(* This file was automatically generated: do not edit *********************)
-include "Basic-1/sn3/defs.ma".
+include "basic_1/sn3/fwd.ma".
-include "Basic-1/nf2/dec.ma".
+include "basic_1/nf2/dec.ma".
-include "Basic-1/nf2/pr3.ma".
+include "basic_1/nf2/pr3.ma".
theorem sn3_nf2:
\forall (c: C).(\forall (t: T).((nf2 c t) \to (sn3 c t)))
\def
- \lambda (c: C).(\lambda (t: T).(\lambda (H: (nf2 c t)).(sn3_sing c t
+ \lambda (c: C).(\lambda (t: T).(\lambda (H: (nf2 c t)).(let TMP_7 \def
(\lambda (t2: T).(\lambda (H0: (((eq T t t2) \to (\forall (P:
Prop).P)))).(\lambda (H1: (pr3 c t t2)).(let H_y \def (nf2_pr3_unfold c t t2
-H1 H) in (let H2 \def (eq_ind_r T t2 (\lambda (t0: T).(pr3 c t t0)) H1 t H_y)
-in (let H3 \def (eq_ind_r T t2 (\lambda (t0: T).((eq T t t0) \to (\forall (P:
-Prop).P))) H0 t H_y) in (eq_ind T t (\lambda (t0: T).(sn3 c t0)) (H3
-(refl_equal T t) (sn3 c t)) t2 H_y)))))))))).
-(* COMMENTS
-Initial nodes: 129
-END *)
+H1 H) in (let TMP_1 \def (\lambda (t0: T).(pr3 c t t0)) in (let H2 \def
+(eq_ind_r T t2 TMP_1 H1 t H_y) in (let TMP_2 \def (\lambda (t0: T).((eq T t
+t0) \to (\forall (P: Prop).P))) in (let H3 \def (eq_ind_r T t2 TMP_2 H0 t
+H_y) in (let TMP_3 \def (\lambda (t0: T).(sn3 c t0)) in (let TMP_4 \def
+(refl_equal T t) in (let TMP_5 \def (sn3 c t) in (let TMP_6 \def (H3 TMP_4
+TMP_5) in (eq_ind T t TMP_3 TMP_6 t2 H_y))))))))))))) in (sn3_sing c t
+TMP_7)))).
theorem nf2_sn3:
\forall (c: C).(\forall (t: T).((sn3 c t) \to (ex2 T (\lambda (u: T).(pr3 c
t u)) (\lambda (u: T).(nf2 c u)))))
\def
- \lambda (c: C).(\lambda (t: T).(\lambda (H: (sn3 c t)).(sn3_ind c (\lambda
-(t0: T).(ex2 T (\lambda (u: T).(pr3 c t0 u)) (\lambda (u: T).(nf2 c u))))
+ \lambda (c: C).(\lambda (t: T).(\lambda (H: (sn3 c t)).(let TMP_3 \def
+(\lambda (t0: T).(let TMP_1 \def (\lambda (u: T).(pr3 c t0 u)) in (let TMP_2
+\def (\lambda (u: T).(nf2 c u)) in (ex2 T TMP_1 TMP_2)))) in (let TMP_32 \def
(\lambda (t1: T).(\lambda (_: ((\forall (t2: T).((((eq T t1 t2) \to (\forall
(P: Prop).P))) \to ((pr3 c t1 t2) \to (sn3 c t2)))))).(\lambda (H1: ((\forall
(t2: T).((((eq T t1 t2) \to (\forall (P: Prop).P))) \to ((pr3 c t1 t2) \to
(ex2 T (\lambda (u: T).(pr3 c t2 u)) (\lambda (u: T).(nf2 c u)))))))).(let
-H_x \def (nf2_dec c t1) in (let H2 \def H_x in (or_ind (nf2 c t1) (ex2 T
-(\lambda (t2: T).((eq T t1 t2) \to (\forall (P: Prop).P))) (\lambda (t2:
-T).(pr2 c t1 t2))) (ex2 T (\lambda (u: T).(pr3 c t1 u)) (\lambda (u: T).(nf2
-c u))) (\lambda (H3: (nf2 c t1)).(ex_intro2 T (\lambda (u: T).(pr3 c t1 u))
-(\lambda (u: T).(nf2 c u)) t1 (pr3_refl c t1) H3)) (\lambda (H3: (ex2 T
-(\lambda (t2: T).((eq T t1 t2) \to (\forall (P: Prop).P))) (\lambda (t2:
-T).(pr2 c t1 t2)))).(ex2_ind T (\lambda (t2: T).((eq T t1 t2) \to (\forall
-(P: Prop).P))) (\lambda (t2: T).(pr2 c t1 t2)) (ex2 T (\lambda (u: T).(pr3 c
-t1 u)) (\lambda (u: T).(nf2 c u))) (\lambda (x: T).(\lambda (H4: (((eq T t1
-x) \to (\forall (P: Prop).P)))).(\lambda (H5: (pr2 c t1 x)).(let H_y \def (H1
-x H4) in (let H6 \def (H_y (pr3_pr2 c t1 x H5)) in (ex2_ind T (\lambda (u:
-T).(pr3 c x u)) (\lambda (u: T).(nf2 c u)) (ex2 T (\lambda (u: T).(pr3 c t1
-u)) (\lambda (u: T).(nf2 c u))) (\lambda (x0: T).(\lambda (H7: (pr3 c x
-x0)).(\lambda (H8: (nf2 c x0)).(ex_intro2 T (\lambda (u: T).(pr3 c t1 u))
-(\lambda (u: T).(nf2 c u)) x0 (pr3_sing c x t1 H5 x0 H7) H8)))) H6)))))) H3))
-H2)))))) t H))).
-(* COMMENTS
-Initial nodes: 443
-END *)
+H_x \def (nf2_dec c t1) in (let H2 \def H_x in (let TMP_4 \def (nf2 c t1) in
+(let TMP_5 \def (\lambda (t2: T).((eq T t1 t2) \to (\forall (P: Prop).P))) in
+(let TMP_6 \def (\lambda (t2: T).(pr2 c t1 t2)) in (let TMP_7 \def (ex2 T
+TMP_5 TMP_6) in (let TMP_8 \def (\lambda (u: T).(pr3 c t1 u)) in (let TMP_9
+\def (\lambda (u: T).(nf2 c u)) in (let TMP_10 \def (ex2 T TMP_8 TMP_9) in
+(let TMP_14 \def (\lambda (H3: (nf2 c t1)).(let TMP_11 \def (\lambda (u:
+T).(pr3 c t1 u)) in (let TMP_12 \def (\lambda (u: T).(nf2 c u)) in (let
+TMP_13 \def (pr3_refl c t1) in (ex_intro2 T TMP_11 TMP_12 t1 TMP_13 H3)))))
+in (let TMP_31 \def (\lambda (H3: (ex2 T (\lambda (t2: T).((eq T t1 t2) \to
+(\forall (P: Prop).P))) (\lambda (t2: T).(pr2 c t1 t2)))).(let TMP_15 \def
+(\lambda (t2: T).((eq T t1 t2) \to (\forall (P: Prop).P))) in (let TMP_16
+\def (\lambda (t2: T).(pr2 c t1 t2)) in (let TMP_17 \def (\lambda (u: T).(pr3
+c t1 u)) in (let TMP_18 \def (\lambda (u: T).(nf2 c u)) in (let TMP_19 \def
+(ex2 T TMP_17 TMP_18) in (let TMP_30 \def (\lambda (x: T).(\lambda (H4: (((eq
+T t1 x) \to (\forall (P: Prop).P)))).(\lambda (H5: (pr2 c t1 x)).(let H_y
+\def (H1 x H4) in (let TMP_20 \def (pr3_pr2 c t1 x H5) in (let H6 \def (H_y
+TMP_20) in (let TMP_21 \def (\lambda (u: T).(pr3 c x u)) in (let TMP_22 \def
+(\lambda (u: T).(nf2 c u)) in (let TMP_23 \def (\lambda (u: T).(pr3 c t1 u))
+in (let TMP_24 \def (\lambda (u: T).(nf2 c u)) in (let TMP_25 \def (ex2 T
+TMP_23 TMP_24) in (let TMP_29 \def (\lambda (x0: T).(\lambda (H7: (pr3 c x
+x0)).(\lambda (H8: (nf2 c x0)).(let TMP_26 \def (\lambda (u: T).(pr3 c t1 u))
+in (let TMP_27 \def (\lambda (u: T).(nf2 c u)) in (let TMP_28 \def (pr3_sing
+c x t1 H5 x0 H7) in (ex_intro2 T TMP_26 TMP_27 x0 TMP_28 H8))))))) in
+(ex2_ind T TMP_21 TMP_22 TMP_25 TMP_29 H6))))))))))))) in (ex2_ind T TMP_15
+TMP_16 TMP_19 TMP_30 H3)))))))) in (or_ind TMP_4 TMP_7 TMP_10 TMP_14 TMP_31
+H2))))))))))))))) in (sn3_ind c TMP_3 TMP_32 t H))))).