(* This file was automatically generated: do not edit *********************)
-include "Basic-1/asucc/defs.ma".
+include "basic_1/asucc/defs.ma".
+
+include "basic_1/A/fwd.ma".
theorem 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)))))))))
\def
- \lambda (g: G).(\lambda (h: nat).(\lambda (n: nat).(\lambda (a: A).(A_ind
-(\lambda (a0: A).((eq A (ASort h n) (asucc g a0)) \to (ex_2 nat nat (\lambda
-(h0: nat).(\lambda (n0: nat).(eq A a0 (ASort h0 n0))))))) (\lambda (n0:
-nat).(\lambda (n1: nat).(\lambda (H: (eq A (ASort h n) (asucc g (ASort n0
-n1)))).(let H0 \def (f_equal A A (\lambda (e: A).e) (ASort h n) (match n0
-with [O \Rightarrow (ASort O (next g n1)) | (S h0) \Rightarrow (ASort h0
-n1)]) H) in (ex_2_intro nat nat (\lambda (h0: nat).(\lambda (n2: nat).(eq A
-(ASort n0 n1) (ASort h0 n2)))) n0 n1 (refl_equal A (ASort n0 n1)))))))
-(\lambda (a0: A).(\lambda (_: (((eq A (ASort h n) (asucc g a0)) \to (ex_2 nat
-nat (\lambda (h0: nat).(\lambda (n0: nat).(eq A a0 (ASort h0
-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 *)
+ \lambda (g: G).(\lambda (h: nat).(\lambda (n: nat).(\lambda (a: A).(let
+TMP_3 \def (\lambda (a0: A).((eq A (ASort h n) (asucc g a0)) \to (let TMP_2
+\def (\lambda (h0: nat).(\lambda (n0: nat).(let TMP_1 \def (ASort h0 n0) in
+(eq A a0 TMP_1)))) in (ex_2 nat nat TMP_2)))) in (let TMP_13 \def (\lambda
+(n0: nat).(\lambda (n1: nat).(\lambda (H: (eq A (ASort h n) (asucc g (ASort
+n0 n1)))).(let TMP_4 \def (\lambda (e: A).e) in (let TMP_5 \def (ASort h n)
+in (let TMP_7 \def (match n0 with [O \Rightarrow (let TMP_6 \def (next g n1)
+in (ASort O TMP_6)) | (S h0) \Rightarrow (ASort h0 n1)]) in (let H0 \def
+(f_equal A A TMP_4 TMP_5 TMP_7 H) in (let TMP_10 \def (\lambda (h0:
+nat).(\lambda (n2: nat).(let TMP_8 \def (ASort n0 n1) in (let TMP_9 \def
+(ASort h0 n2) in (eq A TMP_8 TMP_9))))) in (let TMP_11 \def (ASort n0 n1) in
+(let TMP_12 \def (refl_equal A TMP_11) in (ex_2_intro nat nat TMP_10 n0 n1
+TMP_12))))))))))) in (let TMP_22 \def (\lambda (a0: A).(\lambda (_: (((eq A
+(ASort h n) (asucc g a0)) \to (ex_2 nat nat (\lambda (h0: nat).(\lambda (n0:
+nat).(eq A a0 (ASort h0 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 TMP_14 \def (ASort h n) in (let TMP_15 \def (\lambda
+(ee: A).(match ee with [(ASort _ _) \Rightarrow True | (AHead _ _)
+\Rightarrow False])) in (let TMP_16 \def (AHead a0 a1) in (let TMP_17 \def
+(asucc g TMP_16) in (let H2 \def (eq_ind A TMP_14 TMP_15 I TMP_17 H1) in (let
+TMP_20 \def (\lambda (h0: nat).(\lambda (n0: nat).(let TMP_18 \def (AHead a0
+a1) in (let TMP_19 \def (ASort h0 n0) in (eq A TMP_18 TMP_19))))) in (let
+TMP_21 \def (ex_2 nat nat TMP_20) in (False_ind TMP_21 H2))))))))))))) in
+(A_ind TMP_3 TMP_13 TMP_22 a))))))).
theorem 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))))))))
\def
- \lambda (g: G).(\lambda (a1: A).(\lambda (a2: A).(\lambda (a: A).(A_ind
-(\lambda (a0: A).((eq A (AHead a1 a2) (asucc g a0)) \to (ex2 A (\lambda (a3:
-A).(eq A a0 (AHead a1 a3))) (\lambda (a3: A).(eq A a2 (asucc g a3))))))
-(\lambda (n: nat).(\lambda (n0: nat).(\lambda (H: (eq A (AHead a1 a2) (asucc
-g (ASort n n0)))).(nat_ind (\lambda (n1: nat).((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 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:
-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
-(a3: A).(eq A a2 (asucc g a3))))))).(\lambda (a3: A).(\lambda (H0: (((eq A
-(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 *)
+ \lambda (g: G).(\lambda (a1: A).(\lambda (a2: A).(\lambda (a: A).(let TMP_5
+\def (\lambda (a0: A).((eq A (AHead a1 a2) (asucc g a0)) \to (let TMP_2 \def
+(\lambda (a3: A).(let TMP_1 \def (AHead a1 a3) in (eq A a0 TMP_1))) in (let
+TMP_4 \def (\lambda (a3: A).(let TMP_3 \def (asucc g a3) in (eq A a2 TMP_3)))
+in (ex2 A TMP_2 TMP_4))))) in (let TMP_34 \def (\lambda (n: nat).(\lambda
+(n0: nat).(\lambda (H: (eq A (AHead a1 a2) (asucc g (ASort n n0)))).(let
+TMP_11 \def (\lambda (n1: nat).((eq A (AHead a1 a2) (asucc g (ASort n1 n0)))
+\to (let TMP_8 \def (\lambda (a0: A).(let TMP_6 \def (ASort n1 n0) in (let
+TMP_7 \def (AHead a1 a0) in (eq A TMP_6 TMP_7)))) in (let TMP_10 \def
+(\lambda (a0: A).(let TMP_9 \def (asucc g a0) in (eq A a2 TMP_9))) in (ex2 A
+TMP_8 TMP_10))))) in (let TMP_22 \def (\lambda (H0: (eq A (AHead a1 a2)
+(asucc g (ASort O n0)))).(let TMP_12 \def (AHead a1 a2) in (let TMP_13 \def
+(\lambda (ee: A).(match ee with [(ASort _ _) \Rightarrow False | (AHead _ _)
+\Rightarrow True])) in (let TMP_14 \def (next g n0) in (let TMP_15 \def
+(ASort O TMP_14) in (let H1 \def (eq_ind A TMP_12 TMP_13 I TMP_15 H0) in (let
+TMP_18 \def (\lambda (a0: A).(let TMP_16 \def (ASort O n0) in (let TMP_17
+\def (AHead a1 a0) in (eq A TMP_16 TMP_17)))) in (let TMP_20 \def (\lambda
+(a0: A).(let TMP_19 \def (asucc g a0) in (eq A a2 TMP_19))) in (let TMP_21
+\def (ex2 A TMP_18 TMP_20) in (False_ind TMP_21 H1)))))))))) in (let TMP_33
+\def (\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 TMP_23 \def (AHead a1 a2) in (let
+TMP_24 \def (\lambda (ee: A).(match ee with [(ASort _ _) \Rightarrow False |
+(AHead _ _) \Rightarrow True])) in (let TMP_25 \def (ASort n1 n0) in (let H1
+\def (eq_ind A TMP_23 TMP_24 I TMP_25 H0) in (let TMP_29 \def (\lambda (a0:
+A).(let TMP_26 \def (S n1) in (let TMP_27 \def (ASort TMP_26 n0) in (let
+TMP_28 \def (AHead a1 a0) in (eq A TMP_27 TMP_28))))) in (let TMP_31 \def
+(\lambda (a0: A).(let TMP_30 \def (asucc g a0) in (eq A a2 TMP_30))) in (let
+TMP_32 \def (ex2 A TMP_29 TMP_31) in (False_ind TMP_32 H1))))))))))) in
+(nat_ind TMP_11 TMP_22 TMP_33 n H))))))) in (let TMP_86 \def (\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 (a3: A).(eq A a2 (asucc g
+a3))))))).(\lambda (a3: A).(\lambda (H0: (((eq A (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 TMP_35 \def (\lambda (e: A).(match e with [(ASort _ _)
+\Rightarrow a1 | (AHead a4 _) \Rightarrow a4])) in (let TMP_36 \def (AHead a1
+a2) in (let TMP_37 \def (asucc g a3) in (let TMP_38 \def (AHead a0 TMP_37) in
+(let H2 \def (f_equal A A TMP_35 TMP_36 TMP_38 H1) in (let TMP_39 \def
+(\lambda (e: A).(match e with [(ASort _ _) \Rightarrow a2 | (AHead _ a4)
+\Rightarrow a4])) in (let TMP_40 \def (AHead a1 a2) in (let TMP_41 \def
+(asucc g a3) in (let TMP_42 \def (AHead a0 TMP_41) in (let H3 \def (f_equal A
+A TMP_39 TMP_40 TMP_42 H1) in (let TMP_85 \def (\lambda (H4: (eq A a1
+a0)).(let TMP_47 \def (\lambda (a4: A).((eq A (AHead a1 a2) (asucc g a4)) \to
+(let TMP_44 \def (\lambda (a5: A).(let TMP_43 \def (AHead a1 a5) in (eq A a4
+TMP_43))) in (let TMP_46 \def (\lambda (a5: A).(let TMP_45 \def (asucc g a5)
+in (eq A a2 TMP_45))) in (ex2 A TMP_44 TMP_46))))) in (let H5 \def (eq_ind_r
+A a0 TMP_47 H a1 H4) in (let TMP_53 \def (\lambda (a4: A).(let TMP_50 \def
+(\lambda (a5: A).(let TMP_48 \def (AHead a4 a3) in (let TMP_49 \def (AHead a1
+a5) in (eq A TMP_48 TMP_49)))) in (let TMP_52 \def (\lambda (a5: A).(let
+TMP_51 \def (asucc g a5) in (eq A a2 TMP_51))) in (ex2 A TMP_50 TMP_52)))) in
+(let TMP_58 \def (\lambda (a4: A).((eq A (AHead a1 a4) (asucc g a3)) \to (let
+TMP_55 \def (\lambda (a5: A).(let TMP_54 \def (AHead a1 a5) in (eq A a3
+TMP_54))) in (let TMP_57 \def (\lambda (a5: A).(let TMP_56 \def (asucc g a5)
+in (eq A a4 TMP_56))) in (ex2 A TMP_55 TMP_57))))) in (let TMP_59 \def (asucc
+g a3) in (let H6 \def (eq_ind A a2 TMP_58 H0 TMP_59 H3) in (let TMP_64 \def
+(\lambda (a4: A).((eq A (AHead a1 a4) (asucc g a1)) \to (let TMP_61 \def
+(\lambda (a5: A).(let TMP_60 \def (AHead a1 a5) in (eq A a1 TMP_60))) in (let
+TMP_63 \def (\lambda (a5: A).(let TMP_62 \def (asucc g a5) in (eq A a4
+TMP_62))) in (ex2 A TMP_61 TMP_63))))) in (let TMP_65 \def (asucc g a3) in
+(let H7 \def (eq_ind A a2 TMP_64 H5 TMP_65 H3) in (let TMP_66 \def (asucc g
+a3) in (let TMP_72 \def (\lambda (a4: A).(let TMP_69 \def (\lambda (a5:
+A).(let TMP_67 \def (AHead a1 a3) in (let TMP_68 \def (AHead a1 a5) in (eq A
+TMP_67 TMP_68)))) in (let TMP_71 \def (\lambda (a5: A).(let TMP_70 \def
+(asucc g a5) in (eq A a4 TMP_70))) in (ex2 A TMP_69 TMP_71)))) in (let TMP_75
+\def (\lambda (a4: A).(let TMP_73 \def (AHead a1 a3) in (let TMP_74 \def
+(AHead a1 a4) in (eq A TMP_73 TMP_74)))) in (let TMP_78 \def (\lambda (a4:
+A).(let TMP_76 \def (asucc g a3) in (let TMP_77 \def (asucc g a4) in (eq A
+TMP_76 TMP_77)))) in (let TMP_79 \def (AHead a1 a3) in (let TMP_80 \def
+(refl_equal A TMP_79) in (let TMP_81 \def (asucc g a3) in (let TMP_82 \def
+(refl_equal A TMP_81) in (let TMP_83 \def (ex_intro2 A TMP_75 TMP_78 a3
+TMP_80 TMP_82) in (let TMP_84 \def (eq_ind_r A TMP_66 TMP_72 TMP_83 a2 H3) in
+(eq_ind A a1 TMP_53 TMP_84 a0 H4))))))))))))))))))))) in (TMP_85
+H2))))))))))))))))) in (A_ind TMP_5 TMP_34 TMP_86 a))))))).
projects / helm.git / blobdiff