(* This file was automatically generated: do not edit *********************)
-include "Basic-1/asucc/defs.ma".
+include "basic_1/asucc/defs.ma".
-theorem asucc_gen_sort:
+include "basic_1/A/fwd.ma".
+
+lemma asucc_gen_sort:
\forall (g: G).(\forall (h: nat).(\forall (n: nat).(\forall (a: A).((eq A
(ASort h n) (asucc g a)) \to (ex_2 nat nat (\lambda (h0: nat).(\lambda (n0:
nat).(eq A a (ASort h0 n0)))))))))
n0)))))))).(\lambda (a1: A).(\lambda (_: (((eq A (ASort h n) (asucc g a1))
\to (ex_2 nat nat (\lambda (h0: nat).(\lambda (n0: nat).(eq A a1 (ASort h0
n0)))))))).(\lambda (H1: (eq A (ASort h n) (asucc g (AHead a0 a1)))).(let H2
-\def (eq_ind A (ASort h n) (\lambda (ee: A).(match ee in A return (\lambda
-(_: A).Prop) with [(ASort _ _) \Rightarrow True | (AHead _ _) \Rightarrow
-False])) I (asucc g (AHead a0 a1)) H1) in (False_ind (ex_2 nat nat (\lambda
-(h0: nat).(\lambda (n0: nat).(eq A (AHead a0 a1) (ASort h0 n0))))) H2)))))))
-a)))).
-(* COMMENTS
-Initial nodes: 317
-END *)
+\def (eq_ind A (ASort h n) (\lambda (ee: A).(match ee with [(ASort _ _)
+\Rightarrow True | (AHead _ _) \Rightarrow False])) I (asucc g (AHead a0 a1))
+H1) in (False_ind (ex_2 nat nat (\lambda (h0: nat).(\lambda (n0: nat).(eq A
+(AHead a0 a1) (ASort h0 n0))))) H2))))))) a)))).
-theorem asucc_gen_head:
+lemma asucc_gen_head:
\forall (g: G).(\forall (a1: A).(\forall (a2: A).(\forall (a: A).((eq A
(AHead a1 a2) (asucc g a)) \to (ex2 A (\lambda (a0: A).(eq A a (AHead a1
a0))) (\lambda (a0: A).(eq A a2 (asucc g a0))))))))
(ASort n1 n0))) \to (ex2 A (\lambda (a0: A).(eq A (ASort n1 n0) (AHead a1
a0))) (\lambda (a0: A).(eq A a2 (asucc g a0)))))) (\lambda (H0: (eq A (AHead
a1 a2) (asucc g (ASort O n0)))).(let H1 \def (eq_ind A (AHead a1 a2) (\lambda
-(ee: A).(match ee in A return (\lambda (_: A).Prop) with [(ASort _ _)
-\Rightarrow False | (AHead _ _) \Rightarrow True])) I (ASort O (next g n0))
-H0) in (False_ind (ex2 A (\lambda (a0: A).(eq A (ASort O n0) (AHead a1 a0)))
-(\lambda (a0: A).(eq A a2 (asucc g a0)))) H1))) (\lambda (n1: nat).(\lambda
-(_: (((eq A (AHead a1 a2) (asucc g (ASort n1 n0))) \to (ex2 A (\lambda (a0:
-A).(eq A (ASort n1 n0) (AHead a1 a0))) (\lambda (a0: A).(eq A a2 (asucc g
-a0))))))).(\lambda (H0: (eq A (AHead a1 a2) (asucc g (ASort (S n1)
-n0)))).(let H1 \def (eq_ind A (AHead a1 a2) (\lambda (ee: A).(match ee in A
-return (\lambda (_: A).Prop) with [(ASort _ _) \Rightarrow False | (AHead _
-_) \Rightarrow True])) I (ASort n1 n0) H0) in (False_ind (ex2 A (\lambda (a0:
+(ee: A).(match ee with [(ASort _ _) \Rightarrow False | (AHead _ _)
+\Rightarrow True])) I (ASort O (next g n0)) H0) in (False_ind (ex2 A (\lambda
+(a0: A).(eq A (ASort O n0) (AHead a1 a0))) (\lambda (a0: A).(eq A a2 (asucc g
+a0)))) H1))) (\lambda (n1: nat).(\lambda (_: (((eq A (AHead a1 a2) (asucc g
+(ASort n1 n0))) \to (ex2 A (\lambda (a0: A).(eq A (ASort n1 n0) (AHead a1
+a0))) (\lambda (a0: A).(eq A a2 (asucc g a0))))))).(\lambda (H0: (eq A (AHead
+a1 a2) (asucc g (ASort (S n1) n0)))).(let H1 \def (eq_ind A (AHead a1 a2)
+(\lambda (ee: A).(match ee with [(ASort _ _) \Rightarrow False | (AHead _ _)
+\Rightarrow True])) I (ASort n1 n0) H0) in (False_ind (ex2 A (\lambda (a0:
A).(eq A (ASort (S n1) n0) (AHead a1 a0))) (\lambda (a0: A).(eq A a2 (asucc g
a0)))) H1))))) n H)))) (\lambda (a0: A).(\lambda (H: (((eq A (AHead a1 a2)
(asucc g a0)) \to (ex2 A (\lambda (a3: A).(eq A a0 (AHead a1 a3))) (\lambda
(AHead a1 a2) (asucc g a3)) \to (ex2 A (\lambda (a4: A).(eq A a3 (AHead a1
a4))) (\lambda (a4: A).(eq A a2 (asucc g a4))))))).(\lambda (H1: (eq A (AHead
a1 a2) (asucc g (AHead a0 a3)))).(let H2 \def (f_equal A A (\lambda (e:
-A).(match e in A return (\lambda (_: A).A) with [(ASort _ _) \Rightarrow a1 |
-(AHead a4 _) \Rightarrow a4])) (AHead a1 a2) (AHead a0 (asucc g a3)) H1) in
-((let H3 \def (f_equal A A (\lambda (e: A).(match e in A return (\lambda (_:
-A).A) with [(ASort _ _) \Rightarrow a2 | (AHead _ a4) \Rightarrow a4]))
-(AHead a1 a2) (AHead a0 (asucc g a3)) H1) in (\lambda (H4: (eq A a1 a0)).(let
-H5 \def (eq_ind_r A a0 (\lambda (a4: A).((eq A (AHead a1 a2) (asucc g a4))
-\to (ex2 A (\lambda (a5: A).(eq A a4 (AHead a1 a5))) (\lambda (a5: A).(eq A
-a2 (asucc g a5)))))) H a1 H4) in (eq_ind A a1 (\lambda (a4: A).(ex2 A
-(\lambda (a5: A).(eq A (AHead a4 a3) (AHead a1 a5))) (\lambda (a5: A).(eq A
-a2 (asucc g a5))))) (let H6 \def (eq_ind A a2 (\lambda (a4: A).((eq A (AHead
-a1 a4) (asucc g a3)) \to (ex2 A (\lambda (a5: A).(eq A a3 (AHead a1 a5)))
-(\lambda (a5: A).(eq A a4 (asucc g a5)))))) H0 (asucc g a3) H3) in (let H7
-\def (eq_ind A a2 (\lambda (a4: A).((eq A (AHead a1 a4) (asucc g a1)) \to
-(ex2 A (\lambda (a5: A).(eq A a1 (AHead a1 a5))) (\lambda (a5: A).(eq A a4
-(asucc g a5)))))) H5 (asucc g a3) H3) in (eq_ind_r A (asucc g a3) (\lambda
-(a4: A).(ex2 A (\lambda (a5: A).(eq A (AHead a1 a3) (AHead a1 a5))) (\lambda
-(a5: A).(eq A a4 (asucc g a5))))) (ex_intro2 A (\lambda (a4: A).(eq A (AHead
-a1 a3) (AHead a1 a4))) (\lambda (a4: A).(eq A (asucc g a3) (asucc g a4))) a3
-(refl_equal A (AHead a1 a3)) (refl_equal A (asucc g a3))) a2 H3))) a0 H4))))
-H2))))))) a)))).
-(* COMMENTS
-Initial nodes: 957
-END *)
+A).(match e with [(ASort _ _) \Rightarrow a1 | (AHead a4 _) \Rightarrow a4]))
+(AHead a1 a2) (AHead a0 (asucc g a3)) H1) in ((let H3 \def (f_equal A A
+(\lambda (e: A).(match e with [(ASort _ _) \Rightarrow a2 | (AHead _ a4)
+\Rightarrow a4])) (AHead a1 a2) (AHead a0 (asucc g a3)) H1) in (\lambda (H4:
+(eq A a1 a0)).(let H5 \def (eq_ind_r A a0 (\lambda (a4: A).((eq A (AHead a1
+a2) (asucc g a4)) \to (ex2 A (\lambda (a5: A).(eq A a4 (AHead a1 a5)))
+(\lambda (a5: A).(eq A a2 (asucc g a5)))))) H a1 H4) in (eq_ind A a1 (\lambda
+(a4: A).(ex2 A (\lambda (a5: A).(eq A (AHead a4 a3) (AHead a1 a5))) (\lambda
+(a5: A).(eq A a2 (asucc g a5))))) (let H6 \def (eq_ind A a2 (\lambda (a4:
+A).((eq A (AHead a1 a4) (asucc g a3)) \to (ex2 A (\lambda (a5: A).(eq A a3
+(AHead a1 a5))) (\lambda (a5: A).(eq A a4 (asucc g a5)))))) H0 (asucc g a3)
+H3) in (let H7 \def (eq_ind A a2 (\lambda (a4: A).((eq A (AHead a1 a4) (asucc
+g a1)) \to (ex2 A (\lambda (a5: A).(eq A a1 (AHead a1 a5))) (\lambda (a5:
+A).(eq A a4 (asucc g a5)))))) H5 (asucc g a3) H3) in (eq_ind_r A (asucc g a3)
+(\lambda (a4: A).(ex2 A (\lambda (a5: A).(eq A (AHead a1 a3) (AHead a1 a5)))
+(\lambda (a5: A).(eq A a4 (asucc g a5))))) (ex_intro2 A (\lambda (a4: A).(eq
+A (AHead a1 a3) (AHead a1 a4))) (\lambda (a4: A).(eq A (asucc g a3) (asucc g
+a4))) a3 (refl_equal A (AHead a1 a3)) (refl_equal A (asucc g a3))) a2 H3)))
+a0 H4)))) H2))))))) a)))).