(* This file was automatically generated: do not edit *********************)
-include "Basic-1/getl/fwd.ma".
+include "basic_1/getl/fwd.ma".
-include "Basic-1/drop/props.ma".
+include "basic_1/clear/props.ma".
-include "Basic-1/clear/props.ma".
+include "basic_1/drop/props.ma".
theorem getl_refl:
\forall (b: B).(\forall (c: C).(\forall (u: T).(getl O (CHead c (Bind b) u)
(CHead c (Bind b) u))))
\def
- \lambda (b: B).(\lambda (c: C).(\lambda (u: T).(getl_intro O (CHead c (Bind
-b) u) (CHead c (Bind b) u) (CHead c (Bind b) u) (drop_refl (CHead c (Bind b)
-u)) (clear_bind b c u)))).
-(* COMMENTS
-Initial nodes: 59
-END *)
+ \lambda (b: B).(\lambda (c: C).(\lambda (u: T).(let TMP_1 \def (Bind b) in
+(let TMP_2 \def (CHead c TMP_1 u) in (let TMP_3 \def (Bind b) in (let TMP_4
+\def (CHead c TMP_3 u) in (let TMP_5 \def (Bind b) in (let TMP_6 \def (CHead
+c TMP_5 u) in (let TMP_7 \def (Bind b) in (let TMP_8 \def (CHead c TMP_7 u)
+in (let TMP_9 \def (drop_refl TMP_8) in (let TMP_10 \def (clear_bind b c u)
+in (getl_intro O TMP_2 TMP_4 TMP_6 TMP_9 TMP_10))))))))))))).
theorem getl_head:
\forall (k: K).(\forall (h: nat).(\forall (c: C).(\forall (e: C).((getl (r k
h) c e) \to (\forall (u: T).(getl (S h) (CHead c k u) e))))))
\def
\lambda (k: K).(\lambda (h: nat).(\lambda (c: C).(\lambda (e: C).(\lambda
-(H: (getl (r k h) c e)).(\lambda (u: T).(let H0 \def (getl_gen_all c e (r k
-h) H) in (ex2_ind C (\lambda (e0: C).(drop (r k h) O c e0)) (\lambda (e0:
-C).(clear e0 e)) (getl (S h) (CHead c k u) e) (\lambda (x: C).(\lambda (H1:
-(drop (r k h) O c x)).(\lambda (H2: (clear x e)).(getl_intro (S h) (CHead c k
-u) e x (drop_drop k h c x H1 u) H2)))) H0))))))).
-(* COMMENTS
-Initial nodes: 137
-END *)
+(H: (getl (r k h) c e)).(\lambda (u: T).(let TMP_1 \def (r k h) in (let H0
+\def (getl_gen_all c e TMP_1 H) in (let TMP_3 \def (\lambda (e0: C).(let
+TMP_2 \def (r k h) in (drop TMP_2 O c e0))) in (let TMP_4 \def (\lambda (e0:
+C).(clear e0 e)) in (let TMP_5 \def (S h) in (let TMP_6 \def (CHead c k u) in
+(let TMP_7 \def (getl TMP_5 TMP_6 e) in (let TMP_11 \def (\lambda (x:
+C).(\lambda (H1: (drop (r k h) O c x)).(\lambda (H2: (clear x e)).(let TMP_8
+\def (S h) in (let TMP_9 \def (CHead c k u) in (let TMP_10 \def (drop_drop k
+h c x H1 u) in (getl_intro TMP_8 TMP_9 e x TMP_10 H2))))))) in (ex2_ind C
+TMP_3 TMP_4 TMP_7 TMP_11 H0)))))))))))))).
theorem getl_flat:
\forall (c: C).(\forall (e: C).(\forall (h: nat).((getl h c e) \to (\forall
\def
\lambda (c: C).(\lambda (e: C).(\lambda (h: nat).(\lambda (H: (getl h c
e)).(\lambda (f: F).(\lambda (u: T).(let H0 \def (getl_gen_all c e h H) in
-(ex2_ind C (\lambda (e0: C).(drop h O c e0)) (\lambda (e0: C).(clear e0 e))
-(getl h (CHead c (Flat f) u) e) (\lambda (x: C).(\lambda (H1: (drop h O c
-x)).(\lambda (H2: (clear x e)).(nat_ind (\lambda (n: nat).((drop n O c x) \to
-(getl n (CHead c (Flat f) u) e))) (\lambda (H3: (drop O O c x)).(let H4 \def
-(eq_ind_r C x (\lambda (c0: C).(clear c0 e)) H2 c (drop_gen_refl c x H3)) in
-(getl_intro O (CHead c (Flat f) u) e (CHead c (Flat f) u) (drop_refl (CHead c
-(Flat f) u)) (clear_flat c e H4 f u)))) (\lambda (h0: nat).(\lambda (_:
-(((drop h0 O c x) \to (getl h0 (CHead c (Flat f) u) e)))).(\lambda (H3: (drop
-(S h0) O c x)).(getl_intro (S h0) (CHead c (Flat f) u) e x (drop_drop (Flat
-f) h0 c x H3 u) H2)))) h H1)))) H0))))))).
-(* COMMENTS
-Initial nodes: 285
-END *)
+(let TMP_1 \def (\lambda (e0: C).(drop h O c e0)) in (let TMP_2 \def (\lambda
+(e0: C).(clear e0 e)) in (let TMP_3 \def (Flat f) in (let TMP_4 \def (CHead c
+TMP_3 u) in (let TMP_5 \def (getl h TMP_4 e) in (let TMP_26 \def (\lambda (x:
+C).(\lambda (H1: (drop h O c x)).(\lambda (H2: (clear x e)).(let TMP_8 \def
+(\lambda (n: nat).((drop n O c x) \to (let TMP_6 \def (Flat f) in (let TMP_7
+\def (CHead c TMP_6 u) in (getl n TMP_7 e))))) in (let TMP_19 \def (\lambda
+(H3: (drop O O c x)).(let TMP_9 \def (\lambda (c0: C).(clear c0 e)) in (let
+TMP_10 \def (drop_gen_refl c x H3) in (let H4 \def (eq_ind_r C x TMP_9 H2 c
+TMP_10) in (let TMP_11 \def (Flat f) in (let TMP_12 \def (CHead c TMP_11 u)
+in (let TMP_13 \def (Flat f) in (let TMP_14 \def (CHead c TMP_13 u) in (let
+TMP_15 \def (Flat f) in (let TMP_16 \def (CHead c TMP_15 u) in (let TMP_17
+\def (drop_refl TMP_16) in (let TMP_18 \def (clear_flat c e H4 f u) in
+(getl_intro O TMP_12 e TMP_14 TMP_17 TMP_18))))))))))))) in (let TMP_25 \def
+(\lambda (h0: nat).(\lambda (_: (((drop h0 O c x) \to (getl h0 (CHead c (Flat
+f) u) e)))).(\lambda (H3: (drop (S h0) O c x)).(let TMP_20 \def (S h0) in
+(let TMP_21 \def (Flat f) in (let TMP_22 \def (CHead c TMP_21 u) in (let
+TMP_23 \def (Flat f) in (let TMP_24 \def (drop_drop TMP_23 h0 c x H3 u) in
+(getl_intro TMP_20 TMP_22 e x TMP_24 H2))))))))) in (nat_ind TMP_8 TMP_19
+TMP_25 h H1))))))) in (ex2_ind C TMP_1 TMP_2 TMP_5 TMP_26 H0))))))))))))).
theorem getl_ctail:
\forall (b: B).(\forall (c: C).(\forall (d: C).(\forall (u: T).(\forall (i:
\def
\lambda (b: B).(\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i:
nat).(\lambda (H: (getl i c (CHead d (Bind b) u))).(\lambda (k: K).(\lambda
-(v: T).(let H0 \def (getl_gen_all c (CHead d (Bind b) u) i H) in (ex2_ind C
-(\lambda (e: C).(drop i O c e)) (\lambda (e: C).(clear e (CHead d (Bind b)
-u))) (getl i (CTail k v c) (CHead (CTail k v d) (Bind b) u)) (\lambda (x:
-C).(\lambda (H1: (drop i O c x)).(\lambda (H2: (clear x (CHead d (Bind b)
-u))).(getl_intro i (CTail k v c) (CHead (CTail k v d) (Bind b) u) (CTail k v
-x) (drop_ctail c x O i H1 k v) (clear_ctail b x d u H2 k v))))) H0))))))))).
-(* COMMENTS
-Initial nodes: 203
-END *)
-
-theorem getl_mono:
- \forall (c: C).(\forall (x1: C).(\forall (h: nat).((getl h c x1) \to
-(\forall (x2: C).((getl h c x2) \to (eq C x1 x2))))))
-\def
- \lambda (c: C).(\lambda (x1: C).(\lambda (h: nat).(\lambda (H: (getl h c
-x1)).(\lambda (x2: C).(\lambda (H0: (getl h c x2)).(let H1 \def (getl_gen_all
-c x2 h H0) in (ex2_ind C (\lambda (e: C).(drop h O c e)) (\lambda (e:
-C).(clear e x2)) (eq C x1 x2) (\lambda (x: C).(\lambda (H2: (drop h O c
-x)).(\lambda (H3: (clear x x2)).(let H4 \def (getl_gen_all c x1 h H) in
-(ex2_ind C (\lambda (e: C).(drop h O c e)) (\lambda (e: C).(clear e x1)) (eq
-C x1 x2) (\lambda (x0: C).(\lambda (H5: (drop h O c x0)).(\lambda (H6: (clear
-x0 x1)).(let H7 \def (eq_ind C x (\lambda (c0: C).(drop h O c c0)) H2 x0
-(drop_mono c x O h H2 x0 H5)) in (let H8 \def (eq_ind_r C x0 (\lambda (c0:
-C).(drop h O c c0)) H7 x (drop_mono c x O h H2 x0 H5)) in (let H9 \def
-(eq_ind_r C x0 (\lambda (c0: C).(clear c0 x1)) H6 x (drop_mono c x O h H2 x0
-H5)) in (clear_mono x x1 H9 x2 H3))))))) H4))))) H1))))))).
-(* COMMENTS
-Initial nodes: 269
-END *)
+(v: T).(let TMP_1 \def (Bind b) in (let TMP_2 \def (CHead d TMP_1 u) in (let
+H0 \def (getl_gen_all c TMP_2 i H) in (let TMP_3 \def (\lambda (e: C).(drop i
+O c e)) in (let TMP_6 \def (\lambda (e: C).(let TMP_4 \def (Bind b) in (let
+TMP_5 \def (CHead d TMP_4 u) in (clear e TMP_5)))) in (let TMP_7 \def (CTail
+k v c) in (let TMP_8 \def (CTail k v d) in (let TMP_9 \def (Bind b) in (let
+TMP_10 \def (CHead TMP_8 TMP_9 u) in (let TMP_11 \def (getl i TMP_7 TMP_10)
+in (let TMP_19 \def (\lambda (x: C).(\lambda (H1: (drop i O c x)).(\lambda
+(H2: (clear x (CHead d (Bind b) u))).(let TMP_12 \def (CTail k v c) in (let
+TMP_13 \def (CTail k v d) in (let TMP_14 \def (Bind b) in (let TMP_15 \def
+(CHead TMP_13 TMP_14 u) in (let TMP_16 \def (CTail k v x) in (let TMP_17 \def
+(drop_ctail c x O i H1 k v) in (let TMP_18 \def (clear_ctail b x d u H2 k v)
+in (getl_intro i TMP_12 TMP_15 TMP_16 TMP_17 TMP_18))))))))))) in (ex2_ind C
+TMP_3 TMP_6 TMP_11 TMP_19 H0))))))))))))))))))).
projects / helm.git / blobdiff