1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
17 include "basic_1/pc3/defs.ma".
19 include "basic_1/nf2/pr3.ma".
22 \forall (c: C).(\forall (t1: T).(\forall (t2: T).((pc3 c t1 t2) \to ((nf2 c
23 t1) \to ((nf2 c t2) \to (eq T t1 t2))))))
25 \lambda (c: C).(\lambda (t1: T).(\lambda (t2: T).(\lambda (H: (pc3 c t1
26 t2)).(\lambda (H0: (nf2 c t1)).(\lambda (H1: (nf2 c t2)).(let H2 \def H in
27 (let TMP_1 \def (\lambda (t: T).(pr3 c t1 t)) in (let TMP_2 \def (\lambda (t:
28 T).(pr3 c t2 t)) in (let TMP_3 \def (eq T t1 t2) in (let TMP_9 \def (\lambda
29 (x: T).(\lambda (H3: (pr3 c t1 x)).(\lambda (H4: (pr3 c t2 x)).(let H_y \def
30 (nf2_pr3_unfold c t1 x H3 H0) in (let TMP_4 \def (\lambda (t: T).(pr3 c t2
31 t)) in (let H5 \def (eq_ind_r T x TMP_4 H4 t1 H_y) in (let TMP_5 \def
32 (\lambda (t: T).(pr3 c t1 t)) in (let H6 \def (eq_ind_r T x TMP_5 H3 t1 H_y)
33 in (let H_y0 \def (nf2_pr3_unfold c t2 t1 H5 H1) in (let TMP_6 \def (\lambda
34 (t: T).(pr3 c t t1)) in (let H7 \def (eq_ind T t2 TMP_6 H5 t1 H_y0) in (let
35 TMP_7 \def (\lambda (t: T).(eq T t1 t)) in (let TMP_8 \def (refl_equal T t1)
36 in (eq_ind_r T t1 TMP_7 TMP_8 t2 H_y0)))))))))))))) in (ex2_ind T TMP_1 TMP_2
37 TMP_3 TMP_9 H2))))))))))).
39 theorem pc3_nf2_unfold:
40 \forall (c: C).(\forall (t1: T).(\forall (t2: T).((pc3 c t1 t2) \to ((nf2 c
41 t2) \to (pr3 c t1 t2)))))
43 \lambda (c: C).(\lambda (t1: T).(\lambda (t2: T).(\lambda (H: (pc3 c t1
44 t2)).(\lambda (H0: (nf2 c t2)).(let H1 \def H in (let TMP_1 \def (\lambda (t:
45 T).(pr3 c t1 t)) in (let TMP_2 \def (\lambda (t: T).(pr3 c t2 t)) in (let
46 TMP_3 \def (pr3 c t1 t2) in (let TMP_5 \def (\lambda (x: T).(\lambda (H2:
47 (pr3 c t1 x)).(\lambda (H3: (pr3 c t2 x)).(let H_y \def (nf2_pr3_unfold c t2
48 x H3 H0) in (let TMP_4 \def (\lambda (t: T).(pr3 c t1 t)) in (let H4 \def
49 (eq_ind_r T x TMP_4 H2 t2 H_y) in H4)))))) in (ex2_ind T TMP_1 TMP_2 TMP_3