(* This file was automatically generated: do not edit *********************)
-include "Basic-1/csubt/defs.ma".
+include "basic_1/csubt/defs.ma".
-theorem csubt_gen_abbr:
+implied rec lemma csubt_ind (g: G) (P: (C \to (C \to Prop))) (f: (\forall (n:
+nat).(P (CSort n) (CSort n)))) (f0: (\forall (c1: C).(\forall (c2: C).((csubt
+g c1 c2) \to ((P c1 c2) \to (\forall (k: K).(\forall (u: T).(P (CHead c1 k u)
+(CHead c2 k u))))))))) (f1: (\forall (c1: C).(\forall (c2: C).((csubt g c1
+c2) \to ((P c1 c2) \to (\forall (b: B).((not (eq B b Void)) \to (\forall (u1:
+T).(\forall (u2: T).(P (CHead c1 (Bind Void) u1) (CHead c2 (Bind b)
+u2))))))))))) (f2: (\forall (c1: C).(\forall (c2: C).((csubt g c1 c2) \to ((P
+c1 c2) \to (\forall (u: T).(\forall (t: T).((ty3 g c1 u t) \to ((ty3 g c2 u
+t) \to (P (CHead c1 (Bind Abst) t) (CHead c2 (Bind Abbr) u))))))))))) (c: C)
+(c0: C) (c1: csubt g c c0) on c1: P c c0 \def match c1 with [(csubt_sort n)
+\Rightarrow (f n) | (csubt_head c2 c3 c4 k u) \Rightarrow (f0 c2 c3 c4
+((csubt_ind g P f f0 f1 f2) c2 c3 c4) k u) | (csubt_void c2 c3 c4 b n u1 u2)
+\Rightarrow (f1 c2 c3 c4 ((csubt_ind g P f f0 f1 f2) c2 c3 c4) b n u1 u2) |
+(csubt_abst c2 c3 c4 u t t0 t1) \Rightarrow (f2 c2 c3 c4 ((csubt_ind g P f f0
+f1 f2) c2 c3 c4) u t t0 t1)].
+
+lemma csubt_gen_abbr:
\forall (g: G).(\forall (e1: C).(\forall (c2: C).(\forall (v: T).((csubt g
(CHead e1 (Bind Abbr) v) c2) \to (ex2 C (\lambda (e2: C).(eq C c2 (CHead e2
(Bind Abbr) v))) (\lambda (e2: C).(csubt g e1 e2)))))))
C).(\lambda (c0: C).((eq C c (CHead e1 (Bind Abbr) v)) \to (ex2 C (\lambda
(e2: C).(eq C c0 (CHead e2 (Bind Abbr) v))) (\lambda (e2: C).(csubt g e1
e2)))))) (\lambda (n: nat).(\lambda (H1: (eq C (CSort n) (CHead e1 (Bind
-Abbr) v))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee in C
-return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _)
-\Rightarrow False])) I (CHead e1 (Bind Abbr) v) H1) in (False_ind (ex2 C
-(\lambda (e2: C).(eq C (CSort n) (CHead e2 (Bind Abbr) v))) (\lambda (e2:
-C).(csubt g e1 e2))) H2)))) (\lambda (c1: C).(\lambda (c3: C).(\lambda (H1:
-(csubt g c1 c3)).(\lambda (H2: (((eq C c1 (CHead e1 (Bind Abbr) v)) \to (ex2
-C (\lambda (e2: C).(eq C c3 (CHead e2 (Bind Abbr) v))) (\lambda (e2:
-C).(csubt g e1 e2)))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3: (eq C
-(CHead c1 k u) (CHead e1 (Bind Abbr) v))).(let H4 \def (f_equal C C (\lambda
-(e: C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c1
-| (CHead c _ _) \Rightarrow c])) (CHead c1 k u) (CHead e1 (Bind Abbr) v) H3)
-in ((let H5 \def (f_equal C K (\lambda (e: C).(match e in C return (\lambda
-(_: C).K) with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0]))
-(CHead c1 k u) (CHead e1 (Bind Abbr) v) H3) in ((let H6 \def (f_equal C T
-(\lambda (e: C).(match e in C return (\lambda (_: C).T) with [(CSort _)
-\Rightarrow u | (CHead _ _ t) \Rightarrow t])) (CHead c1 k u) (CHead e1 (Bind
-Abbr) v) H3) in (\lambda (H7: (eq K k (Bind Abbr))).(\lambda (H8: (eq C c1
-e1)).(eq_ind_r T v (\lambda (t: T).(ex2 C (\lambda (e2: C).(eq C (CHead c3 k
-t) (CHead e2 (Bind Abbr) v))) (\lambda (e2: C).(csubt g e1 e2)))) (eq_ind_r K
-(Bind Abbr) (\lambda (k0: K).(ex2 C (\lambda (e2: C).(eq C (CHead c3 k0 v)
-(CHead e2 (Bind Abbr) v))) (\lambda (e2: C).(csubt g e1 e2)))) (let H9 \def
-(eq_ind C c1 (\lambda (c: C).((eq C c (CHead e1 (Bind Abbr) v)) \to (ex2 C
-(\lambda (e2: C).(eq C c3 (CHead e2 (Bind Abbr) v))) (\lambda (e2: C).(csubt
-g e1 e2))))) H2 e1 H8) in (let H10 \def (eq_ind C c1 (\lambda (c: C).(csubt g
-c c3)) H1 e1 H8) in (ex_intro2 C (\lambda (e2: C).(eq C (CHead c3 (Bind Abbr)
-v) (CHead e2 (Bind Abbr) v))) (\lambda (e2: C).(csubt g e1 e2)) c3
-(refl_equal C (CHead c3 (Bind Abbr) v)) H10))) k H7) u H6)))) H5))
-H4))))))))) (\lambda (c1: C).(\lambda (c3: C).(\lambda (_: (csubt g c1
-c3)).(\lambda (_: (((eq C c1 (CHead e1 (Bind Abbr) v)) \to (ex2 C (\lambda
-(e2: C).(eq C c3 (CHead e2 (Bind Abbr) v))) (\lambda (e2: C).(csubt g e1
-e2)))))).(\lambda (b: B).(\lambda (_: (not (eq B b Void))).(\lambda (u1:
-T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c1 (Bind Void) u1) (CHead e1
-(Bind Abbr) v))).(let H5 \def (eq_ind C (CHead c1 (Bind Void) u1) (\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 b0) \Rightarrow (match b0 in B return (\lambda (_:
-B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow False | Void
-\Rightarrow True]) | (Flat _) \Rightarrow False])])) I (CHead e1 (Bind Abbr)
-v) H4) in (False_ind (ex2 C (\lambda (e2: C).(eq C (CHead c3 (Bind b) u2)
-(CHead e2 (Bind Abbr) v))) (\lambda (e2: C).(csubt g e1 e2))) H5)))))))))))
-(\lambda (c1: C).(\lambda (c3: C).(\lambda (_: (csubt g c1 c3)).(\lambda (_:
-(((eq C c1 (CHead e1 (Bind Abbr) v)) \to (ex2 C (\lambda (e2: C).(eq C c3
-(CHead e2 (Bind Abbr) v))) (\lambda (e2: C).(csubt g e1 e2)))))).(\lambda (u:
+Abbr) v))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee with
+[(CSort _) \Rightarrow True | (CHead _ _ _) \Rightarrow False])) I (CHead e1
+(Bind Abbr) v) H1) in (False_ind (ex2 C (\lambda (e2: C).(eq C (CSort n)
+(CHead e2 (Bind Abbr) v))) (\lambda (e2: C).(csubt g e1 e2))) H2)))) (\lambda
+(c1: C).(\lambda (c3: C).(\lambda (H1: (csubt g c1 c3)).(\lambda (H2: (((eq C
+c1 (CHead e1 (Bind Abbr) v)) \to (ex2 C (\lambda (e2: C).(eq C c3 (CHead e2
+(Bind Abbr) v))) (\lambda (e2: C).(csubt g e1 e2)))))).(\lambda (k:
+K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c1 k u) (CHead e1 (Bind Abbr)
+v))).(let H4 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow c1 | (CHead c _ _) \Rightarrow c])) (CHead c1 k u) (CHead e1
+(Bind Abbr) v) H3) in ((let H5 \def (f_equal C K (\lambda (e: C).(match e
+with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c1 k
+u) (CHead e1 (Bind Abbr) v) H3) in ((let H6 \def (f_equal C T (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t]))
+(CHead c1 k u) (CHead e1 (Bind Abbr) v) H3) in (\lambda (H7: (eq K k (Bind
+Abbr))).(\lambda (H8: (eq C c1 e1)).(eq_ind_r T v (\lambda (t: T).(ex2 C
+(\lambda (e2: C).(eq C (CHead c3 k t) (CHead e2 (Bind Abbr) v))) (\lambda
+(e2: C).(csubt g e1 e2)))) (eq_ind_r K (Bind Abbr) (\lambda (k0: K).(ex2 C
+(\lambda (e2: C).(eq C (CHead c3 k0 v) (CHead e2 (Bind Abbr) v))) (\lambda
+(e2: C).(csubt g e1 e2)))) (let H9 \def (eq_ind C c1 (\lambda (c: C).((eq C c
+(CHead e1 (Bind Abbr) v)) \to (ex2 C (\lambda (e2: C).(eq C c3 (CHead e2
+(Bind Abbr) v))) (\lambda (e2: C).(csubt g e1 e2))))) H2 e1 H8) in (let H10
+\def (eq_ind C c1 (\lambda (c: C).(csubt g c c3)) H1 e1 H8) in (ex_intro2 C
+(\lambda (e2: C).(eq C (CHead c3 (Bind Abbr) v) (CHead e2 (Bind Abbr) v)))
+(\lambda (e2: C).(csubt g e1 e2)) c3 (refl_equal C (CHead c3 (Bind Abbr) v))
+H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1: C).(\lambda (c3:
+C).(\lambda (_: (csubt g c1 c3)).(\lambda (_: (((eq C c1 (CHead e1 (Bind
+Abbr) v)) \to (ex2 C (\lambda (e2: C).(eq C c3 (CHead e2 (Bind Abbr) v)))
+(\lambda (e2: C).(csubt g e1 e2)))))).(\lambda (b: B).(\lambda (_: (not (eq B
+b Void))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c1
+(Bind Void) u1) (CHead e1 (Bind Abbr) v))).(let H5 \def (eq_ind C (CHead c1
+(Bind Void) u1) (\lambda (ee: C).(match ee with [(CSort _) \Rightarrow False
+| (CHead _ k _) \Rightarrow (match k with [(Bind b0) \Rightarrow (match b0
+with [Abbr \Rightarrow False | Abst \Rightarrow False | Void \Rightarrow
+True]) | (Flat _) \Rightarrow False])])) I (CHead e1 (Bind Abbr) v) H4) in
+(False_ind (ex2 C (\lambda (e2: C).(eq C (CHead c3 (Bind b) u2) (CHead e2
+(Bind Abbr) v))) (\lambda (e2: C).(csubt g e1 e2))) H5))))))))))) (\lambda
+(c1: C).(\lambda (c3: C).(\lambda (_: (csubt g c1 c3)).(\lambda (_: (((eq C
+c1 (CHead e1 (Bind Abbr) v)) \to (ex2 C (\lambda (e2: C).(eq C c3 (CHead e2
+(Bind Abbr) v))) (\lambda (e2: C).(csubt g e1 e2)))))).(\lambda (u:
T).(\lambda (t: T).(\lambda (_: (ty3 g c1 u t)).(\lambda (_: (ty3 g c3 u
t)).(\lambda (H5: (eq C (CHead c1 (Bind Abst) t) (CHead e1 (Bind Abbr)
v))).(let H6 \def (eq_ind C (CHead c1 (Bind Abst) t) (\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 e1 (Bind Abbr) v) H5) in (False_ind (ex2 C
-(\lambda (e2: C).(eq C (CHead c3 (Bind Abbr) u) (CHead e2 (Bind Abbr) v)))
-(\lambda (e2: C).(csubt g e1 e2))) H6))))))))))) y c2 H0))) H))))).
-(* COMMENTS
-Initial nodes: 1111
-END *)
+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 e1 (Bind Abbr) v) H5) in (False_ind (ex2 C (\lambda (e2: C).(eq C
+(CHead c3 (Bind Abbr) u) (CHead e2 (Bind Abbr) v))) (\lambda (e2: C).(csubt g
+e1 e2))) H6))))))))))) y c2 H0))) H))))).
-theorem csubt_gen_abst:
+lemma csubt_gen_abst:
\forall (g: G).(\forall (e1: C).(\forall (c2: C).(\forall (v1: T).((csubt g
(CHead e1 (Bind Abst) v1) c2) \to (or (ex2 C (\lambda (e2: C).(eq C c2 (CHead
e2 (Bind Abst) v1))) (\lambda (e2: C).(csubt g e1 e2))) (ex4_2 C T (\lambda
e2))) (\lambda (_: C).(\lambda (v2: T).(ty3 g e1 v2 v1))) (\lambda (e2:
C).(\lambda (v2: T).(ty3 g e2 v2 v1)))))))) (\lambda (n: nat).(\lambda (H1:
(eq C (CSort n) (CHead e1 (Bind Abst) v1))).(let H2 \def (eq_ind C (CSort n)
-(\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _)
-\Rightarrow True | (CHead _ _ _) \Rightarrow False])) I (CHead e1 (Bind Abst)
-v1) H1) in (False_ind (or (ex2 C (\lambda (e2: C).(eq C (CSort n) (CHead e2
-(Bind Abst) v1))) (\lambda (e2: C).(csubt g e1 e2))) (ex4_2 C T (\lambda (e2:
-C).(\lambda (v2: T).(eq C (CSort n) (CHead e2 (Bind Abbr) v2)))) (\lambda
-(e2: C).(\lambda (_: T).(csubt g e1 e2))) (\lambda (_: C).(\lambda (v2:
-T).(ty3 g e1 v2 v1))) (\lambda (e2: C).(\lambda (v2: T).(ty3 g e2 v2 v1)))))
-H2)))) (\lambda (c1: C).(\lambda (c3: C).(\lambda (H1: (csubt g c1
-c3)).(\lambda (H2: (((eq C c1 (CHead e1 (Bind Abst) v1)) \to (or (ex2 C
-(\lambda (e2: C).(eq C c3 (CHead e2 (Bind Abst) v1))) (\lambda (e2: C).(csubt
-g e1 e2))) (ex4_2 C T (\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2
-(Bind Abbr) v2)))) (\lambda (e2: C).(\lambda (_: T).(csubt g e1 e2)))
-(\lambda (_: C).(\lambda (v2: T).(ty3 g e1 v2 v1))) (\lambda (e2: C).(\lambda
-(v2: T).(ty3 g e2 v2 v1)))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3:
-(eq C (CHead c1 k u) (CHead e1 (Bind Abst) v1))).(let H4 \def (f_equal C C
-(\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
-\Rightarrow c1 | (CHead c _ _) \Rightarrow c])) (CHead c1 k u) (CHead e1
-(Bind Abst) v1) H3) in ((let H5 \def (f_equal C K (\lambda (e: C).(match e in
-C return (\lambda (_: C).K) with [(CSort _) \Rightarrow k | (CHead _ k0 _)
-\Rightarrow k0])) (CHead c1 k u) (CHead e1 (Bind Abst) v1) H3) in ((let H6
-\def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T)
-with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t])) (CHead c1 k u)
-(CHead e1 (Bind Abst) v1) H3) in (\lambda (H7: (eq K k (Bind Abst))).(\lambda
-(H8: (eq C c1 e1)).(eq_ind_r T v1 (\lambda (t: T).(or (ex2 C (\lambda (e2:
-C).(eq C (CHead c3 k t) (CHead e2 (Bind Abst) v1))) (\lambda (e2: C).(csubt g
-e1 e2))) (ex4_2 C T (\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 k t)
-(CHead e2 (Bind Abbr) v2)))) (\lambda (e2: C).(\lambda (_: T).(csubt g e1
-e2))) (\lambda (_: C).(\lambda (v2: T).(ty3 g e1 v2 v1))) (\lambda (e2:
-C).(\lambda (v2: T).(ty3 g e2 v2 v1)))))) (eq_ind_r K (Bind Abst) (\lambda
-(k0: K).(or (ex2 C (\lambda (e2: C).(eq C (CHead c3 k0 v1) (CHead e2 (Bind
-Abst) v1))) (\lambda (e2: C).(csubt g e1 e2))) (ex4_2 C T (\lambda (e2:
-C).(\lambda (v2: T).(eq C (CHead c3 k0 v1) (CHead e2 (Bind Abbr) v2))))
-(\lambda (e2: C).(\lambda (_: T).(csubt g e1 e2))) (\lambda (_: C).(\lambda
-(v2: T).(ty3 g e1 v2 v1))) (\lambda (e2: C).(\lambda (v2: T).(ty3 g e2 v2
-v1)))))) (let H9 \def (eq_ind C c1 (\lambda (c: C).((eq C c (CHead e1 (Bind
-Abst) v1)) \to (or (ex2 C (\lambda (e2: C).(eq C c3 (CHead e2 (Bind Abst)
-v1))) (\lambda (e2: C).(csubt g e1 e2))) (ex4_2 C T (\lambda (e2: C).(\lambda
-(v2: T).(eq C c3 (CHead e2 (Bind Abbr) v2)))) (\lambda (e2: C).(\lambda (_:
+(\lambda (ee: C).(match ee with [(CSort _) \Rightarrow True | (CHead _ _ _)
+\Rightarrow False])) I (CHead e1 (Bind Abst) v1) H1) in (False_ind (or (ex2 C
+(\lambda (e2: C).(eq C (CSort n) (CHead e2 (Bind Abst) v1))) (\lambda (e2:
+C).(csubt g e1 e2))) (ex4_2 C T (\lambda (e2: C).(\lambda (v2: T).(eq C
+(CSort n) (CHead e2 (Bind Abbr) v2)))) (\lambda (e2: C).(\lambda (_:
T).(csubt g e1 e2))) (\lambda (_: C).(\lambda (v2: T).(ty3 g e1 v2 v1)))
-(\lambda (e2: C).(\lambda (v2: T).(ty3 g e2 v2 v1))))))) H2 e1 H8) in (let
-H10 \def (eq_ind C c1 (\lambda (c: C).(csubt g c c3)) H1 e1 H8) in (or_introl
-(ex2 C (\lambda (e2: C).(eq C (CHead c3 (Bind Abst) v1) (CHead e2 (Bind Abst)
-v1))) (\lambda (e2: C).(csubt g e1 e2))) (ex4_2 C T (\lambda (e2: C).(\lambda
-(v2: T).(eq C (CHead c3 (Bind Abst) v1) (CHead e2 (Bind Abbr) v2)))) (\lambda
-(e2: C).(\lambda (_: T).(csubt g e1 e2))) (\lambda (_: C).(\lambda (v2:
-T).(ty3 g e1 v2 v1))) (\lambda (e2: C).(\lambda (v2: T).(ty3 g e2 v2 v1))))
-(ex_intro2 C (\lambda (e2: C).(eq C (CHead c3 (Bind Abst) v1) (CHead e2 (Bind
-Abst) v1))) (\lambda (e2: C).(csubt g e1 e2)) c3 (refl_equal C (CHead c3
-(Bind Abst) v1)) H10)))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
-C).(\lambda (c3: C).(\lambda (_: (csubt g c1 c3)).(\lambda (_: (((eq C c1
+(\lambda (e2: C).(\lambda (v2: T).(ty3 g e2 v2 v1))))) H2)))) (\lambda (c1:
+C).(\lambda (c3: C).(\lambda (H1: (csubt g c1 c3)).(\lambda (H2: (((eq C c1
(CHead e1 (Bind Abst) v1)) \to (or (ex2 C (\lambda (e2: C).(eq C c3 (CHead e2
(Bind Abst) v1))) (\lambda (e2: C).(csubt g e1 e2))) (ex4_2 C T (\lambda (e2:
C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind Abbr) v2)))) (\lambda (e2:
C).(\lambda (_: T).(csubt g e1 e2))) (\lambda (_: C).(\lambda (v2: T).(ty3 g
e1 v2 v1))) (\lambda (e2: C).(\lambda (v2: T).(ty3 g e2 v2
-v1)))))))).(\lambda (b: B).(\lambda (_: (not (eq B b Void))).(\lambda (u1:
-T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c1 (Bind Void) u1) (CHead e1
-(Bind Abst) v1))).(let H5 \def (eq_ind C (CHead c1 (Bind Void) u1) (\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 b0) \Rightarrow (match b0 in B return (\lambda (_:
-B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow False | Void
-\Rightarrow True]) | (Flat _) \Rightarrow False])])) I (CHead e1 (Bind Abst)
-v1) H4) in (False_ind (or (ex2 C (\lambda (e2: C).(eq C (CHead c3 (Bind b)
-u2) (CHead e2 (Bind Abst) v1))) (\lambda (e2: C).(csubt g e1 e2))) (ex4_2 C T
-(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 (Bind b) u2) (CHead e2
+v1)))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c1 k u)
+(CHead e1 (Bind Abst) v1))).(let H4 \def (f_equal C C (\lambda (e: C).(match
+e with [(CSort _) \Rightarrow c1 | (CHead c _ _) \Rightarrow c])) (CHead c1 k
+u) (CHead e1 (Bind Abst) v1) H3) in ((let H5 \def (f_equal C K (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0]))
+(CHead c1 k u) (CHead e1 (Bind Abst) v1) H3) in ((let H6 \def (f_equal C T
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow u | (CHead _ _ t)
+\Rightarrow t])) (CHead c1 k u) (CHead e1 (Bind Abst) v1) H3) in (\lambda
+(H7: (eq K k (Bind Abst))).(\lambda (H8: (eq C c1 e1)).(eq_ind_r T v1
+(\lambda (t: T).(or (ex2 C (\lambda (e2: C).(eq C (CHead c3 k t) (CHead e2
+(Bind Abst) v1))) (\lambda (e2: C).(csubt g e1 e2))) (ex4_2 C T (\lambda (e2:
+C).(\lambda (v2: T).(eq C (CHead c3 k t) (CHead e2 (Bind Abbr) v2))))
+(\lambda (e2: C).(\lambda (_: T).(csubt g e1 e2))) (\lambda (_: C).(\lambda
+(v2: T).(ty3 g e1 v2 v1))) (\lambda (e2: C).(\lambda (v2: T).(ty3 g e2 v2
+v1)))))) (eq_ind_r K (Bind Abst) (\lambda (k0: K).(or (ex2 C (\lambda (e2:
+C).(eq C (CHead c3 k0 v1) (CHead e2 (Bind Abst) v1))) (\lambda (e2: C).(csubt
+g e1 e2))) (ex4_2 C T (\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 k0
+v1) (CHead e2 (Bind Abbr) v2)))) (\lambda (e2: C).(\lambda (_: T).(csubt g e1
+e2))) (\lambda (_: C).(\lambda (v2: T).(ty3 g e1 v2 v1))) (\lambda (e2:
+C).(\lambda (v2: T).(ty3 g e2 v2 v1)))))) (let H9 \def (eq_ind C c1 (\lambda
+(c: C).((eq C c (CHead e1 (Bind Abst) v1)) \to (or (ex2 C (\lambda (e2:
+C).(eq C c3 (CHead e2 (Bind Abst) v1))) (\lambda (e2: C).(csubt g e1 e2)))
+(ex4_2 C T (\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind Abbr)
+v2)))) (\lambda (e2: C).(\lambda (_: T).(csubt g e1 e2))) (\lambda (_:
+C).(\lambda (v2: T).(ty3 g e1 v2 v1))) (\lambda (e2: C).(\lambda (v2: T).(ty3
+g e2 v2 v1))))))) H2 e1 H8) in (let H10 \def (eq_ind C c1 (\lambda (c:
+C).(csubt g c c3)) H1 e1 H8) in (or_introl (ex2 C (\lambda (e2: C).(eq C
+(CHead c3 (Bind Abst) v1) (CHead e2 (Bind Abst) v1))) (\lambda (e2: C).(csubt
+g e1 e2))) (ex4_2 C T (\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 (Bind
+Abst) v1) (CHead e2 (Bind Abbr) v2)))) (\lambda (e2: C).(\lambda (_:
+T).(csubt g e1 e2))) (\lambda (_: C).(\lambda (v2: T).(ty3 g e1 v2 v1)))
+(\lambda (e2: C).(\lambda (v2: T).(ty3 g e2 v2 v1)))) (ex_intro2 C (\lambda
+(e2: C).(eq C (CHead c3 (Bind Abst) v1) (CHead e2 (Bind Abst) v1))) (\lambda
+(e2: C).(csubt g e1 e2)) c3 (refl_equal C (CHead c3 (Bind Abst) v1)) H10))))
+k H7) u H6)))) H5)) H4))))))))) (\lambda (c1: C).(\lambda (c3: C).(\lambda
+(_: (csubt g c1 c3)).(\lambda (_: (((eq C c1 (CHead e1 (Bind Abst) v1)) \to
+(or (ex2 C (\lambda (e2: C).(eq C c3 (CHead e2 (Bind Abst) v1))) (\lambda
+(e2: C).(csubt g e1 e2))) (ex4_2 C T (\lambda (e2: C).(\lambda (v2: T).(eq C
+c3 (CHead e2 (Bind Abbr) v2)))) (\lambda (e2: C).(\lambda (_: T).(csubt g e1
+e2))) (\lambda (_: C).(\lambda (v2: T).(ty3 g e1 v2 v1))) (\lambda (e2:
+C).(\lambda (v2: T).(ty3 g e2 v2 v1)))))))).(\lambda (b: B).(\lambda (_: (not
+(eq B b Void))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead
+c1 (Bind Void) u1) (CHead e1 (Bind Abst) v1))).(let H5 \def (eq_ind C (CHead
+c1 (Bind Void) u1) (\lambda (ee: C).(match ee with [(CSort _) \Rightarrow
+False | (CHead _ k _) \Rightarrow (match k with [(Bind b0) \Rightarrow (match
+b0 with [Abbr \Rightarrow False | Abst \Rightarrow False | Void \Rightarrow
+True]) | (Flat _) \Rightarrow False])])) I (CHead e1 (Bind Abst) v1) H4) in
+(False_ind (or (ex2 C (\lambda (e2: C).(eq C (CHead c3 (Bind b) u2) (CHead e2
+(Bind Abst) v1))) (\lambda (e2: C).(csubt g e1 e2))) (ex4_2 C T (\lambda (e2:
+C).(\lambda (v2: T).(eq C (CHead c3 (Bind b) u2) (CHead e2 (Bind Abbr) v2))))
+(\lambda (e2: C).(\lambda (_: T).(csubt g e1 e2))) (\lambda (_: C).(\lambda
+(v2: T).(ty3 g e1 v2 v1))) (\lambda (e2: C).(\lambda (v2: T).(ty3 g e2 v2
+v1))))) H5))))))))))) (\lambda (c1: C).(\lambda (c3: C).(\lambda (H1: (csubt
+g c1 c3)).(\lambda (H2: (((eq C c1 (CHead e1 (Bind Abst) v1)) \to (or (ex2 C
+(\lambda (e2: C).(eq C c3 (CHead e2 (Bind Abst) v1))) (\lambda (e2: C).(csubt
+g e1 e2))) (ex4_2 C T (\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2
(Bind Abbr) v2)))) (\lambda (e2: C).(\lambda (_: T).(csubt g e1 e2)))
(\lambda (_: C).(\lambda (v2: T).(ty3 g e1 v2 v1))) (\lambda (e2: C).(\lambda
-(v2: T).(ty3 g e2 v2 v1))))) H5))))))))))) (\lambda (c1: C).(\lambda (c3:
-C).(\lambda (H1: (csubt g c1 c3)).(\lambda (H2: (((eq C c1 (CHead e1 (Bind
-Abst) v1)) \to (or (ex2 C (\lambda (e2: C).(eq C c3 (CHead e2 (Bind Abst)
-v1))) (\lambda (e2: C).(csubt g e1 e2))) (ex4_2 C T (\lambda (e2: C).(\lambda
-(v2: T).(eq C c3 (CHead e2 (Bind Abbr) v2)))) (\lambda (e2: C).(\lambda (_:
-T).(csubt g e1 e2))) (\lambda (_: C).(\lambda (v2: T).(ty3 g e1 v2 v1)))
-(\lambda (e2: C).(\lambda (v2: T).(ty3 g e2 v2 v1)))))))).(\lambda (u:
-T).(\lambda (t: T).(\lambda (H3: (ty3 g c1 u t)).(\lambda (H4: (ty3 g c3 u
-t)).(\lambda (H5: (eq C (CHead c1 (Bind Abst) t) (CHead e1 (Bind Abst)
-v1))).(let H6 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda
-(_: C).C) with [(CSort _) \Rightarrow c1 | (CHead c _ _) \Rightarrow c]))
-(CHead c1 (Bind Abst) t) (CHead e1 (Bind Abst) v1) H5) in ((let H7 \def
-(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with
-[(CSort _) \Rightarrow t | (CHead _ _ t0) \Rightarrow t0])) (CHead c1 (Bind
-Abst) t) (CHead e1 (Bind Abst) v1) H5) in (\lambda (H8: (eq C c1 e1)).(let H9
-\def (eq_ind T t (\lambda (t0: T).(ty3 g c3 u t0)) H4 v1 H7) in (let H10 \def
-(eq_ind T t (\lambda (t0: T).(ty3 g c1 u t0)) H3 v1 H7) in (let H11 \def
-(eq_ind C c1 (\lambda (c: C).(ty3 g c u v1)) H10 e1 H8) in (let H12 \def
-(eq_ind C c1 (\lambda (c: C).((eq C c (CHead e1 (Bind Abst) v1)) \to (or (ex2
-C (\lambda (e2: C).(eq C c3 (CHead e2 (Bind Abst) v1))) (\lambda (e2:
-C).(csubt g e1 e2))) (ex4_2 C T (\lambda (e2: C).(\lambda (v2: T).(eq C c3
+(v2: T).(ty3 g e2 v2 v1)))))))).(\lambda (u: T).(\lambda (t: T).(\lambda (H3:
+(ty3 g c1 u t)).(\lambda (H4: (ty3 g c3 u t)).(\lambda (H5: (eq C (CHead c1
+(Bind Abst) t) (CHead e1 (Bind Abst) v1))).(let H6 \def (f_equal C C (\lambda
+(e: C).(match e with [(CSort _) \Rightarrow c1 | (CHead c _ _) \Rightarrow
+c])) (CHead c1 (Bind Abst) t) (CHead e1 (Bind Abst) v1) H5) in ((let H7 \def
+(f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow t | (CHead
+_ _ t0) \Rightarrow t0])) (CHead c1 (Bind Abst) t) (CHead e1 (Bind Abst) v1)
+H5) in (\lambda (H8: (eq C c1 e1)).(let H9 \def (eq_ind T t (\lambda (t0:
+T).(ty3 g c3 u t0)) H4 v1 H7) in (let H10 \def (eq_ind T t (\lambda (t0:
+T).(ty3 g c1 u t0)) H3 v1 H7) in (let H11 \def (eq_ind C c1 (\lambda (c:
+C).(ty3 g c u v1)) H10 e1 H8) in (let H12 \def (eq_ind C c1 (\lambda (c:
+C).((eq C c (CHead e1 (Bind Abst) v1)) \to (or (ex2 C (\lambda (e2: C).(eq C
+c3 (CHead e2 (Bind Abst) v1))) (\lambda (e2: C).(csubt g e1 e2))) (ex4_2 C T
+(\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind Abbr) v2))))
+(\lambda (e2: C).(\lambda (_: T).(csubt g e1 e2))) (\lambda (_: C).(\lambda
+(v2: T).(ty3 g e1 v2 v1))) (\lambda (e2: C).(\lambda (v2: T).(ty3 g e2 v2
+v1))))))) H2 e1 H8) in (let H13 \def (eq_ind C c1 (\lambda (c: C).(csubt g c
+c3)) H1 e1 H8) in (or_intror (ex2 C (\lambda (e2: C).(eq C (CHead c3 (Bind
+Abbr) u) (CHead e2 (Bind Abst) v1))) (\lambda (e2: C).(csubt g e1 e2)))
+(ex4_2 C T (\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 (Bind Abbr) u)
(CHead e2 (Bind Abbr) v2)))) (\lambda (e2: C).(\lambda (_: T).(csubt g e1
e2))) (\lambda (_: C).(\lambda (v2: T).(ty3 g e1 v2 v1))) (\lambda (e2:
-C).(\lambda (v2: T).(ty3 g e2 v2 v1))))))) H2 e1 H8) in (let H13 \def (eq_ind
-C c1 (\lambda (c: C).(csubt g c c3)) H1 e1 H8) in (or_intror (ex2 C (\lambda
-(e2: C).(eq C (CHead c3 (Bind Abbr) u) (CHead e2 (Bind Abst) v1))) (\lambda
-(e2: C).(csubt g e1 e2))) (ex4_2 C T (\lambda (e2: C).(\lambda (v2: T).(eq C
-(CHead c3 (Bind Abbr) u) (CHead e2 (Bind Abbr) v2)))) (\lambda (e2:
-C).(\lambda (_: T).(csubt g e1 e2))) (\lambda (_: C).(\lambda (v2: T).(ty3 g
-e1 v2 v1))) (\lambda (e2: C).(\lambda (v2: T).(ty3 g e2 v2 v1))))
-(ex4_2_intro C T (\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 (Bind
-Abbr) u) (CHead e2 (Bind Abbr) v2)))) (\lambda (e2: C).(\lambda (_: T).(csubt
-g e1 e2))) (\lambda (_: C).(\lambda (v2: T).(ty3 g e1 v2 v1))) (\lambda (e2:
-C).(\lambda (v2: T).(ty3 g e2 v2 v1))) c3 u (refl_equal C (CHead c3 (Bind
-Abbr) u)) H13 H11 H9))))))))) H6))))))))))) y c2 H0))) H))))).
-(* COMMENTS
-Initial nodes: 2362
-END *)
+C).(\lambda (v2: T).(ty3 g e2 v2 v1)))) (ex4_2_intro C T (\lambda (e2:
+C).(\lambda (v2: T).(eq C (CHead c3 (Bind Abbr) u) (CHead e2 (Bind Abbr)
+v2)))) (\lambda (e2: C).(\lambda (_: T).(csubt g e1 e2))) (\lambda (_:
+C).(\lambda (v2: T).(ty3 g e1 v2 v1))) (\lambda (e2: C).(\lambda (v2: T).(ty3
+g e2 v2 v1))) c3 u (refl_equal C (CHead c3 (Bind Abbr) u)) H13 H11
+H9))))))))) H6))))))))))) y c2 H0))) H))))).
-theorem csubt_gen_flat:
+lemma csubt_gen_flat:
\forall (g: G).(\forall (e1: C).(\forall (c2: C).(\forall (v: T).(\forall
(f: F).((csubt g (CHead e1 (Flat f) v) c2) \to (ex2 C (\lambda (e2: C).(eq C
c2 (CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g e1 e2))))))))
(c: C).(\lambda (c0: C).((eq C c (CHead e1 (Flat f) v)) \to (ex2 C (\lambda
(e2: C).(eq C c0 (CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g e1
e2)))))) (\lambda (n: nat).(\lambda (H1: (eq C (CSort n) (CHead e1 (Flat f)
-v))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee in C return
-(\lambda (_: C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _)
-\Rightarrow False])) I (CHead e1 (Flat f) v) H1) in (False_ind (ex2 C
-(\lambda (e2: C).(eq C (CSort n) (CHead e2 (Flat f) v))) (\lambda (e2:
-C).(csubt g e1 e2))) H2)))) (\lambda (c1: C).(\lambda (c3: C).(\lambda (H1:
-(csubt g c1 c3)).(\lambda (H2: (((eq C c1 (CHead e1 (Flat f) v)) \to (ex2 C
+v))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee with [(CSort
+_) \Rightarrow True | (CHead _ _ _) \Rightarrow False])) I (CHead e1 (Flat f)
+v) H1) in (False_ind (ex2 C (\lambda (e2: C).(eq C (CSort n) (CHead e2 (Flat
+f) v))) (\lambda (e2: C).(csubt g e1 e2))) H2)))) (\lambda (c1: C).(\lambda
+(c3: C).(\lambda (H1: (csubt g c1 c3)).(\lambda (H2: (((eq C c1 (CHead e1
+(Flat f) v)) \to (ex2 C (\lambda (e2: C).(eq C c3 (CHead e2 (Flat f) v)))
+(\lambda (e2: C).(csubt g e1 e2)))))).(\lambda (k: K).(\lambda (u:
+T).(\lambda (H3: (eq C (CHead c1 k u) (CHead e1 (Flat f) v))).(let H4 \def
+(f_equal C C (\lambda (e: C).(match e with [(CSort _) \Rightarrow c1 | (CHead
+c _ _) \Rightarrow c])) (CHead c1 k u) (CHead e1 (Flat f) v) H3) in ((let H5
+\def (f_equal C K (\lambda (e: C).(match e with [(CSort _) \Rightarrow k |
+(CHead _ k0 _) \Rightarrow k0])) (CHead c1 k u) (CHead e1 (Flat f) v) H3) in
+((let H6 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow u | (CHead _ _ t) \Rightarrow t])) (CHead c1 k u) (CHead e1 (Flat
+f) v) H3) in (\lambda (H7: (eq K k (Flat f))).(\lambda (H8: (eq C c1
+e1)).(eq_ind_r T v (\lambda (t: T).(ex2 C (\lambda (e2: C).(eq C (CHead c3 k
+t) (CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g e1 e2)))) (eq_ind_r K
+(Flat f) (\lambda (k0: K).(ex2 C (\lambda (e2: C).(eq C (CHead c3 k0 v)
+(CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g e1 e2)))) (let H9 \def
+(eq_ind C c1 (\lambda (c: C).((eq C c (CHead e1 (Flat f) v)) \to (ex2 C
(\lambda (e2: C).(eq C c3 (CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g
-e1 e2)))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c1 k
-u) (CHead e1 (Flat f) v))).(let H4 \def (f_equal C C (\lambda (e: C).(match e
-in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c1 | (CHead c _ _)
-\Rightarrow c])) (CHead c1 k u) (CHead e1 (Flat f) v) H3) in ((let H5 \def
-(f_equal C K (\lambda (e: C).(match e in C return (\lambda (_: C).K) with
-[(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c1 k u)
-(CHead e1 (Flat f) v) H3) in ((let H6 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u |
-(CHead _ _ t) \Rightarrow t])) (CHead c1 k u) (CHead e1 (Flat f) v) H3) in
-(\lambda (H7: (eq K k (Flat f))).(\lambda (H8: (eq C c1 e1)).(eq_ind_r T v
-(\lambda (t: T).(ex2 C (\lambda (e2: C).(eq C (CHead c3 k t) (CHead e2 (Flat
-f) v))) (\lambda (e2: C).(csubt g e1 e2)))) (eq_ind_r K (Flat f) (\lambda
-(k0: K).(ex2 C (\lambda (e2: C).(eq C (CHead c3 k0 v) (CHead e2 (Flat f) v)))
-(\lambda (e2: C).(csubt g e1 e2)))) (let H9 \def (eq_ind C c1 (\lambda (c:
-C).((eq C c (CHead e1 (Flat f) v)) \to (ex2 C (\lambda (e2: C).(eq C c3
-(CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g e1 e2))))) H2 e1 H8) in
-(let H10 \def (eq_ind C c1 (\lambda (c: C).(csubt g c c3)) H1 e1 H8) in
-(ex_intro2 C (\lambda (e2: C).(eq C (CHead c3 (Flat f) v) (CHead e2 (Flat f)
-v))) (\lambda (e2: C).(csubt g e1 e2)) c3 (refl_equal C (CHead c3 (Flat f)
-v)) H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1: C).(\lambda (c3:
-C).(\lambda (_: (csubt g c1 c3)).(\lambda (_: (((eq C c1 (CHead e1 (Flat f)
-v)) \to (ex2 C (\lambda (e2: C).(eq C c3 (CHead e2 (Flat f) v))) (\lambda
-(e2: C).(csubt g e1 e2)))))).(\lambda (b: B).(\lambda (_: (not (eq B b
-Void))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c1 (Bind
-Void) u1) (CHead e1 (Flat f) v))).(let H5 \def (eq_ind C (CHead c1 (Bind
-Void) u1) (\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 _) \Rightarrow True | (Flat _) \Rightarrow
-False])])) I (CHead e1 (Flat f) v) H4) in (False_ind (ex2 C (\lambda (e2:
-C).(eq C (CHead c3 (Bind b) u2) (CHead e2 (Flat f) v))) (\lambda (e2:
-C).(csubt g e1 e2))) H5))))))))))) (\lambda (c1: C).(\lambda (c3: C).(\lambda
-(_: (csubt g c1 c3)).(\lambda (_: (((eq C c1 (CHead e1 (Flat f) v)) \to (ex2
-C (\lambda (e2: C).(eq C c3 (CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g
-e1 e2)))))).(\lambda (u: T).(\lambda (t: T).(\lambda (_: (ty3 g c1 u
-t)).(\lambda (_: (ty3 g c3 u t)).(\lambda (H5: (eq C (CHead c1 (Bind Abst) t)
-(CHead e1 (Flat f) v))).(let H6 \def (eq_ind C (CHead c1 (Bind Abst) t)
-(\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 _) \Rightarrow True | (Flat _) \Rightarrow
-False])])) I (CHead e1 (Flat f) v) H5) in (False_ind (ex2 C (\lambda (e2:
-C).(eq C (CHead c3 (Bind Abbr) u) (CHead e2 (Flat f) v))) (\lambda (e2:
-C).(csubt g e1 e2))) H6))))))))))) y c2 H0))) H)))))).
-(* COMMENTS
-Initial nodes: 1103
-END *)
+e1 e2))))) H2 e1 H8) in (let H10 \def (eq_ind C c1 (\lambda (c: C).(csubt g c
+c3)) H1 e1 H8) in (ex_intro2 C (\lambda (e2: C).(eq C (CHead c3 (Flat f) v)
+(CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g e1 e2)) c3 (refl_equal C
+(CHead c3 (Flat f) v)) H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
+C).(\lambda (c3: C).(\lambda (_: (csubt g c1 c3)).(\lambda (_: (((eq C c1
+(CHead e1 (Flat f) v)) \to (ex2 C (\lambda (e2: C).(eq C c3 (CHead e2 (Flat
+f) v))) (\lambda (e2: C).(csubt g e1 e2)))))).(\lambda (b: B).(\lambda (_:
+(not (eq B b Void))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (H4: (eq C
+(CHead c1 (Bind Void) u1) (CHead e1 (Flat f) v))).(let H5 \def (eq_ind C
+(CHead c1 (Bind Void) u1) (\lambda (ee: C).(match ee with [(CSort _)
+\Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind _)
+\Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead e1 (Flat f) v)
+H4) in (False_ind (ex2 C (\lambda (e2: C).(eq C (CHead c3 (Bind b) u2) (CHead
+e2 (Flat f) v))) (\lambda (e2: C).(csubt g e1 e2))) H5))))))))))) (\lambda
+(c1: C).(\lambda (c3: C).(\lambda (_: (csubt g c1 c3)).(\lambda (_: (((eq C
+c1 (CHead e1 (Flat f) v)) \to (ex2 C (\lambda (e2: C).(eq C c3 (CHead e2
+(Flat f) v))) (\lambda (e2: C).(csubt g e1 e2)))))).(\lambda (u: T).(\lambda
+(t: T).(\lambda (_: (ty3 g c1 u t)).(\lambda (_: (ty3 g c3 u t)).(\lambda
+(H5: (eq C (CHead c1 (Bind Abst) t) (CHead e1 (Flat f) v))).(let H6 \def
+(eq_ind C (CHead c1 (Bind Abst) t) (\lambda (ee: C).(match ee with [(CSort _)
+\Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind _)
+\Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead e1 (Flat f) v)
+H5) in (False_ind (ex2 C (\lambda (e2: C).(eq C (CHead c3 (Bind Abbr) u)
+(CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g e1 e2))) H6))))))))))) y c2
+H0))) H)))))).
-theorem csubt_gen_bind:
+lemma csubt_gen_bind:
\forall (g: G).(\forall (b1: B).(\forall (e1: C).(\forall (c2: C).(\forall
(v1: T).((csubt g (CHead e1 (Bind b1) v1) c2) \to (ex2_3 B C T (\lambda (b2:
B).(\lambda (e2: C).(\lambda (v2: T).(eq C c2 (CHead e2 (Bind b2) v2)))))
T).(eq C c0 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
C).(\lambda (_: T).(csubt g e1 e2)))))))) (\lambda (n: nat).(\lambda (H1: (eq
C (CSort n) (CHead e1 (Bind b1) v1))).(let H2 \def (eq_ind C (CSort n)
-(\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _)
-\Rightarrow True | (CHead _ _ _) \Rightarrow False])) I (CHead e1 (Bind b1)
-v1) H1) in (False_ind (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda
-(v2: T).(eq C (CSort n) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda
-(e2: C).(\lambda (_: T).(csubt g e1 e2))))) H2)))) (\lambda (c1: C).(\lambda
-(c3: C).(\lambda (H1: (csubt g c1 c3)).(\lambda (H2: (((eq C c1 (CHead e1
-(Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda
-(v2: T).(eq C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
-C).(\lambda (_: T).(csubt g e1 e2)))))))).(\lambda (k: K).(\lambda (u:
-T).(\lambda (H3: (eq C (CHead c1 k u) (CHead e1 (Bind b1) v1))).(let H4 \def
-(f_equal C C (\lambda (e: C).(match e in C return (\lambda (_: C).C) with
-[(CSort _) \Rightarrow c1 | (CHead c _ _) \Rightarrow c])) (CHead c1 k u)
-(CHead e1 (Bind b1) v1) H3) in ((let H5 \def (f_equal C K (\lambda (e:
-C).(match e in C return (\lambda (_: C).K) with [(CSort _) \Rightarrow k |
-(CHead _ k0 _) \Rightarrow k0])) (CHead c1 k u) (CHead e1 (Bind b1) v1) H3)
-in ((let H6 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda
-(_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t]))
-(CHead c1 k u) (CHead e1 (Bind b1) v1) H3) in (\lambda (H7: (eq K k (Bind
-b1))).(\lambda (H8: (eq C c1 e1)).(eq_ind_r T v1 (\lambda (t: T).(ex2_3 B C T
-(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 k t)
-(CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csubt g e1 e2)))))) (eq_ind_r K (Bind b1) (\lambda (k0: K).(ex2_3 B C T
-(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 k0 v1)
-(CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csubt g e1 e2)))))) (let H9 \def (eq_ind C c1 (\lambda (c: C).((eq C c
-(CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2:
-C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_:
-B).(\lambda (e2: C).(\lambda (_: T).(csubt g e1 e2))))))) H2 e1 H8) in (let
-H10 \def (eq_ind C c1 (\lambda (c: C).(csubt g c c3)) H1 e1 H8) in
-(ex2_3_intro B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C
-(CHead c3 (Bind b1) v1) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda
-(e2: C).(\lambda (_: T).(csubt g e1 e2)))) b1 c3 v1 (refl_equal C (CHead c3
-(Bind b1) v1)) H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
+(\lambda (ee: C).(match ee with [(CSort _) \Rightarrow True | (CHead _ _ _)
+\Rightarrow False])) I (CHead e1 (Bind b1) v1) H1) in (False_ind (ex2_3 B C T
+(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CSort n) (CHead e2
+(Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csubt g
+e1 e2))))) H2)))) (\lambda (c1: C).(\lambda (c3: C).(\lambda (H1: (csubt g c1
+c3)).(\lambda (H2: (((eq C c1 (CHead e1 (Bind b1) v1)) \to (ex2_3 B C T
+(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind
+b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csubt g e1
+e2)))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c1 k u)
+(CHead e1 (Bind b1) v1))).(let H4 \def (f_equal C C (\lambda (e: C).(match e
+with [(CSort _) \Rightarrow c1 | (CHead c _ _) \Rightarrow c])) (CHead c1 k
+u) (CHead e1 (Bind b1) v1) H3) in ((let H5 \def (f_equal C K (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0]))
+(CHead c1 k u) (CHead e1 (Bind b1) v1) H3) in ((let H6 \def (f_equal C T
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow u | (CHead _ _ t)
+\Rightarrow t])) (CHead c1 k u) (CHead e1 (Bind b1) v1) H3) in (\lambda (H7:
+(eq K k (Bind b1))).(\lambda (H8: (eq C c1 e1)).(eq_ind_r T v1 (\lambda (t:
+T).(ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C
+(CHead c3 k t) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
+C).(\lambda (_: T).(csubt g e1 e2)))))) (eq_ind_r K (Bind b1) (\lambda (k0:
+K).(ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C
+(CHead c3 k0 v1) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
+C).(\lambda (_: T).(csubt g e1 e2)))))) (let H9 \def (eq_ind C c1 (\lambda
+(c: C).((eq C c (CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2:
+B).(\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind b2) v2)))))
+(\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csubt g e1 e2))))))) H2 e1
+H8) in (let H10 \def (eq_ind C c1 (\lambda (c: C).(csubt g c c3)) H1 e1 H8)
+in (ex2_3_intro B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq
+C (CHead c3 (Bind b1) v1) (CHead e2 (Bind b2) v2))))) (\lambda (_:
+B).(\lambda (e2: C).(\lambda (_: T).(csubt g e1 e2)))) b1 c3 v1 (refl_equal C
+(CHead c3 (Bind b1) v1)) H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
C).(\lambda (c3: C).(\lambda (H1: (csubt g c1 c3)).(\lambda (H2: (((eq C c1
(CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2:
C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_:
B).(\lambda (e2: C).(\lambda (_: T).(csubt g e1 e2)))))))).(\lambda (b:
B).(\lambda (_: (not (eq B b Void))).(\lambda (u1: T).(\lambda (u2:
T).(\lambda (H4: (eq C (CHead c1 (Bind Void) u1) (CHead e1 (Bind b1)
-v1))).(let H5 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda
-(_: C).C) with [(CSort _) \Rightarrow c1 | (CHead c _ _) \Rightarrow c]))
-(CHead c1 (Bind Void) u1) (CHead e1 (Bind b1) v1) H4) in ((let H6 \def
-(f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with
-[(CSort _) \Rightarrow Void | (CHead _ k _) \Rightarrow (match k in K return
-(\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow
-Void])])) (CHead c1 (Bind Void) u1) (CHead e1 (Bind b1) v1) H4) in ((let H7
-\def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T)
-with [(CSort _) \Rightarrow u1 | (CHead _ _ t) \Rightarrow t])) (CHead c1
-(Bind Void) u1) (CHead e1 (Bind b1) v1) H4) in (\lambda (H8: (eq B Void
-b1)).(\lambda (H9: (eq C c1 e1)).(let H10 \def (eq_ind C c1 (\lambda (c:
-C).((eq C c (CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2:
-B).(\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind b2) v2)))))
-(\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csubt g e1 e2))))))) H2 e1
-H9) in (let H11 \def (eq_ind C c1 (\lambda (c: C).(csubt g c c3)) H1 e1 H9)
-in (let H12 \def (eq_ind_r B b1 (\lambda (b0: B).((eq C e1 (CHead e1 (Bind
-b0) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2:
+v1))).(let H5 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow c1 | (CHead c _ _) \Rightarrow c])) (CHead c1 (Bind Void) u1)
+(CHead e1 (Bind b1) v1) H4) in ((let H6 \def (f_equal C B (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow Void | (CHead _ k _) \Rightarrow
+(match k with [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow Void])]))
+(CHead c1 (Bind Void) u1) (CHead e1 (Bind b1) v1) H4) in ((let H7 \def
+(f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow u1 | (CHead
+_ _ t) \Rightarrow t])) (CHead c1 (Bind Void) u1) (CHead e1 (Bind b1) v1) H4)
+in (\lambda (H8: (eq B Void b1)).(\lambda (H9: (eq C c1 e1)).(let H10 \def
+(eq_ind C c1 (\lambda (c: C).((eq C c (CHead e1 (Bind b1) v1)) \to (ex2_3 B C
+T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind
+b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csubt g e1
+e2))))))) H2 e1 H9) in (let H11 \def (eq_ind C c1 (\lambda (c: C).(csubt g c
+c3)) H1 e1 H9) in (let H12 \def (eq_ind_r B b1 (\lambda (b0: B).((eq C e1
+(CHead e1 (Bind b0) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2:
+C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_:
+B).(\lambda (e2: C).(\lambda (_: T).(csubt g e1 e2))))))) H10 Void H8) in
+(ex2_3_intro B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C
+(CHead c3 (Bind b) u2) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda
+(e2: C).(\lambda (_: T).(csubt g e1 e2)))) b c3 u2 (refl_equal C (CHead c3
+(Bind b) u2)) H11))))))) H6)) H5))))))))))) (\lambda (c1: C).(\lambda (c3:
+C).(\lambda (H1: (csubt g c1 c3)).(\lambda (H2: (((eq C c1 (CHead e1 (Bind
+b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2:
T).(eq C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
-C).(\lambda (_: T).(csubt g e1 e2))))))) H10 Void H8) in (ex2_3_intro B C T
-(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 (Bind b)
-u2) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csubt g e1 e2)))) b c3 u2 (refl_equal C (CHead c3 (Bind b) u2))
-H11))))))) H6)) H5))))))))))) (\lambda (c1: C).(\lambda (c3: C).(\lambda (H1:
-(csubt g c1 c3)).(\lambda (H2: (((eq C c1 (CHead e1 (Bind b1) v1)) \to (ex2_3
-B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2
-(Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csubt g
-e1 e2)))))))).(\lambda (u: T).(\lambda (t: T).(\lambda (H3: (ty3 g c1 u
-t)).(\lambda (H4: (ty3 g c3 u t)).(\lambda (H5: (eq C (CHead c1 (Bind Abst)
-t) (CHead e1 (Bind b1) v1))).(let H6 \def (f_equal C C (\lambda (e: C).(match
-e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c1 | (CHead c _
-_) \Rightarrow c])) (CHead c1 (Bind Abst) t) (CHead e1 (Bind b1) v1) H5) in
-((let H7 \def (f_equal C B (\lambda (e: C).(match e in C return (\lambda (_:
-C).B) with [(CSort _) \Rightarrow Abst | (CHead _ k _) \Rightarrow (match k
-in K return (\lambda (_: K).B) with [(Bind b) \Rightarrow b | (Flat _)
-\Rightarrow Abst])])) (CHead c1 (Bind Abst) t) (CHead e1 (Bind b1) v1) H5) in
-((let H8 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_:
-C).T) with [(CSort _) \Rightarrow t | (CHead _ _ t0) \Rightarrow t0])) (CHead
-c1 (Bind Abst) t) (CHead e1 (Bind b1) v1) H5) in (\lambda (H9: (eq B Abst
-b1)).(\lambda (H10: (eq C c1 e1)).(let H11 \def (eq_ind T t (\lambda (t0:
-T).(ty3 g c3 u t0)) H4 v1 H8) in (let H12 \def (eq_ind T t (\lambda (t0:
+C).(\lambda (_: T).(csubt g e1 e2)))))))).(\lambda (u: T).(\lambda (t:
+T).(\lambda (H3: (ty3 g c1 u t)).(\lambda (H4: (ty3 g c3 u t)).(\lambda (H5:
+(eq C (CHead c1 (Bind Abst) t) (CHead e1 (Bind b1) v1))).(let H6 \def
+(f_equal C C (\lambda (e: C).(match e with [(CSort _) \Rightarrow c1 | (CHead
+c _ _) \Rightarrow c])) (CHead c1 (Bind Abst) t) (CHead e1 (Bind b1) v1) H5)
+in ((let H7 \def (f_equal C B (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow Abst | (CHead _ k _) \Rightarrow (match k with [(Bind b)
+\Rightarrow b | (Flat _) \Rightarrow Abst])])) (CHead c1 (Bind Abst) t)
+(CHead e1 (Bind b1) v1) H5) in ((let H8 \def (f_equal C T (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow t | (CHead _ _ t0) \Rightarrow t0]))
+(CHead c1 (Bind Abst) t) (CHead e1 (Bind b1) v1) H5) in (\lambda (H9: (eq B
+Abst b1)).(\lambda (H10: (eq C c1 e1)).(let H11 \def (eq_ind T t (\lambda
+(t0: T).(ty3 g c3 u t0)) H4 v1 H8) in (let H12 \def (eq_ind T t (\lambda (t0:
T).(ty3 g c1 u t0)) H3 v1 H8) in (let H13 \def (eq_ind C c1 (\lambda (c:
C).(ty3 g c u v1)) H12 e1 H10) in (let H14 \def (eq_ind C c1 (\lambda (c:
C).((eq C c (CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2:
(Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csubt g
e1 e2)))) Abbr c3 u (refl_equal C (CHead c3 (Bind Abbr) u)) H15))))))))))
H7)) H6))))))))))) y c2 H0))) H)))))).
-(* COMMENTS
-Initial nodes: 1899
-END *)
projects / helm.git / blobdiff