--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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 "LambdaDelta-1/sty1/props.ma".
+
+include "LambdaDelta-1/cnt/props.ma".
+
+theorem sty1_cnt:
+ \forall (g: G).(\forall (c: C).(\forall (t1: T).(\forall (t: T).((sty0 g c
+t1 t) \to (ex2 T (\lambda (t2: T).(sty1 g c t1 t2)) (\lambda (t2: T).(cnt
+t2)))))))
+\def
+ \lambda (g: G).(\lambda (c: C).(\lambda (t1: T).(\lambda (t: T).(\lambda (H:
+(sty0 g c t1 t)).(sty0_ind g (\lambda (c0: C).(\lambda (t0: T).(\lambda (_:
+T).(ex2 T (\lambda (t3: T).(sty1 g c0 t0 t3)) (\lambda (t3: T).(cnt t3))))))
+(\lambda (c0: C).(\lambda (n: nat).(ex_intro2 T (\lambda (t2: T).(sty1 g c0
+(TSort n) t2)) (\lambda (t2: T).(cnt t2)) (TSort (next g n)) (sty1_sty0 g c0
+(TSort n) (TSort (next g n)) (sty0_sort g c0 n)) (cnt_sort (next g n)))))
+(\lambda (c0: C).(\lambda (d: C).(\lambda (v: T).(\lambda (i: nat).(\lambda
+(H0: (getl i c0 (CHead d (Bind Abbr) v))).(\lambda (w: T).(\lambda (_: (sty0
+g d v w)).(\lambda (H2: (ex2 T (\lambda (t2: T).(sty1 g d v t2)) (\lambda
+(t2: T).(cnt t2)))).(let H3 \def H2 in (ex2_ind T (\lambda (t2: T).(sty1 g d
+v t2)) (\lambda (t2: T).(cnt t2)) (ex2 T (\lambda (t2: T).(sty1 g c0 (TLRef
+i) t2)) (\lambda (t2: T).(cnt t2))) (\lambda (x: T).(\lambda (H4: (sty1 g d v
+x)).(\lambda (H5: (cnt x)).(ex_intro2 T (\lambda (t2: T).(sty1 g c0 (TLRef i)
+t2)) (\lambda (t2: T).(cnt t2)) (lift (S i) O x) (sty1_abbr g c0 d v i H0 x
+H4) (cnt_lift x H5 (S i) O))))) H3)))))))))) (\lambda (c0: C).(\lambda (d:
+C).(\lambda (v: T).(\lambda (i: nat).(\lambda (H0: (getl i c0 (CHead d (Bind
+Abst) v))).(\lambda (w: T).(\lambda (H1: (sty0 g d v w)).(\lambda (H2: (ex2 T
+(\lambda (t2: T).(sty1 g d v t2)) (\lambda (t2: T).(cnt t2)))).(let H3 \def
+H2 in (ex2_ind T (\lambda (t2: T).(sty1 g d v t2)) (\lambda (t2: T).(cnt t2))
+(ex2 T (\lambda (t2: T).(sty1 g c0 (TLRef i) t2)) (\lambda (t2: T).(cnt t2)))
+(\lambda (x: T).(\lambda (H4: (sty1 g d v x)).(\lambda (H5: (cnt
+x)).(ex_intro2 T (\lambda (t2: T).(sty1 g c0 (TLRef i) t2)) (\lambda (t2:
+T).(cnt t2)) (lift (S i) O x) (sty1_trans g c0 (TLRef i) (lift (S i) O v)
+(sty1_sty0 g c0 (TLRef i) (lift (S i) O v) (sty0_abst g c0 d v i H0 w H1))
+(lift (S i) O x) (sty1_lift g d v x H4 c0 (S i) O (getl_drop Abst c0 d v i
+H0))) (cnt_lift x H5 (S i) O))))) H3)))))))))) (\lambda (b: B).(\lambda (c0:
+C).(\lambda (v: T).(\lambda (t2: T).(\lambda (t3: T).(\lambda (_: (sty0 g
+(CHead c0 (Bind b) v) t2 t3)).(\lambda (H1: (ex2 T (\lambda (t4: T).(sty1 g
+(CHead c0 (Bind b) v) t2 t4)) (\lambda (t4: T).(cnt t4)))).(let H2 \def H1 in
+(ex2_ind T (\lambda (t4: T).(sty1 g (CHead c0 (Bind b) v) t2 t4)) (\lambda
+(t4: T).(cnt t4)) (ex2 T (\lambda (t4: T).(sty1 g c0 (THead (Bind b) v t2)
+t4)) (\lambda (t4: T).(cnt t4))) (\lambda (x: T).(\lambda (H3: (sty1 g (CHead
+c0 (Bind b) v) t2 x)).(\lambda (H4: (cnt x)).(ex_intro2 T (\lambda (t4:
+T).(sty1 g c0 (THead (Bind b) v t2) t4)) (\lambda (t4: T).(cnt t4)) (THead
+(Bind b) v x) (sty1_bind g b c0 v t2 x H3) (cnt_head x H4 (Bind b) v)))))
+H2))))))))) (\lambda (c0: C).(\lambda (v: T).(\lambda (t2: T).(\lambda (t3:
+T).(\lambda (_: (sty0 g c0 t2 t3)).(\lambda (H1: (ex2 T (\lambda (t4:
+T).(sty1 g c0 t2 t4)) (\lambda (t4: T).(cnt t4)))).(let H2 \def H1 in
+(ex2_ind T (\lambda (t4: T).(sty1 g c0 t2 t4)) (\lambda (t4: T).(cnt t4))
+(ex2 T (\lambda (t4: T).(sty1 g c0 (THead (Flat Appl) v t2) t4)) (\lambda
+(t4: T).(cnt t4))) (\lambda (x: T).(\lambda (H3: (sty1 g c0 t2 x)).(\lambda
+(H4: (cnt x)).(ex_intro2 T (\lambda (t4: T).(sty1 g c0 (THead (Flat Appl) v
+t2) t4)) (\lambda (t4: T).(cnt t4)) (THead (Flat Appl) v x) (sty1_appl g c0 v
+t2 x H3) (cnt_head x H4 (Flat Appl) v))))) H2)))))))) (\lambda (c0:
+C).(\lambda (v1: T).(\lambda (v2: T).(\lambda (H0: (sty0 g c0 v1
+v2)).(\lambda (_: (ex2 T (\lambda (t2: T).(sty1 g c0 v1 t2)) (\lambda (t2:
+T).(cnt t2)))).(\lambda (t2: T).(\lambda (t3: T).(\lambda (_: (sty0 g c0 t2
+t3)).(\lambda (H3: (ex2 T (\lambda (t4: T).(sty1 g c0 t2 t4)) (\lambda (t4:
+T).(cnt t4)))).(let H4 \def H3 in (ex2_ind T (\lambda (t4: T).(sty1 g c0 t2
+t4)) (\lambda (t4: T).(cnt t4)) (ex2 T (\lambda (t4: T).(sty1 g c0 (THead
+(Flat Cast) v1 t2) t4)) (\lambda (t4: T).(cnt t4))) (\lambda (x: T).(\lambda
+(H5: (sty1 g c0 t2 x)).(\lambda (H6: (cnt x)).(let H_x \def (sty1_cast2 g c0
+t2 x H5 v1 v2 H0) in (let H7 \def H_x in (ex2_ind T (\lambda (v3: T).(sty1 g
+c0 v1 v3)) (\lambda (v3: T).(sty1 g c0 (THead (Flat Cast) v1 t2) (THead (Flat
+Cast) v3 x))) (ex2 T (\lambda (t4: T).(sty1 g c0 (THead (Flat Cast) v1 t2)
+t4)) (\lambda (t4: T).(cnt t4))) (\lambda (x0: T).(\lambda (_: (sty1 g c0 v1
+x0)).(\lambda (H9: (sty1 g c0 (THead (Flat Cast) v1 t2) (THead (Flat Cast) x0
+x))).(ex_intro2 T (\lambda (t4: T).(sty1 g c0 (THead (Flat Cast) v1 t2) t4))
+(\lambda (t4: T).(cnt t4)) (THead (Flat Cast) x0 x) H9 (cnt_head x H6 (Flat
+Cast) x0))))) H7)))))) H4))))))))))) c t1 t H))))).
+
projects / helm.git / blobdiff