update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / ty3 / sty0.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/ty3/sty0.ma b/matita/matita/contribs/lambdadelta/basic_1/ty3/sty0.ma
index 3c630662cc1efb4f7128e8871104feece3031956..e590a65e06294230bce7d0579be90885f0b543a3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/ty3/sty0.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/ty3/sty0.ma
@@ -14,11 +14,11 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/ty3/pr3_props.ma".
+include "basic_1/ty3/pr3_props.ma".
 
-include "Basic-1/sty0/fwd.ma".
+include "basic_1/sty0/fwd.ma".
 
-theorem ty3_sty0:
+lemma ty3_sty0:
  \forall (g: G).(\forall (c: C).(\forall (u: T).(\forall (t1: T).((ty3 g c u 
 t1) \to (\forall (t2: T).((sty0 g c u t2) \to (ty3 g c u t2)))))))
 \def
@@ -61,23 +61,22 @@ T).(\lambda (t0: T).(eq T t2 (lift (S n) O t0))))) (ty3 g c0 (TLRef n) t2)
 g c0 (TLRef n) t0)) (let H10 \def (eq_ind C (CHead d (Bind Abbr) u0) (\lambda 
 (c1: C).(getl n c0 c1)) H0 (CHead x0 (Bind Abbr) x1) (getl_mono c0 (CHead d 
 (Bind Abbr) u0) n H0 (CHead x0 (Bind Abbr) x1) H6)) in (let H11 \def (f_equal 
-C C (\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _) 
-\Rightarrow d | (CHead c1 _ _) \Rightarrow c1])) (CHead d (Bind Abbr) u0) 
-(CHead x0 (Bind Abbr) x1) (getl_mono c0 (CHead d (Bind Abbr) u0) n H0 (CHead 
-x0 (Bind Abbr) x1) H6)) in ((let H12 \def (f_equal C T (\lambda (e: C).(match 
-e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u0 | (CHead _ _ 
-t0) \Rightarrow t0])) (CHead d (Bind Abbr) u0) (CHead x0 (Bind Abbr) x1) 
+C C (\lambda (e: C).(match e with [(CSort _) \Rightarrow d | (CHead c1 _ _) 
+\Rightarrow c1])) (CHead d (Bind Abbr) u0) (CHead x0 (Bind Abbr) x1) 
 (getl_mono c0 (CHead d (Bind Abbr) u0) n H0 (CHead x0 (Bind Abbr) x1) H6)) in 
-(\lambda (H13: (eq C d x0)).(let H14 \def (eq_ind_r T x1 (\lambda (t0: 
-T).(getl n c0 (CHead x0 (Bind Abbr) t0))) H10 u0 H12) in (let H15 \def 
-(eq_ind_r T x1 (\lambda (t0: T).(sty0 g x0 t0 x2)) H7 u0 H12) in (let H16 
-\def (eq_ind_r C x0 (\lambda (c1: C).(getl n c0 (CHead c1 (Bind Abbr) u0))) 
-H14 d H13) in (let H17 \def (eq_ind_r C x0 (\lambda (c1: C).(sty0 g c1 u0 
-x2)) H15 d H13) in (ty3_abbr g n c0 d u0 H16 x2 (H2 x2 H17)))))))) H11))) t2 
-H9)))))))) H5)) (\lambda (H5: (ex3_3 C T T (\lambda (e: C).(\lambda (u1: 
-T).(\lambda (_: T).(getl n c0 (CHead e (Bind Abst) u1))))) (\lambda (e: 
-C).(\lambda (u1: T).(\lambda (t0: T).(sty0 g e u1 t0)))) (\lambda (_: 
-C).(\lambda (u1: T).(\lambda (_: T).(eq T t2 (lift (S n) O 
+((let H12 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _) 
+\Rightarrow u0 | (CHead _ _ t0) \Rightarrow t0])) (CHead d (Bind Abbr) u0) 
+(CHead x0 (Bind Abbr) x1) (getl_mono c0 (CHead d (Bind Abbr) u0) n H0 (CHead 
+x0 (Bind Abbr) x1) H6)) in (\lambda (H13: (eq C d x0)).(let H14 \def 
+(eq_ind_r T x1 (\lambda (t0: T).(getl n c0 (CHead x0 (Bind Abbr) t0))) H10 u0 
+H12) in (let H15 \def (eq_ind_r T x1 (\lambda (t0: T).(sty0 g x0 t0 x2)) H7 
+u0 H12) in (let H16 \def (eq_ind_r C x0 (\lambda (c1: C).(getl n c0 (CHead c1 
+(Bind Abbr) u0))) H14 d H13) in (let H17 \def (eq_ind_r C x0 (\lambda (c1: 
+C).(sty0 g c1 u0 x2)) H15 d H13) in (ty3_abbr g n c0 d u0 H16 x2 (H2 x2 
+H17)))))))) H11))) t2 H9)))))))) H5)) (\lambda (H5: (ex3_3 C T T (\lambda (e: 
+C).(\lambda (u1: T).(\lambda (_: T).(getl n c0 (CHead e (Bind Abst) u1))))) 
+(\lambda (e: C).(\lambda (u1: T).(\lambda (t0: T).(sty0 g e u1 t0)))) 
+(\lambda (_: C).(\lambda (u1: T).(\lambda (_: T).(eq T t2 (lift (S n) O 
 u1))))))).(ex3_3_ind C T T (\lambda (e: C).(\lambda (u1: T).(\lambda (_: 
 T).(getl n c0 (CHead e (Bind Abst) u1))))) (\lambda (e: C).(\lambda (u1: 
 T).(\lambda (t0: T).(sty0 g e u1 t0)))) (\lambda (_: C).(\lambda (u1: 
@@ -89,67 +88,64 @@ T t2 (lift (S n) O x1))).(let H9 \def (f_equal T T (\lambda (e: T).e) t2
 g c0 (TLRef n) t0)) (let H10 \def (eq_ind C (CHead d (Bind Abbr) u0) (\lambda 
 (c1: C).(getl n c0 c1)) H0 (CHead x0 (Bind Abst) x1) (getl_mono c0 (CHead d 
 (Bind Abbr) u0) n H0 (CHead x0 (Bind Abst) x1) H6)) in (let H11 \def (eq_ind 
-C (CHead d (Bind Abbr) u0) (\lambda (ee: C).(match ee in C return (\lambda 
-(_: C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow 
-(match k in K return (\lambda (_: K).Prop) with [(Bind b) \Rightarrow (match 
-b in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow True | Abst 
-\Rightarrow False | Void \Rightarrow False]) | (Flat _) \Rightarrow 
-False])])) I (CHead x0 (Bind Abst) x1) (getl_mono c0 (CHead d (Bind Abbr) u0) 
-n H0 (CHead x0 (Bind Abst) x1) H6)) in (False_ind (ty3 g c0 (TLRef n) (lift 
-(S n) O x1)) H11))) t2 H9)))))))) H5)) H4))))))))))))) (\lambda (n: 
-nat).(\lambda (c0: C).(\lambda (d: C).(\lambda (u0: T).(\lambda (H0: (getl n 
-c0 (CHead d (Bind Abst) u0))).(\lambda (t: T).(\lambda (H1: (ty3 g d u0 
-t)).(\lambda (_: ((\forall (t2: T).((sty0 g d u0 t2) \to (ty3 g d u0 
-t2))))).(\lambda (t2: T).(\lambda (H3: (sty0 g c0 (TLRef n) t2)).(let H_x 
-\def (sty0_gen_lref g c0 t2 n H3) in (let H4 \def H_x in (or_ind (ex3_3 C T T 
-(\lambda (e: C).(\lambda (u1: T).(\lambda (_: T).(getl n c0 (CHead e (Bind 
-Abbr) u1))))) (\lambda (e: C).(\lambda (u1: T).(\lambda (t0: T).(sty0 g e u1 
-t0)))) (\lambda (_: C).(\lambda (_: T).(\lambda (t0: T).(eq T t2 (lift (S n) 
-O t0)))))) (ex3_3 C T T (\lambda (e: C).(\lambda (u1: T).(\lambda (_: 
-T).(getl n c0 (CHead e (Bind Abst) u1))))) (\lambda (e: C).(\lambda (u1: 
-T).(\lambda (t0: T).(sty0 g e u1 t0)))) (\lambda (_: C).(\lambda (u1: 
-T).(\lambda (_: T).(eq T t2 (lift (S n) O u1)))))) (ty3 g c0 (TLRef n) t2) 
-(\lambda (H5: (ex3_3 C T T (\lambda (e: C).(\lambda (u1: T).(\lambda (_: 
+C (CHead d (Bind Abbr) u0) (\lambda (ee: C).(match ee with [(CSort _) 
+\Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind b) 
+\Rightarrow (match b with [Abbr \Rightarrow True | Abst \Rightarrow False | 
+Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead x0 (Bind 
+Abst) x1) (getl_mono c0 (CHead d (Bind Abbr) u0) n H0 (CHead x0 (Bind Abst) 
+x1) H6)) in (False_ind (ty3 g c0 (TLRef n) (lift (S n) O x1)) H11))) t2 
+H9)))))))) H5)) H4))))))))))))) (\lambda (n: nat).(\lambda (c0: C).(\lambda 
+(d: C).(\lambda (u0: T).(\lambda (H0: (getl n c0 (CHead d (Bind Abst) 
+u0))).(\lambda (t: T).(\lambda (H1: (ty3 g d u0 t)).(\lambda (_: ((\forall 
+(t2: T).((sty0 g d u0 t2) \to (ty3 g d u0 t2))))).(\lambda (t2: T).(\lambda 
+(H3: (sty0 g c0 (TLRef n) t2)).(let H_x \def (sty0_gen_lref g c0 t2 n H3) in 
+(let H4 \def H_x in (or_ind (ex3_3 C T T (\lambda (e: C).(\lambda (u1: 
+T).(\lambda (_: T).(getl n c0 (CHead e (Bind Abbr) u1))))) (\lambda (e: 
+C).(\lambda (u1: T).(\lambda (t0: T).(sty0 g e u1 t0)))) (\lambda (_: 
+C).(\lambda (_: T).(\lambda (t0: T).(eq T t2 (lift (S n) O t0)))))) (ex3_3 C 
+T T (\lambda (e: C).(\lambda (u1: T).(\lambda (_: T).(getl n c0 (CHead e 
+(Bind Abst) u1))))) (\lambda (e: C).(\lambda (u1: T).(\lambda (t0: T).(sty0 g 
+e u1 t0)))) (\lambda (_: C).(\lambda (u1: T).(\lambda (_: T).(eq T t2 (lift 
+(S n) O u1)))))) (ty3 g c0 (TLRef n) t2) (\lambda (H5: (ex3_3 C T T (\lambda 
+(e: C).(\lambda (u1: T).(\lambda (_: T).(getl n c0 (CHead e (Bind Abbr) 
+u1))))) (\lambda (e: C).(\lambda (u1: T).(\lambda (t0: T).(sty0 g e u1 t0)))) 
+(\lambda (_: C).(\lambda (_: T).(\lambda (t0: T).(eq T t2 (lift (S n) O 
+t0))))))).(ex3_3_ind C T T (\lambda (e: C).(\lambda (u1: T).(\lambda (_: 
 T).(getl n c0 (CHead e (Bind Abbr) u1))))) (\lambda (e: C).(\lambda (u1: 
 T).(\lambda (t0: T).(sty0 g e u1 t0)))) (\lambda (_: C).(\lambda (_: 
-T).(\lambda (t0: T).(eq T t2 (lift (S n) O t0))))))).(ex3_3_ind C T T 
-(\lambda (e: C).(\lambda (u1: T).(\lambda (_: T).(getl n c0 (CHead e (Bind 
-Abbr) u1))))) (\lambda (e: C).(\lambda (u1: T).(\lambda (t0: T).(sty0 g e u1 
-t0)))) (\lambda (_: C).(\lambda (_: T).(\lambda (t0: T).(eq T t2 (lift (S n) 
-O t0))))) (ty3 g c0 (TLRef n) t2) (\lambda (x0: C).(\lambda (x1: T).(\lambda 
-(x2: T).(\lambda (H6: (getl n c0 (CHead x0 (Bind Abbr) x1))).(\lambda (_: 
-(sty0 g x0 x1 x2)).(\lambda (H8: (eq T t2 (lift (S n) O x2))).(let H9 \def 
-(f_equal T T (\lambda (e: T).e) t2 (lift (S n) O x2) H8) in (eq_ind_r T (lift 
-(S n) O x2) (\lambda (t0: T).(ty3 g c0 (TLRef n) t0)) (let H10 \def (eq_ind C 
-(CHead d (Bind Abst) u0) (\lambda (c1: C).(getl n c0 c1)) H0 (CHead x0 (Bind 
+T).(\lambda (t0: T).(eq T t2 (lift (S n) O t0))))) (ty3 g c0 (TLRef n) t2) 
+(\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: T).(\lambda (H6: (getl n c0 
+(CHead x0 (Bind Abbr) x1))).(\lambda (_: (sty0 g x0 x1 x2)).(\lambda (H8: (eq 
+T t2 (lift (S n) O x2))).(let H9 \def (f_equal T T (\lambda (e: T).e) t2 
+(lift (S n) O x2) H8) in (eq_ind_r T (lift (S n) O x2) (\lambda (t0: T).(ty3 
+g c0 (TLRef n) t0)) (let H10 \def (eq_ind C (CHead d (Bind Abst) u0) (\lambda 
+(c1: C).(getl n c0 c1)) H0 (CHead x0 (Bind Abbr) x1) (getl_mono c0 (CHead d 
+(Bind Abst) u0) n H0 (CHead x0 (Bind Abbr) x1) H6)) in (let H11 \def (eq_ind 
+C (CHead d (Bind Abst) u0) (\lambda (ee: C).(match ee with [(CSort _) 
+\Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind b) 
+\Rightarrow (match b with [Abbr \Rightarrow False | Abst \Rightarrow True | 
+Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead x0 (Bind 
 Abbr) x1) (getl_mono c0 (CHead d (Bind Abst) u0) n H0 (CHead x0 (Bind Abbr) 
-x1) H6)) in (let H11 \def (eq_ind C (CHead d (Bind Abst) u0) (\lambda (ee: 
-C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow 
-False | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop) 
-with [(Bind b) \Rightarrow (match b in B return (\lambda (_: B).Prop) with 
-[Abbr \Rightarrow False | Abst \Rightarrow True | Void \Rightarrow False]) | 
-(Flat _) \Rightarrow False])])) I (CHead x0 (Bind Abbr) x1) (getl_mono c0 
-(CHead d (Bind Abst) u0) n H0 (CHead x0 (Bind Abbr) x1) H6)) in (False_ind 
-(ty3 g c0 (TLRef n) (lift (S n) O x2)) H11))) t2 H9)))))))) H5)) (\lambda 
-(H5: (ex3_3 C T T (\lambda (e: C).(\lambda (u1: T).(\lambda (_: T).(getl n c0 
-(CHead e (Bind Abst) u1))))) (\lambda (e: C).(\lambda (u1: T).(\lambda (t0: 
-T).(sty0 g e u1 t0)))) (\lambda (_: C).(\lambda (u1: T).(\lambda (_: T).(eq T 
-t2 (lift (S n) O u1))))))).(ex3_3_ind C T T (\lambda (e: C).(\lambda (u1: 
+x1) H6)) in (False_ind (ty3 g c0 (TLRef n) (lift (S n) O x2)) H11))) t2 
+H9)))))))) H5)) (\lambda (H5: (ex3_3 C T T (\lambda (e: C).(\lambda (u1: 
 T).(\lambda (_: T).(getl n c0 (CHead e (Bind Abst) u1))))) (\lambda (e: 
 C).(\lambda (u1: T).(\lambda (t0: T).(sty0 g e u1 t0)))) (\lambda (_: 
-C).(\lambda (u1: T).(\lambda (_: T).(eq T t2 (lift (S n) O u1))))) (ty3 g c0 
-(TLRef n) t2) (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: T).(\lambda 
-(H6: (getl n c0 (CHead x0 (Bind Abst) x1))).(\lambda (H7: (sty0 g x0 x1 
-x2)).(\lambda (H8: (eq T t2 (lift (S n) O x1))).(let H9 \def (f_equal T T 
-(\lambda (e: T).e) t2 (lift (S n) O x1) H8) in (eq_ind_r T (lift (S n) O x1) 
-(\lambda (t0: T).(ty3 g c0 (TLRef n) t0)) (let H10 \def (eq_ind C (CHead d 
-(Bind Abst) u0) (\lambda (c1: C).(getl n c0 c1)) H0 (CHead x0 (Bind Abst) x1) 
+C).(\lambda (u1: T).(\lambda (_: T).(eq T t2 (lift (S n) O 
+u1))))))).(ex3_3_ind C T T (\lambda (e: C).(\lambda (u1: T).(\lambda (_: 
+T).(getl n c0 (CHead e (Bind Abst) u1))))) (\lambda (e: C).(\lambda (u1: 
+T).(\lambda (t0: T).(sty0 g e u1 t0)))) (\lambda (_: C).(\lambda (u1: 
+T).(\lambda (_: T).(eq T t2 (lift (S n) O u1))))) (ty3 g c0 (TLRef n) t2) 
+(\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: T).(\lambda (H6: (getl n c0 
+(CHead x0 (Bind Abst) x1))).(\lambda (H7: (sty0 g x0 x1 x2)).(\lambda (H8: 
+(eq T t2 (lift (S n) O x1))).(let H9 \def (f_equal T T (\lambda (e: T).e) t2 
+(lift (S n) O x1) H8) in (eq_ind_r T (lift (S n) O x1) (\lambda (t0: T).(ty3 
+g c0 (TLRef n) t0)) (let H10 \def (eq_ind C (CHead d (Bind Abst) u0) (\lambda 
+(c1: C).(getl n c0 c1)) H0 (CHead x0 (Bind Abst) x1) (getl_mono c0 (CHead d 
+(Bind Abst) u0) n H0 (CHead x0 (Bind Abst) x1) H6)) in (let H11 \def (f_equal 
+C C (\lambda (e: C).(match e with [(CSort _) \Rightarrow d | (CHead c1 _ _) 
+\Rightarrow c1])) (CHead d (Bind Abst) u0) (CHead x0 (Bind Abst) x1) 
 (getl_mono c0 (CHead d (Bind Abst) u0) n H0 (CHead x0 (Bind Abst) x1) H6)) in 
-(let H11 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda (_: 
-C).C) with [(CSort _) \Rightarrow d | (CHead c1 _ _) \Rightarrow c1])) (CHead 
-d (Bind Abst) u0) (CHead x0 (Bind Abst) x1) (getl_mono c0 (CHead d (Bind 
-Abst) u0) n H0 (CHead x0 (Bind Abst) x1) H6)) in ((let H12 \def (f_equal C T 
-(\lambda (e: C).(match e in C return (\lambda (_: C).T) with [(CSort _) 
+((let H12 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _) 
 \Rightarrow u0 | (CHead _ _ t0) \Rightarrow t0])) (CHead d (Bind Abst) u0) 
 (CHead x0 (Bind Abst) x1) (getl_mono c0 (CHead d (Bind Abst) u0) n H0 (CHead 
 x0 (Bind Abst) x1) H6)) in (\lambda (H13: (eq C d x0)).(let H14 \def 
@@ -231,7 +227,4 @@ c0 x1 x2 H12 t3 x0 H_y0 H10) x H11) (THead (Flat Cast) t3 t2) (THead (Flat
 Cast) x0 t3) (ty3_cast g c0 t2 t3 H0 x0 H_y0) (pc3_thin_dx c0 t3 x1 
 (ty3_unique g c0 t2 t3 H0 x1 H_y) x0 Cast)))) (ty3_correct g c0 t2 x1 H_y)))) 
 (ty3_correct g c0 t3 x0 H_y0))))) t4 H9))))))) H5))))))))))))) c u t1 H))))).
-(* COMMENTS
-Initial nodes: 4539
-END *)