(* This file was automatically generated: do not edit *********************)
-include "Basic-1/iso/defs.ma".
+include "basic_1/iso/defs.ma".
-include "Basic-1/tlist/defs.ma".
+include "basic_1/tlist/defs.ma".
+
+theorem iso_ind:
+ \forall (P: ((T \to (T \to Prop)))).(((\forall (n1: nat).(\forall (n2:
+nat).(P (TSort n1) (TSort n2))))) \to (((\forall (i1: nat).(\forall (i2:
+nat).(P (TLRef i1) (TLRef i2))))) \to (((\forall (v1: T).(\forall (v2:
+T).(\forall (t1: T).(\forall (t2: T).(\forall (k: K).(P (THead k v1 t1)
+(THead k v2 t2)))))))) \to (\forall (t: T).(\forall (t0: T).((iso t t0) \to
+(P t t0)))))))
+\def
+ \lambda (P: ((T \to (T \to Prop)))).(\lambda (f: ((\forall (n1:
+nat).(\forall (n2: nat).(P (TSort n1) (TSort n2)))))).(\lambda (f0: ((\forall
+(i1: nat).(\forall (i2: nat).(P (TLRef i1) (TLRef i2)))))).(\lambda (f1:
+((\forall (v1: T).(\forall (v2: T).(\forall (t1: T).(\forall (t2: T).(\forall
+(k: K).(P (THead k v1 t1) (THead k v2 t2))))))))).(\lambda (t: T).(\lambda
+(t0: T).(\lambda (i: (iso t t0)).(match i with [(iso_sort x x0) \Rightarrow
+(f x x0) | (iso_lref x x0) \Rightarrow (f0 x x0) | (iso_head x x0 x1 x2 x3)
+\Rightarrow (f1 x x0 x1 x2 x3)]))))))).
theorem iso_gen_sort:
\forall (u2: T).(\forall (n1: nat).((iso (TSort n1) u2) \to (ex nat (\lambda
(n2: nat).(eq T u2 (TSort n2))))))
\def
- \lambda (u2: T).(\lambda (n1: nat).(\lambda (H: (iso (TSort n1)
-u2)).(insert_eq T (TSort n1) (\lambda (t: T).(iso t u2)) (\lambda (_: T).(ex
-nat (\lambda (n2: nat).(eq T u2 (TSort n2))))) (\lambda (y: T).(\lambda (H0:
-(iso y u2)).(iso_ind (\lambda (t: T).(\lambda (t0: T).((eq T t (TSort n1))
-\to (ex nat (\lambda (n2: nat).(eq T t0 (TSort n2))))))) (\lambda (n0:
-nat).(\lambda (n2: nat).(\lambda (H1: (eq T (TSort n0) (TSort n1))).(let H2
-\def (f_equal T nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat)
-with [(TSort n) \Rightarrow n | (TLRef _) \Rightarrow n0 | (THead _ _ _)
-\Rightarrow n0])) (TSort n0) (TSort n1) H1) in (ex_intro nat (\lambda (n3:
-nat).(eq T (TSort n2) (TSort n3))) n2 (refl_equal T (TSort n2))))))) (\lambda
-(i1: nat).(\lambda (i2: nat).(\lambda (H1: (eq T (TLRef i1) (TSort n1))).(let
-H2 \def (eq_ind T (TLRef i1) (\lambda (ee: T).(match ee in T return (\lambda
-(_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True |
-(THead _ _ _) \Rightarrow False])) I (TSort n1) H1) in (False_ind (ex nat
-(\lambda (n2: nat).(eq T (TLRef i2) (TSort n2)))) H2))))) (\lambda (v1:
-T).(\lambda (v2: T).(\lambda (t1: T).(\lambda (t2: T).(\lambda (k:
-K).(\lambda (H1: (eq T (THead k v1 t1) (TSort n1))).(let H2 \def (eq_ind T
-(THead k v1 t1) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop)
-with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _
-_) \Rightarrow True])) I (TSort n1) H1) in (False_ind (ex nat (\lambda (n2:
-nat).(eq T (THead k v2 t2) (TSort n2)))) H2)))))))) y u2 H0))) H))).
-(* COMMENTS
-Initial nodes: 321
-END *)
+ \lambda (u2: T).(\lambda (n1: nat).(\lambda (H: (iso (TSort n1) u2)).(let
+TMP_1 \def (TSort n1) in (let TMP_2 \def (\lambda (t: T).(iso t u2)) in (let
+TMP_5 \def (\lambda (_: T).(let TMP_4 \def (\lambda (n2: nat).(let TMP_3 \def
+(TSort n2) in (eq T u2 TMP_3))) in (ex nat TMP_4))) in (let TMP_34 \def
+(\lambda (y: T).(\lambda (H0: (iso y u2)).(let TMP_8 \def (\lambda (t:
+T).(\lambda (t0: T).((eq T t (TSort n1)) \to (let TMP_7 \def (\lambda (n2:
+nat).(let TMP_6 \def (TSort n2) in (eq T t0 TMP_6))) in (ex nat TMP_7))))) in
+(let TMP_17 \def (\lambda (n0: nat).(\lambda (n2: nat).(\lambda (H1: (eq T
+(TSort n0) (TSort n1))).(let TMP_9 \def (\lambda (e: T).(match e with [(TSort
+n) \Rightarrow n | (TLRef _) \Rightarrow n0 | (THead _ _ _) \Rightarrow n0]))
+in (let TMP_10 \def (TSort n0) in (let TMP_11 \def (TSort n1) in (let H2 \def
+(f_equal T nat TMP_9 TMP_10 TMP_11 H1) in (let TMP_14 \def (\lambda (n3:
+nat).(let TMP_12 \def (TSort n2) in (let TMP_13 \def (TSort n3) in (eq T
+TMP_12 TMP_13)))) in (let TMP_15 \def (TSort n2) in (let TMP_16 \def
+(refl_equal T TMP_15) in (ex_intro nat TMP_14 n2 TMP_16))))))))))) in (let
+TMP_25 \def (\lambda (i1: nat).(\lambda (i2: nat).(\lambda (H1: (eq T (TLRef
+i1) (TSort n1))).(let TMP_18 \def (TLRef i1) in (let TMP_19 \def (\lambda
+(ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow
+True | (THead _ _ _) \Rightarrow False])) in (let TMP_20 \def (TSort n1) in
+(let H2 \def (eq_ind T TMP_18 TMP_19 I TMP_20 H1) in (let TMP_23 \def
+(\lambda (n2: nat).(let TMP_21 \def (TLRef i2) in (let TMP_22 \def (TSort n2)
+in (eq T TMP_21 TMP_22)))) in (let TMP_24 \def (ex nat TMP_23) in (False_ind
+TMP_24 H2)))))))))) in (let TMP_33 \def (\lambda (v1: T).(\lambda (v2:
+T).(\lambda (t1: T).(\lambda (t2: T).(\lambda (k: K).(\lambda (H1: (eq T
+(THead k v1 t1) (TSort n1))).(let TMP_26 \def (THead k v1 t1) in (let TMP_27
+\def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
+\Rightarrow False | (THead _ _ _) \Rightarrow True])) in (let TMP_28 \def
+(TSort n1) in (let H2 \def (eq_ind T TMP_26 TMP_27 I TMP_28 H1) in (let
+TMP_31 \def (\lambda (n2: nat).(let TMP_29 \def (THead k v2 t2) in (let
+TMP_30 \def (TSort n2) in (eq T TMP_29 TMP_30)))) in (let TMP_32 \def (ex nat
+TMP_31) in (False_ind TMP_32 H2))))))))))))) in (iso_ind TMP_8 TMP_17 TMP_25
+TMP_33 y u2 H0))))))) in (insert_eq T TMP_1 TMP_2 TMP_5 TMP_34 H))))))).
theorem iso_gen_lref:
\forall (u2: T).(\forall (n1: nat).((iso (TLRef n1) u2) \to (ex nat (\lambda
(n2: nat).(eq T u2 (TLRef n2))))))
\def
- \lambda (u2: T).(\lambda (n1: nat).(\lambda (H: (iso (TLRef n1)
-u2)).(insert_eq T (TLRef n1) (\lambda (t: T).(iso t u2)) (\lambda (_: T).(ex
-nat (\lambda (n2: nat).(eq T u2 (TLRef n2))))) (\lambda (y: T).(\lambda (H0:
-(iso y u2)).(iso_ind (\lambda (t: T).(\lambda (t0: T).((eq T t (TLRef n1))
-\to (ex nat (\lambda (n2: nat).(eq T t0 (TLRef n2))))))) (\lambda (n0:
-nat).(\lambda (n2: nat).(\lambda (H1: (eq T (TSort n0) (TLRef n1))).(let H2
-\def (eq_ind T (TSort n0) (\lambda (ee: T).(match ee in T return (\lambda (_:
-T).Prop) with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False |
-(THead _ _ _) \Rightarrow False])) I (TLRef n1) H1) in (False_ind (ex nat
-(\lambda (n3: nat).(eq T (TSort n2) (TLRef n3)))) H2))))) (\lambda (i1:
-nat).(\lambda (i2: nat).(\lambda (H1: (eq T (TLRef i1) (TLRef n1))).(let H2
-\def (f_equal T nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat)
-with [(TSort _) \Rightarrow i1 | (TLRef n) \Rightarrow n | (THead _ _ _)
-\Rightarrow i1])) (TLRef i1) (TLRef n1) H1) in (ex_intro nat (\lambda (n2:
-nat).(eq T (TLRef i2) (TLRef n2))) i2 (refl_equal T (TLRef i2))))))) (\lambda
-(v1: T).(\lambda (v2: T).(\lambda (t1: T).(\lambda (t2: T).(\lambda (k:
-K).(\lambda (H1: (eq T (THead k v1 t1) (TLRef n1))).(let H2 \def (eq_ind T
-(THead k v1 t1) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop)
-with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _
-_) \Rightarrow True])) I (TLRef n1) H1) in (False_ind (ex nat (\lambda (n2:
-nat).(eq T (THead k v2 t2) (TLRef n2)))) H2)))))))) y u2 H0))) H))).
-(* COMMENTS
-Initial nodes: 321
-END *)
+ \lambda (u2: T).(\lambda (n1: nat).(\lambda (H: (iso (TLRef n1) u2)).(let
+TMP_1 \def (TLRef n1) in (let TMP_2 \def (\lambda (t: T).(iso t u2)) in (let
+TMP_5 \def (\lambda (_: T).(let TMP_4 \def (\lambda (n2: nat).(let TMP_3 \def
+(TLRef n2) in (eq T u2 TMP_3))) in (ex nat TMP_4))) in (let TMP_34 \def
+(\lambda (y: T).(\lambda (H0: (iso y u2)).(let TMP_8 \def (\lambda (t:
+T).(\lambda (t0: T).((eq T t (TLRef n1)) \to (let TMP_7 \def (\lambda (n2:
+nat).(let TMP_6 \def (TLRef n2) in (eq T t0 TMP_6))) in (ex nat TMP_7))))) in
+(let TMP_16 \def (\lambda (n0: nat).(\lambda (n2: nat).(\lambda (H1: (eq T
+(TSort n0) (TLRef n1))).(let TMP_9 \def (TSort n0) in (let TMP_10 \def
+(\lambda (ee: T).(match ee with [(TSort _) \Rightarrow True | (TLRef _)
+\Rightarrow False | (THead _ _ _) \Rightarrow False])) in (let TMP_11 \def
+(TLRef n1) in (let H2 \def (eq_ind T TMP_9 TMP_10 I TMP_11 H1) in (let TMP_14
+\def (\lambda (n3: nat).(let TMP_12 \def (TSort n2) in (let TMP_13 \def
+(TLRef n3) in (eq T TMP_12 TMP_13)))) in (let TMP_15 \def (ex nat TMP_14) in
+(False_ind TMP_15 H2)))))))))) in (let TMP_25 \def (\lambda (i1:
+nat).(\lambda (i2: nat).(\lambda (H1: (eq T (TLRef i1) (TLRef n1))).(let
+TMP_17 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow i1 | (TLRef
+n) \Rightarrow n | (THead _ _ _) \Rightarrow i1])) in (let TMP_18 \def (TLRef
+i1) in (let TMP_19 \def (TLRef n1) in (let H2 \def (f_equal T nat TMP_17
+TMP_18 TMP_19 H1) in (let TMP_22 \def (\lambda (n2: nat).(let TMP_20 \def
+(TLRef i2) in (let TMP_21 \def (TLRef n2) in (eq T TMP_20 TMP_21)))) in (let
+TMP_23 \def (TLRef i2) in (let TMP_24 \def (refl_equal T TMP_23) in (ex_intro
+nat TMP_22 i2 TMP_24))))))))))) in (let TMP_33 \def (\lambda (v1: T).(\lambda
+(v2: T).(\lambda (t1: T).(\lambda (t2: T).(\lambda (k: K).(\lambda (H1: (eq T
+(THead k v1 t1) (TLRef n1))).(let TMP_26 \def (THead k v1 t1) in (let TMP_27
+\def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
+\Rightarrow False | (THead _ _ _) \Rightarrow True])) in (let TMP_28 \def
+(TLRef n1) in (let H2 \def (eq_ind T TMP_26 TMP_27 I TMP_28 H1) in (let
+TMP_31 \def (\lambda (n2: nat).(let TMP_29 \def (THead k v2 t2) in (let
+TMP_30 \def (TLRef n2) in (eq T TMP_29 TMP_30)))) in (let TMP_32 \def (ex nat
+TMP_31) in (False_ind TMP_32 H2))))))))))))) in (iso_ind TMP_8 TMP_16 TMP_25
+TMP_33 y u2 H0))))))) in (insert_eq T TMP_1 TMP_2 TMP_5 TMP_34 H))))))).
theorem iso_gen_head:
\forall (k: K).(\forall (v1: T).(\forall (t1: T).(\forall (u2: T).((iso
(THead k v2 t2)))))))))
\def
\lambda (k: K).(\lambda (v1: T).(\lambda (t1: T).(\lambda (u2: T).(\lambda
-(H: (iso (THead k v1 t1) u2)).(insert_eq T (THead k v1 t1) (\lambda (t:
-T).(iso t u2)) (\lambda (_: T).(ex_2 T T (\lambda (v2: T).(\lambda (t2:
-T).(eq T u2 (THead k v2 t2)))))) (\lambda (y: T).(\lambda (H0: (iso y
-u2)).(iso_ind (\lambda (t: T).(\lambda (t0: T).((eq T t (THead k v1 t1)) \to
-(ex_2 T T (\lambda (v2: T).(\lambda (t2: T).(eq T t0 (THead k v2 t2))))))))
-(\lambda (n1: nat).(\lambda (n2: nat).(\lambda (H1: (eq T (TSort n1) (THead k
-v1 t1))).(let H2 \def (eq_ind T (TSort n1) (\lambda (ee: T).(match ee in T
-return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow True | (TLRef _)
-\Rightarrow False | (THead _ _ _) \Rightarrow False])) I (THead k v1 t1) H1)
-in (False_ind (ex_2 T T (\lambda (v2: T).(\lambda (t2: T).(eq T (TSort n2)
-(THead k v2 t2))))) H2))))) (\lambda (i1: nat).(\lambda (i2: nat).(\lambda
-(H1: (eq T (TLRef i1) (THead k v1 t1))).(let H2 \def (eq_ind T (TLRef i1)
-(\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _)
-\Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow
-False])) I (THead k v1 t1) H1) in (False_ind (ex_2 T T (\lambda (v2:
-T).(\lambda (t2: T).(eq T (TLRef i2) (THead k v2 t2))))) H2))))) (\lambda
-(v0: T).(\lambda (v2: T).(\lambda (t0: T).(\lambda (t2: T).(\lambda (k0:
-K).(\lambda (H1: (eq T (THead k0 v0 t0) (THead k v1 t1))).(let H2 \def
-(f_equal T K (\lambda (e: T).(match e in T return (\lambda (_: T).K) with
-[(TSort _) \Rightarrow k0 | (TLRef _) \Rightarrow k0 | (THead k1 _ _)
-\Rightarrow k1])) (THead k0 v0 t0) (THead k v1 t1) H1) in ((let H3 \def
-(f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with
+(H: (iso (THead k v1 t1) u2)).(let TMP_1 \def (THead k v1 t1) in (let TMP_2
+\def (\lambda (t: T).(iso t u2)) in (let TMP_5 \def (\lambda (_: T).(let
+TMP_4 \def (\lambda (v2: T).(\lambda (t2: T).(let TMP_3 \def (THead k v2 t2)
+in (eq T u2 TMP_3)))) in (ex_2 T T TMP_4))) in (let TMP_47 \def (\lambda (y:
+T).(\lambda (H0: (iso y u2)).(let TMP_8 \def (\lambda (t: T).(\lambda (t0:
+T).((eq T t (THead k v1 t1)) \to (let TMP_7 \def (\lambda (v2: T).(\lambda
+(t2: T).(let TMP_6 \def (THead k v2 t2) in (eq T t0 TMP_6)))) in (ex_2 T T
+TMP_7))))) in (let TMP_16 \def (\lambda (n1: nat).(\lambda (n2: nat).(\lambda
+(H1: (eq T (TSort n1) (THead k v1 t1))).(let TMP_9 \def (TSort n1) in (let
+TMP_10 \def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow True |
+(TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow False])) in (let
+TMP_11 \def (THead k v1 t1) in (let H2 \def (eq_ind T TMP_9 TMP_10 I TMP_11
+H1) in (let TMP_14 \def (\lambda (v2: T).(\lambda (t2: T).(let TMP_12 \def
+(TSort n2) in (let TMP_13 \def (THead k v2 t2) in (eq T TMP_12 TMP_13))))) in
+(let TMP_15 \def (ex_2 T T TMP_14) in (False_ind TMP_15 H2)))))))))) in (let
+TMP_24 \def (\lambda (i1: nat).(\lambda (i2: nat).(\lambda (H1: (eq T (TLRef
+i1) (THead k v1 t1))).(let TMP_17 \def (TLRef i1) in (let TMP_18 \def
+(\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
+\Rightarrow True | (THead _ _ _) \Rightarrow False])) in (let TMP_19 \def
+(THead k v1 t1) in (let H2 \def (eq_ind T TMP_17 TMP_18 I TMP_19 H1) in (let
+TMP_22 \def (\lambda (v2: T).(\lambda (t2: T).(let TMP_20 \def (TLRef i2) in
+(let TMP_21 \def (THead k v2 t2) in (eq T TMP_20 TMP_21))))) in (let TMP_23
+\def (ex_2 T T TMP_22) in (False_ind TMP_23 H2)))))))))) in (let TMP_46 \def
+(\lambda (v0: T).(\lambda (v2: T).(\lambda (t0: T).(\lambda (t2: T).(\lambda
+(k0: K).(\lambda (H1: (eq T (THead k0 v0 t0) (THead k v1 t1))).(let TMP_25
+\def (\lambda (e: T).(match e with [(TSort _) \Rightarrow k0 | (TLRef _)
+\Rightarrow k0 | (THead k1 _ _) \Rightarrow k1])) in (let TMP_26 \def (THead
+k0 v0 t0) in (let TMP_27 \def (THead k v1 t1) in (let H2 \def (f_equal T K
+TMP_25 TMP_26 TMP_27 H1) in (let TMP_28 \def (\lambda (e: T).(match e with
[(TSort _) \Rightarrow v0 | (TLRef _) \Rightarrow v0 | (THead _ t _)
-\Rightarrow t])) (THead k0 v0 t0) (THead k v1 t1) H1) in ((let H4 \def
-(f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with
-[(TSort _) \Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t)
-\Rightarrow t])) (THead k0 v0 t0) (THead k v1 t1) H1) in (\lambda (_: (eq T
-v0 v1)).(\lambda (H6: (eq K k0 k)).(eq_ind_r K k (\lambda (k1: K).(ex_2 T T
-(\lambda (v3: T).(\lambda (t3: T).(eq T (THead k1 v2 t2) (THead k v3 t3))))))
-(ex_2_intro T T (\lambda (v3: T).(\lambda (t3: T).(eq T (THead k v2 t2)
-(THead k v3 t3)))) v2 t2 (refl_equal T (THead k v2 t2))) k0 H6)))) H3))
-H2)))))))) y u2 H0))) H))))).
-(* COMMENTS
-Initial nodes: 545
-END *)
+\Rightarrow t])) in (let TMP_29 \def (THead k0 v0 t0) in (let TMP_30 \def
+(THead k v1 t1) in (let H3 \def (f_equal T T TMP_28 TMP_29 TMP_30 H1) in (let
+TMP_31 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow t0 | (TLRef
+_) \Rightarrow t0 | (THead _ _ t) \Rightarrow t])) in (let TMP_32 \def (THead
+k0 v0 t0) in (let TMP_33 \def (THead k v1 t1) in (let H4 \def (f_equal T T
+TMP_31 TMP_32 TMP_33 H1) in (let TMP_44 \def (\lambda (_: (eq T v0
+v1)).(\lambda (H6: (eq K k0 k)).(let TMP_37 \def (\lambda (k1: K).(let TMP_36
+\def (\lambda (v3: T).(\lambda (t3: T).(let TMP_34 \def (THead k1 v2 t2) in
+(let TMP_35 \def (THead k v3 t3) in (eq T TMP_34 TMP_35))))) in (ex_2 T T
+TMP_36))) in (let TMP_40 \def (\lambda (v3: T).(\lambda (t3: T).(let TMP_38
+\def (THead k v2 t2) in (let TMP_39 \def (THead k v3 t3) in (eq T TMP_38
+TMP_39))))) in (let TMP_41 \def (THead k v2 t2) in (let TMP_42 \def
+(refl_equal T TMP_41) in (let TMP_43 \def (ex_2_intro T T TMP_40 v2 t2
+TMP_42) in (eq_ind_r K k TMP_37 TMP_43 k0 H6)))))))) in (let TMP_45 \def
+(TMP_44 H3) in (TMP_45 H2))))))))))))))))))))) in (iso_ind TMP_8 TMP_16
+TMP_24 TMP_46 y u2 H0))))))) in (insert_eq T TMP_1 TMP_2 TMP_5 TMP_47
+H))))))))).
theorem iso_flats_lref_bind_false:
\forall (f: F).(\forall (b: B).(\forall (i: nat).(\forall (v: T).(\forall
b) v t)) \to (\forall (P: Prop).P)))))))
\def
\lambda (f: F).(\lambda (b: B).(\lambda (i: nat).(\lambda (v: T).(\lambda
-(t: T).(\lambda (vs: TList).(TList_ind (\lambda (t0: TList).((iso (THeads
-(Flat f) t0 (TLRef i)) (THead (Bind b) v t)) \to (\forall (P: Prop).P)))
-(\lambda (H: (iso (TLRef i) (THead (Bind b) v t))).(\lambda (P: Prop).(let
-H_x \def (iso_gen_lref (THead (Bind b) v t) i H) in (let H0 \def H_x in
-(ex_ind nat (\lambda (n2: nat).(eq T (THead (Bind b) v t) (TLRef n2))) P
-(\lambda (x: nat).(\lambda (H1: (eq T (THead (Bind b) v t) (TLRef x))).(let
-H2 \def (eq_ind T (THead (Bind b) v t) (\lambda (ee: T).(match ee in T return
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TLRef x) H1) in
-(False_ind P H2)))) H0))))) (\lambda (t0: T).(\lambda (t1: TList).(\lambda
-(_: (((iso (THeads (Flat f) t1 (TLRef i)) (THead (Bind b) v t)) \to (\forall
-(P: Prop).P)))).(\lambda (H0: (iso (THead (Flat f) t0 (THeads (Flat f) t1
-(TLRef i))) (THead (Bind b) v t))).(\lambda (P: Prop).(let H_x \def
-(iso_gen_head (Flat f) t0 (THeads (Flat f) t1 (TLRef i)) (THead (Bind b) v t)
-H0) in (let H1 \def H_x in (ex_2_ind T T (\lambda (v2: T).(\lambda (t2:
-T).(eq T (THead (Bind b) v t) (THead (Flat f) v2 t2)))) P (\lambda (x0:
-T).(\lambda (x1: T).(\lambda (H2: (eq T (THead (Bind b) v t) (THead (Flat f)
-x0 x1))).(let H3 \def (eq_ind T (THead (Bind b) v t) (\lambda (ee: T).(match
-ee in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False |
-(TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow (match k in K return
-(\lambda (_: K).Prop) with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow
-False])])) I (THead (Flat f) x0 x1) H2) in (False_ind P H3))))) H1))))))))
-vs)))))).
-(* COMMENTS
-Initial nodes: 391
-END *)
+(t: T).(\lambda (vs: TList).(let TMP_1 \def (\lambda (t0: TList).((iso
+(THeads (Flat f) t0 (TLRef i)) (THead (Bind b) v t)) \to (\forall (P:
+Prop).P))) in (let TMP_13 \def (\lambda (H: (iso (TLRef i) (THead (Bind b) v
+t))).(\lambda (P: Prop).(let TMP_2 \def (Bind b) in (let TMP_3 \def (THead
+TMP_2 v t) in (let H_x \def (iso_gen_lref TMP_3 i H) in (let H0 \def H_x in
+(let TMP_7 \def (\lambda (n2: nat).(let TMP_4 \def (Bind b) in (let TMP_5
+\def (THead TMP_4 v t) in (let TMP_6 \def (TLRef n2) in (eq T TMP_5
+TMP_6))))) in (let TMP_12 \def (\lambda (x: nat).(\lambda (H1: (eq T (THead
+(Bind b) v t) (TLRef x))).(let TMP_8 \def (Bind b) in (let TMP_9 \def (THead
+TMP_8 v t) in (let TMP_10 \def (\lambda (ee: T).(match ee with [(TSort _)
+\Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow
+True])) in (let TMP_11 \def (TLRef x) in (let H2 \def (eq_ind T TMP_9 TMP_10
+I TMP_11 H1) in (False_ind P H2)))))))) in (ex_ind nat TMP_7 P TMP_12
+H0))))))))) in (let TMP_31 \def (\lambda (t0: T).(\lambda (t1:
+TList).(\lambda (_: (((iso (THeads (Flat f) t1 (TLRef i)) (THead (Bind b) v
+t)) \to (\forall (P: Prop).P)))).(\lambda (H0: (iso (THead (Flat f) t0
+(THeads (Flat f) t1 (TLRef i))) (THead (Bind b) v t))).(\lambda (P:
+Prop).(let TMP_14 \def (Flat f) in (let TMP_15 \def (Flat f) in (let TMP_16
+\def (TLRef i) in (let TMP_17 \def (THeads TMP_15 t1 TMP_16) in (let TMP_18
+\def (Bind b) in (let TMP_19 \def (THead TMP_18 v t) in (let H_x \def
+(iso_gen_head TMP_14 t0 TMP_17 TMP_19 H0) in (let H1 \def H_x in (let TMP_24
+\def (\lambda (v2: T).(\lambda (t2: T).(let TMP_20 \def (Bind b) in (let
+TMP_21 \def (THead TMP_20 v t) in (let TMP_22 \def (Flat f) in (let TMP_23
+\def (THead TMP_22 v2 t2) in (eq T TMP_21 TMP_23))))))) in (let TMP_30 \def
+(\lambda (x0: T).(\lambda (x1: T).(\lambda (H2: (eq T (THead (Bind b) v t)
+(THead (Flat f) x0 x1))).(let TMP_25 \def (Bind b) in (let TMP_26 \def (THead
+TMP_25 v t) in (let TMP_27 \def (\lambda (ee: T).(match ee with [(TSort _)
+\Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow
+(match k with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) in
+(let TMP_28 \def (Flat f) in (let TMP_29 \def (THead TMP_28 x0 x1) in (let H3
+\def (eq_ind T TMP_26 TMP_27 I TMP_29 H2) in (False_ind P H3)))))))))) in
+(ex_2_ind T T TMP_24 P TMP_30 H1)))))))))))))))) in (TList_ind TMP_1 TMP_13
+TMP_31 vs))))))))).
theorem iso_flats_flat_bind_false:
\forall (f1: F).(\forall (f2: F).(\forall (b: B).(\forall (v: T).(\forall
Prop).P)))))))))
\def
\lambda (f1: F).(\lambda (f2: F).(\lambda (b: B).(\lambda (v: T).(\lambda
-(v2: T).(\lambda (t: T).(\lambda (t2: T).(\lambda (vs: TList).(TList_ind
+(v2: T).(\lambda (t: T).(\lambda (t2: T).(\lambda (vs: TList).(let TMP_1 \def
(\lambda (t0: TList).((iso (THeads (Flat f1) t0 (THead (Flat f2) v2 t2))
-(THead (Bind b) v t)) \to (\forall (P: Prop).P))) (\lambda (H: (iso (THead
-(Flat f2) v2 t2) (THead (Bind b) v t))).(\lambda (P: Prop).(let H_x \def
-(iso_gen_head (Flat f2) v2 t2 (THead (Bind b) v t) H) in (let H0 \def H_x in
-(ex_2_ind T T (\lambda (v3: T).(\lambda (t3: T).(eq T (THead (Bind b) v t)
-(THead (Flat f2) v3 t3)))) P (\lambda (x0: T).(\lambda (x1: T).(\lambda (H1:
-(eq T (THead (Bind b) v t) (THead (Flat f2) x0 x1))).(let H2 \def (eq_ind T
-(THead (Bind b) v t) (\lambda (ee: T).(match ee in T return (\lambda (_:
-T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False |
-(THead k _ _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with
-[(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) I (THead (Flat
-f2) x0 x1) H1) in (False_ind P H2))))) H0))))) (\lambda (t0: T).(\lambda (t1:
-TList).(\lambda (_: (((iso (THeads (Flat f1) t1 (THead (Flat f2) v2 t2))
-(THead (Bind b) v t)) \to (\forall (P: Prop).P)))).(\lambda (H0: (iso (THead
-(Flat f1) t0 (THeads (Flat f1) t1 (THead (Flat f2) v2 t2))) (THead (Bind b) v
-t))).(\lambda (P: Prop).(let H_x \def (iso_gen_head (Flat f1) t0 (THeads
-(Flat f1) t1 (THead (Flat f2) v2 t2)) (THead (Bind b) v t) H0) in (let H1
-\def H_x in (ex_2_ind T T (\lambda (v3: T).(\lambda (t3: T).(eq T (THead
-(Bind b) v t) (THead (Flat f1) v3 t3)))) P (\lambda (x0: T).(\lambda (x1:
-T).(\lambda (H2: (eq T (THead (Bind b) v t) (THead (Flat f1) x0 x1))).(let H3
-\def (eq_ind T (THead (Bind b) v t) (\lambda (ee: T).(match ee in T return
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow False | (THead k _ _) \Rightarrow (match k in K return (\lambda
-(_: K).Prop) with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow
-False])])) I (THead (Flat f1) x0 x1) H2) in (False_ind P H3))))) H1))))))))
-vs)))))))).
-(* COMMENTS
-Initial nodes: 461
-END *)
+(THead (Bind b) v t)) \to (\forall (P: Prop).P))) in (let TMP_16 \def
+(\lambda (H: (iso (THead (Flat f2) v2 t2) (THead (Bind b) v t))).(\lambda (P:
+Prop).(let TMP_2 \def (Flat f2) in (let TMP_3 \def (Bind b) in (let TMP_4
+\def (THead TMP_3 v t) in (let H_x \def (iso_gen_head TMP_2 v2 t2 TMP_4 H) in
+(let H0 \def H_x in (let TMP_9 \def (\lambda (v3: T).(\lambda (t3: T).(let
+TMP_5 \def (Bind b) in (let TMP_6 \def (THead TMP_5 v t) in (let TMP_7 \def
+(Flat f2) in (let TMP_8 \def (THead TMP_7 v3 t3) in (eq T TMP_6 TMP_8)))))))
+in (let TMP_15 \def (\lambda (x0: T).(\lambda (x1: T).(\lambda (H1: (eq T
+(THead (Bind b) v t) (THead (Flat f2) x0 x1))).(let TMP_10 \def (Bind b) in
+(let TMP_11 \def (THead TMP_10 v t) in (let TMP_12 \def (\lambda (ee:
+T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False
+| (THead k _ _) \Rightarrow (match k with [(Bind _) \Rightarrow True | (Flat
+_) \Rightarrow False])])) in (let TMP_13 \def (Flat f2) in (let TMP_14 \def
+(THead TMP_13 x0 x1) in (let H2 \def (eq_ind T TMP_11 TMP_12 I TMP_14 H1) in
+(False_ind P H2)))))))))) in (ex_2_ind T T TMP_9 P TMP_15 H0)))))))))) in
+(let TMP_35 \def (\lambda (t0: T).(\lambda (t1: TList).(\lambda (_: (((iso
+(THeads (Flat f1) t1 (THead (Flat f2) v2 t2)) (THead (Bind b) v t)) \to
+(\forall (P: Prop).P)))).(\lambda (H0: (iso (THead (Flat f1) t0 (THeads (Flat
+f1) t1 (THead (Flat f2) v2 t2))) (THead (Bind b) v t))).(\lambda (P:
+Prop).(let TMP_17 \def (Flat f1) in (let TMP_18 \def (Flat f1) in (let TMP_19
+\def (Flat f2) in (let TMP_20 \def (THead TMP_19 v2 t2) in (let TMP_21 \def
+(THeads TMP_18 t1 TMP_20) in (let TMP_22 \def (Bind b) in (let TMP_23 \def
+(THead TMP_22 v t) in (let H_x \def (iso_gen_head TMP_17 t0 TMP_21 TMP_23 H0)
+in (let H1 \def H_x in (let TMP_28 \def (\lambda (v3: T).(\lambda (t3:
+T).(let TMP_24 \def (Bind b) in (let TMP_25 \def (THead TMP_24 v t) in (let
+TMP_26 \def (Flat f1) in (let TMP_27 \def (THead TMP_26 v3 t3) in (eq T
+TMP_25 TMP_27))))))) in (let TMP_34 \def (\lambda (x0: T).(\lambda (x1:
+T).(\lambda (H2: (eq T (THead (Bind b) v t) (THead (Flat f1) x0 x1))).(let
+TMP_29 \def (Bind b) in (let TMP_30 \def (THead TMP_29 v t) in (let TMP_31
+\def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
+\Rightarrow False | (THead k _ _) \Rightarrow (match k with [(Bind _)
+\Rightarrow True | (Flat _) \Rightarrow False])])) in (let TMP_32 \def (Flat
+f1) in (let TMP_33 \def (THead TMP_32 x0 x1) in (let H3 \def (eq_ind T TMP_30
+TMP_31 I TMP_33 H2) in (False_ind P H3)))))))))) in (ex_2_ind T T TMP_28 P
+TMP_34 H1))))))))))))))))) in (TList_ind TMP_1 TMP_16 TMP_35 vs))))))))))).
projects / helm.git / blobdiff