include "basic_1/ty3/arity.ma".
-theorem csubt_csuba:
+lemma csubt_csuba:
\forall (g: G).(\forall (c1: C).(\forall (c2: C).((csubt g c1 c2) \to (csuba
g c1 c2))))
\def
\lambda (g: G).(\lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csubt g c1
-c2)).(let TMP_1 \def (\lambda (c: C).(\lambda (c0: C).(csuba g c c0))) in
-(let TMP_3 \def (\lambda (n: nat).(let TMP_2 \def (CSort n) in (csuba_refl g
-TMP_2))) in (let TMP_4 \def (\lambda (c3: C).(\lambda (c4: C).(\lambda (_:
-(csubt g c3 c4)).(\lambda (H1: (csuba g c3 c4)).(\lambda (k: K).(\lambda (u:
-T).(csuba_head g c3 c4 H1 k u))))))) in (let TMP_5 \def (\lambda (c3:
-C).(\lambda (c4: C).(\lambda (_: (csubt g c3 c4)).(\lambda (H1: (csuba g c3
-c4)).(\lambda (b: B).(\lambda (H2: (not (eq B b Void))).(\lambda (u1:
-T).(\lambda (u2: T).(csuba_void g c3 c4 H1 b H2 u1 u2))))))))) in (let TMP_16
-\def (\lambda (c3: C).(\lambda (c4: C).(\lambda (_: (csubt g c3 c4)).(\lambda
-(H1: (csuba g c3 c4)).(\lambda (u: T).(\lambda (t: T).(\lambda (H2: (ty3 g c3
-u t)).(\lambda (_: (ty3 g c4 u t)).(let H_x \def (ty3_arity g c3 u t H2) in
-(let H4 \def H_x in (let TMP_6 \def (\lambda (a1: A).(arity g c3 u a1)) in
-(let TMP_8 \def (\lambda (a1: A).(let TMP_7 \def (asucc g a1) in (arity g c3
-t TMP_7))) in (let TMP_9 \def (Bind Abst) in (let TMP_10 \def (CHead c3 TMP_9
-t) in (let TMP_11 \def (Bind Abbr) in (let TMP_12 \def (CHead c4 TMP_11 u) in
-(let TMP_13 \def (csuba g TMP_10 TMP_12) in (let TMP_15 \def (\lambda (x:
-A).(\lambda (H5: (arity g c3 u x)).(\lambda (H6: (arity g c3 t (asucc g
-x))).(let TMP_14 \def (csuba_arity g c3 u x H5 c4 H1) in (csuba_abst g c3 c4
-H1 t x H6 u TMP_14))))) in (ex2_ind A TMP_6 TMP_8 TMP_13 TMP_15
-H4))))))))))))))))))) in (csubt_ind g TMP_1 TMP_3 TMP_4 TMP_5 TMP_16 c1 c2
-H))))))))).
+c2)).(csubt_ind g (\lambda (c: C).(\lambda (c0: C).(csuba g c c0))) (\lambda
+(n: nat).(csuba_refl g (CSort n))) (\lambda (c3: C).(\lambda (c4: C).(\lambda
+(_: (csubt g c3 c4)).(\lambda (H1: (csuba g c3 c4)).(\lambda (k: K).(\lambda
+(u: T).(csuba_head g c3 c4 H1 k u))))))) (\lambda (c3: C).(\lambda (c4:
+C).(\lambda (_: (csubt g c3 c4)).(\lambda (H1: (csuba g c3 c4)).(\lambda (b:
+B).(\lambda (H2: (not (eq B b Void))).(\lambda (u1: T).(\lambda (u2:
+T).(csuba_void g c3 c4 H1 b H2 u1 u2))))))))) (\lambda (c3: C).(\lambda (c4:
+C).(\lambda (_: (csubt g c3 c4)).(\lambda (H1: (csuba g c3 c4)).(\lambda (u:
+T).(\lambda (t: T).(\lambda (H2: (ty3 g c3 u t)).(\lambda (_: (ty3 g c4 u
+t)).(let H_x \def (ty3_arity g c3 u t H2) in (let H4 \def H_x in (ex2_ind A
+(\lambda (a1: A).(arity g c3 u a1)) (\lambda (a1: A).(arity g c3 t (asucc g
+a1))) (csuba g (CHead c3 (Bind Abst) t) (CHead c4 (Bind Abbr) u)) (\lambda
+(x: A).(\lambda (H5: (arity g c3 u x)).(\lambda (H6: (arity g c3 t (asucc g
+x))).(csuba_abst g c3 c4 H1 t x H6 u (csuba_arity g c3 u x H5 c4 H1)))))
+H4))))))))))) c1 c2 H)))).