--- /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 *********************)
+
+set "baseuri" "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/cimp/props".
+
+include "cimp/defs.ma".
+
+include "getl/getl.ma".
+
+theorem cimp_flat_sx:
+ \forall (f: F).(\forall (c: C).(\forall (v: T).(cimp (CHead c (Flat f) v)
+c)))
+\def
+ \lambda (f: F).(\lambda (c: C).(\lambda (v: T).(\lambda (b: B).(\lambda (d1:
+C).(\lambda (w: T).(\lambda (h: nat).(\lambda (H: (getl h (CHead c (Flat f)
+v) (CHead d1 (Bind b) w))).((match h in nat return (\lambda (n: nat).((getl n
+(CHead c (Flat f) v) (CHead d1 (Bind b) w)) \to (ex C (\lambda (d2: C).(getl
+n c (CHead d2 (Bind b) w)))))) with [O \Rightarrow (\lambda (H0: (getl O
+(CHead c (Flat f) v) (CHead d1 (Bind b) w))).(ex_intro C (\lambda (d2:
+C).(getl O c (CHead d2 (Bind b) w))) d1 (getl_intro O c (CHead d1 (Bind b) w)
+c (drop_refl c) (clear_gen_flat f c (CHead d1 (Bind b) w) v (getl_gen_O
+(CHead c (Flat f) v) (CHead d1 (Bind b) w) H0))))) | (S n) \Rightarrow
+(\lambda (H0: (getl (S n) (CHead c (Flat f) v) (CHead d1 (Bind b)
+w))).(ex_intro C (\lambda (d2: C).(getl (S n) c (CHead d2 (Bind b) w))) d1
+(getl_gen_S (Flat f) c (CHead d1 (Bind b) w) v n H0)))]) H)))))))).
+
+theorem cimp_flat_dx:
+ \forall (f: F).(\forall (c: C).(\forall (v: T).(cimp c (CHead c (Flat f)
+v))))
+\def
+ \lambda (f: F).(\lambda (c: C).(\lambda (v: T).(\lambda (b: B).(\lambda (d1:
+C).(\lambda (w: T).(\lambda (h: nat).(\lambda (H: (getl h c (CHead d1 (Bind
+b) w))).(ex_intro C (\lambda (d2: C).(getl h (CHead c (Flat f) v) (CHead d2
+(Bind b) w))) d1 (getl_flat c (CHead d1 (Bind b) w) h H f v))))))))).
+
+theorem cimp_bind:
+ \forall (c1: C).(\forall (c2: C).((cimp c1 c2) \to (\forall (b: B).(\forall
+(v: T).(cimp (CHead c1 (Bind b) v) (CHead c2 (Bind b) v))))))
+\def
+ \lambda (c1: C).(\lambda (c2: C).(\lambda (H: ((\forall (b: B).(\forall (d1:
+C).(\forall (w: T).(\forall (h: nat).((getl h c1 (CHead d1 (Bind b) w)) \to
+(ex C (\lambda (d2: C).(getl h c2 (CHead d2 (Bind b) w))))))))))).(\lambda
+(b: B).(\lambda (v: T).(\lambda (b0: B).(\lambda (d1: C).(\lambda (w:
+T).(\lambda (h: nat).(\lambda (H0: (getl h (CHead c1 (Bind b) v) (CHead d1
+(Bind b0) w))).((match h in nat return (\lambda (n: nat).((getl n (CHead c1
+(Bind b) v) (CHead d1 (Bind b0) w)) \to (ex C (\lambda (d2: C).(getl n (CHead
+c2 (Bind b) v) (CHead d2 (Bind b0) w)))))) with [O \Rightarrow (\lambda (H1:
+(getl O (CHead c1 (Bind b) v) (CHead d1 (Bind b0) w))).(let H2 \def (f_equal
+C C (\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
+\Rightarrow d1 | (CHead c _ _) \Rightarrow c])) (CHead d1 (Bind b0) w) (CHead
+c1 (Bind b) v) (clear_gen_bind b c1 (CHead d1 (Bind b0) w) v (getl_gen_O
+(CHead c1 (Bind b) v) (CHead d1 (Bind b0) w) H1))) in ((let H3 \def (f_equal
+C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with [(CSort _)
+\Rightarrow b0 | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_:
+K).B) with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow b0])])) (CHead d1
+(Bind b0) w) (CHead c1 (Bind b) v) (clear_gen_bind b c1 (CHead d1 (Bind b0)
+w) v (getl_gen_O (CHead c1 (Bind b) v) (CHead d1 (Bind b0) w) H1))) in ((let
+H4 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T)
+with [(CSort _) \Rightarrow w | (CHead _ _ t) \Rightarrow t])) (CHead d1
+(Bind b0) w) (CHead c1 (Bind b) v) (clear_gen_bind b c1 (CHead d1 (Bind b0)
+w) v (getl_gen_O (CHead c1 (Bind b) v) (CHead d1 (Bind b0) w) H1))) in
+(\lambda (H5: (eq B b0 b)).(\lambda (_: (eq C d1 c1)).(eq_ind_r T v (\lambda
+(t: T).(ex C (\lambda (d2: C).(getl O (CHead c2 (Bind b) v) (CHead d2 (Bind
+b0) t))))) (eq_ind_r B b (\lambda (b1: B).(ex C (\lambda (d2: C).(getl O
+(CHead c2 (Bind b) v) (CHead d2 (Bind b1) v))))) (ex_intro C (\lambda (d2:
+C).(getl O (CHead c2 (Bind b) v) (CHead d2 (Bind b) v))) c2 (getl_refl b c2
+v)) b0 H5) w H4)))) H3)) H2))) | (S n) \Rightarrow (\lambda (H1: (getl (S n)
+(CHead c1 (Bind b) v) (CHead d1 (Bind b0) w))).(let H_x \def (H b0 d1 w (r
+(Bind b) n) (getl_gen_S (Bind b) c1 (CHead d1 (Bind b0) w) v n H1)) in (let
+H2 \def H_x in (ex_ind C (\lambda (d2: C).(getl (r (Bind b) n) c2 (CHead d2
+(Bind b0) w))) (ex C (\lambda (d2: C).(getl (S n) (CHead c2 (Bind b) v)
+(CHead d2 (Bind b0) w)))) (\lambda (x: C).(\lambda (H3: (getl (r (Bind b) n)
+c2 (CHead x (Bind b0) w))).(ex_intro C (\lambda (d2: C).(getl (S n) (CHead c2
+(Bind b) v) (CHead d2 (Bind b0) w))) x (getl_head (Bind b) n c2 (CHead x
+(Bind b0) w) H3 v)))) H2))))]) H0)))))))))).
+
+theorem cimp_getl_conf:
+ \forall (c1: C).(\forall (c2: C).((cimp c1 c2) \to (\forall (b: B).(\forall
+(d1: C).(\forall (w: T).(\forall (i: nat).((getl i c1 (CHead d1 (Bind b) w))
+\to (ex2 C (\lambda (d2: C).(cimp d1 d2)) (\lambda (d2: C).(getl i c2 (CHead
+d2 (Bind b) w)))))))))))
+\def
+ \lambda (c1: C).(\lambda (c2: C).(\lambda (H: ((\forall (b: B).(\forall (d1:
+C).(\forall (w: T).(\forall (h: nat).((getl h c1 (CHead d1 (Bind b) w)) \to
+(ex C (\lambda (d2: C).(getl h c2 (CHead d2 (Bind b) w))))))))))).(\lambda
+(b: B).(\lambda (d1: C).(\lambda (w: T).(\lambda (i: nat).(\lambda (H0: (getl
+i c1 (CHead d1 (Bind b) w))).(let H_x \def (H b d1 w i H0) in (let H1 \def
+H_x in (ex_ind C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind b) w))) (ex2 C
+(\lambda (d2: C).(\forall (b0: B).(\forall (d3: C).(\forall (w0: T).(\forall
+(h: nat).((getl h d1 (CHead d3 (Bind b0) w0)) \to (ex C (\lambda (d4:
+C).(getl h d2 (CHead d4 (Bind b0) w0)))))))))) (\lambda (d2: C).(getl i c2
+(CHead d2 (Bind b) w)))) (\lambda (x: C).(\lambda (H2: (getl i c2 (CHead x
+(Bind b) w))).(ex_intro2 C (\lambda (d2: C).(\forall (b0: B).(\forall (d3:
+C).(\forall (w0: T).(\forall (h: nat).((getl h d1 (CHead d3 (Bind b0) w0))
+\to (ex C (\lambda (d4: C).(getl h d2 (CHead d4 (Bind b0) w0))))))))))
+(\lambda (d2: C).(getl i c2 (CHead d2 (Bind b) w))) x (\lambda (b0:
+B).(\lambda (d0: C).(\lambda (w0: T).(\lambda (h: nat).(\lambda (H3: (getl h
+d1 (CHead d0 (Bind b0) w0))).(let H_y \def (getl_trans (S h) c1 (CHead d1
+(Bind b) w) i H0) in (let H_x0 \def (H b0 d0 w0 (plus (S h) i) (H_y (CHead d0
+(Bind b0) w0) (getl_head (Bind b) h d1 (CHead d0 (Bind b0) w0) H3 w))) in
+(let H4 \def H_x0 in (ex_ind C (\lambda (d2: C).(getl (plus (S h) i) c2
+(CHead d2 (Bind b0) w0))) (ex C (\lambda (d2: C).(getl h x (CHead d2 (Bind
+b0) w0)))) (\lambda (x0: C).(\lambda (H5: (getl (plus (S h) i) c2 (CHead x0
+(Bind b0) w0))).(let H_y0 \def (getl_conf_le (plus (S h) i) (CHead x0 (Bind
+b0) w0) c2 H5 (CHead x (Bind b) w) i H2) in (let H6 \def (eq_ind nat (minus
+(plus (S h) i) i) (\lambda (n: nat).(getl n (CHead x (Bind b) w) (CHead x0
+(Bind b0) w0))) (H_y0 (le_plus_r (S h) i)) (S h) (minus_plus_r (S h) i)) in
+(ex_intro C (\lambda (d2: C).(getl h x (CHead d2 (Bind b0) w0))) x0
+(getl_gen_S (Bind b) x (CHead x0 (Bind b0) w0) w h H6)))))) H4))))))))) H2)))
+H1)))))))))).
+
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