \forall (k: K).(\forall (v: T).(\forall (t: T).((eq T (THead k v t) t) \to 
 (\forall (P: Prop).P))))
 \def
- \lambda (k: K).(\lambda (v: T).(\lambda (t: T).(let TMP_676 \def (\lambda 
-(t0: T).((eq T (THead k v t0) t0) \to (\forall (P: Prop).P))) in (let TMP_675 
-\def (\lambda (n: nat).(\lambda (H: (eq T (THead k v (TSort n)) (TSort 
-n))).(\lambda (P: Prop).(let TMP_673 \def (TSort n) in (let TMP_674 \def 
-(THead k v TMP_673) in (let TMP_672 \def (\lambda (ee: T).(match ee in T with 
-[(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _) 
-\Rightarrow True])) in (let TMP_671 \def (TSort n) in (let H0 \def (eq_ind T 
-TMP_674 TMP_672 I TMP_671 H) in (False_ind P H0))))))))) in (let TMP_670 \def 
-(\lambda (n: nat).(\lambda (H: (eq T (THead k v (TLRef n)) (TLRef 
-n))).(\lambda (P: Prop).(let TMP_668 \def (TLRef n) in (let TMP_669 \def 
-(THead k v TMP_668) in (let TMP_667 \def (\lambda (ee: T).(match ee in T with 
-[(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _) 
-\Rightarrow True])) in (let TMP_666 \def (TLRef n) in (let H0 \def (eq_ind T 
-TMP_669 TMP_667 I TMP_666 H) in (False_ind P H0))))))))) in (let TMP_665 \def 
-(\lambda (k0: K).(\lambda (t0: T).(\lambda (_: (((eq T (THead k v t0) t0) \to 
-(\forall (P: Prop).P)))).(\lambda (t1: T).(\lambda (H0: (((eq T (THead k v 
-t1) t1) \to (\forall (P: Prop).P)))).(\lambda (H1: (eq T (THead k v (THead k0 
-t0 t1)) (THead k0 t0 t1))).(\lambda (P: Prop).(let TMP_652 \def (\lambda (e: 
-T).(match e in T with [(TSort _) \Rightarrow k | (TLRef _) \Rightarrow k | 
-(THead k1 _ _) \Rightarrow k1])) in (let TMP_650 \def (THead k0 t0 t1) in 
-(let TMP_651 \def (THead k v TMP_650) in (let TMP_649 \def (THead k0 t0 t1) 
-in (let H2 \def (f_equal T K TMP_652 TMP_651 TMP_649 H1) in (let TMP_656 \def 
-(\lambda (e: T).(match e in T with [(TSort _) \Rightarrow v | (TLRef _) 
-\Rightarrow v | (THead _ t2 _) \Rightarrow t2])) in (let TMP_654 \def (THead 
-k0 t0 t1) in (let TMP_655 \def (THead k v TMP_654) in (let TMP_653 \def 
-(THead k0 t0 t1) in (let H3 \def (f_equal T T TMP_656 TMP_655 TMP_653 H1) in 
-(let TMP_660 \def (\lambda (e: T).(match e in T with [(TSort _) \Rightarrow 
-(THead k0 t0 t1) | (TLRef _) \Rightarrow (THead k0 t0 t1) | (THead _ _ t2) 
-\Rightarrow t2])) in (let TMP_658 \def (THead k0 t0 t1) in (let TMP_659 \def 
-(THead k v TMP_658) in (let TMP_657 \def (THead k0 t0 t1) in (let H4 \def 
-(f_equal T T TMP_660 TMP_659 TMP_657 H1) in (let TMP_663 \def (\lambda (H5: 
-(eq T v t0)).(\lambda (H6: (eq K k k0)).(let TMP_661 \def (\lambda (t2: 
-T).((eq T (THead k t2 t1) t1) \to (\forall (P0: Prop).P0))) in (let H7 \def 
-(eq_ind T v TMP_661 H0 t0 H5) in (let TMP_662 \def (\lambda (k1: K).((eq T 
-(THead k1 t0 t1) t1) \to (\forall (P0: Prop).P0))) in (let H8 \def (eq_ind K 
-k TMP_662 H7 k0 H6) in (H8 H4 P))))))) in (let TMP_664 \def (TMP_663 H3) in 
-(TMP_664 H2))))))))))))))))))))))))) in (T_ind TMP_676 TMP_675 TMP_670 
-TMP_665 t))))))).
+ \lambda (k: K).(\lambda (v: T).(\lambda (t: T).(T_ind (\lambda (t0: T).((eq 
+T (THead k v t0) t0) \to (\forall (P: Prop).P))) (\lambda (n: nat).(\lambda 
+(H: (eq T (THead k v (TSort n)) (TSort n))).(\lambda (P: Prop).(let H0 \def 
+(eq_ind T (THead k v (TSort n)) (\lambda (ee: T).(match ee with [(TSort _) 
+\Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow 
+True])) I (TSort n) H) in (False_ind P H0))))) (\lambda (n: nat).(\lambda (H: 
+(eq T (THead k v (TLRef n)) (TLRef n))).(\lambda (P: Prop).(let H0 \def 
+(eq_ind T (THead k v (TLRef n)) (\lambda (ee: T).(match ee with [(TSort _) 
+\Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow 
+True])) I (TLRef n) H) in (False_ind P H0))))) (\lambda (k0: K).(\lambda (t0: 
+T).(\lambda (_: (((eq T (THead k v t0) t0) \to (\forall (P: 
+Prop).P)))).(\lambda (t1: T).(\lambda (H0: (((eq T (THead k v t1) t1) \to 
+(\forall (P: Prop).P)))).(\lambda (H1: (eq T (THead k v (THead k0 t0 t1)) 
+(THead k0 t0 t1))).(\lambda (P: Prop).(let H2 \def (f_equal T K (\lambda (e: 
+T).(match e with [(TSort _) \Rightarrow k | (TLRef _) \Rightarrow k | (THead 
+k1 _ _) \Rightarrow k1])) (THead k v (THead k0 t0 t1)) (THead k0 t0 t1) H1) 
+in ((let H3 \def (f_equal T T (\lambda (e: T).(match e with [(TSort _) 
+\Rightarrow v | (TLRef _) \Rightarrow v | (THead _ t2 _) \Rightarrow t2])) 
+(THead k v (THead k0 t0 t1)) (THead k0 t0 t1) H1) in ((let H4 \def (f_equal T 
+T (\lambda (e: T).(match e with [(TSort _) \Rightarrow (THead k0 t0 t1) | 
+(TLRef _) \Rightarrow (THead k0 t0 t1) | (THead _ _ t2) \Rightarrow t2])) 
+(THead k v (THead k0 t0 t1)) (THead k0 t0 t1) H1) in (\lambda (H5: (eq T v 
+t0)).(\lambda (H6: (eq K k k0)).(let H7 \def (eq_ind T v (\lambda (t2: 
+T).((eq T (THead k t2 t1) t1) \to (\forall (P0: Prop).P0))) H0 t0 H5) in (let 
+H8 \def (eq_ind K k (\lambda (k1: K).((eq T (THead k1 t0 t1) t1) \to (\forall 
+(P0: Prop).P0))) H7 k0 H6) in (H8 H4 P)))))) H3)) H2))))))))) t))).