(* This file was automatically generated: do not edit *********************)
-include "Basic-1/pr2/defs.ma".
+include "basic_1/pr2/defs.ma".
-include "Basic-1/pr0/pr0.ma".
+include "basic_1/pr0/pr0.ma".
-include "Basic-1/getl/props.ma".
+include "basic_1/getl/fwd.ma".
theorem pr2_confluence__pr2_free_free:
\forall (c: C).(\forall (t0: T).(\forall (t1: T).(\forall (t2: T).((pr0 t0
x)).(\lambda (H2: (pr0 t1 x)).(ex_intro2 T (\lambda (t: T).(pr2 c t1 t))
(\lambda (t: T).(pr2 c t2 t)) x (pr2_free c t1 x H2) (pr2_free c t2 x H1)))))
(pr0_confluence t0 t2 H0 t1 H))))))).
-(* COMMENTS
-Initial nodes: 135
-END *)
theorem pr2_confluence__pr2_free_delta:
\forall (c: C).(\forall (d: C).(\forall (t0: T).(\forall (t1: T).(\forall
T).(pr2 c t2 t)) x0 (pr2_delta c d u i H0 t1 x H4 x0 H7) (pr2_free c t2 x0
H6))))) H5)) (pr0_subst0 t4 x H3 u t2 i H2 u (pr0_refl u))))))
(pr0_confluence t0 t4 H1 t1 H))))))))))))).
-(* COMMENTS
-Initial nodes: 403
-END *)
theorem pr2_confluence__pr2_delta_delta:
\forall (c: C).(\forall (d: C).(\forall (d0: C).(\forall (t0: T).(\forall
H2 i H13) in (let H16 \def (eq_ind C (CHead d (Bind Abbr) u) (\lambda (c0:
C).(getl i c c0)) H (CHead d0 (Bind Abbr) u0) (getl_mono c (CHead d (Bind
Abbr) u) i H (CHead d0 (Bind Abbr) u0) H15)) in (let H17 \def (f_equal C C
-(\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
-\Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind Abbr) u)
-(CHead d0 (Bind Abbr) u0) (getl_mono c (CHead d (Bind Abbr) u) i H (CHead d0
-(Bind Abbr) u0) H15)) in ((let H18 \def (f_equal C T (\lambda (e: C).(match e
-in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t)
-\Rightarrow t])) (CHead d (Bind Abbr) u) (CHead d0 (Bind Abbr) u0) (getl_mono
-c (CHead d (Bind Abbr) u) i H (CHead d0 (Bind Abbr) u0) H15)) in (\lambda
-(H19: (eq C d d0)).(let H20 \def (eq_ind_r T u0 (\lambda (t: T).(subst0 i t x
-x1)) H14 u H18) in (let H21 \def (eq_ind_r T u0 (\lambda (t: T).(getl i c
-(CHead d0 (Bind Abbr) t))) H16 u H18) in (let H22 \def (eq_ind_r C d0
-(\lambda (c0: C).(getl i c (CHead c0 (Bind Abbr) u))) H21 d H19) in (or4_ind
-(eq T x1 x0) (ex2 T (\lambda (t: T).(subst0 i u x1 t)) (\lambda (t:
-T).(subst0 i u x0 t))) (subst0 i u x1 x0) (subst0 i u x0 x1) (ex2 T (\lambda
-(t: T).(pr2 c t1 t)) (\lambda (t: T).(pr2 c t2 t))) (\lambda (H23: (eq T x1
-x0)).(let H24 \def (eq_ind T x1 (\lambda (t: T).(pr0 t2 t)) H11 x0 H23) in
-(ex_intro2 T (\lambda (t: T).(pr2 c t1 t)) (\lambda (t: T).(pr2 c t2 t)) x0
-(pr2_free c t1 x0 H8) (pr2_free c t2 x0 H24)))) (\lambda (H23: (ex2 T
-(\lambda (t: T).(subst0 i u x1 t)) (\lambda (t: T).(subst0 i u x0
-t)))).(ex2_ind T (\lambda (t: T).(subst0 i u x1 t)) (\lambda (t: T).(subst0 i
-u x0 t)) (ex2 T (\lambda (t: T).(pr2 c t1 t)) (\lambda (t: T).(pr2 c t2 t)))
-(\lambda (x2: T).(\lambda (H24: (subst0 i u x1 x2)).(\lambda (H25: (subst0 i
-u x0 x2)).(ex_intro2 T (\lambda (t: T).(pr2 c t1 t)) (\lambda (t: T).(pr2 c
-t2 t)) x2 (pr2_delta c d u i H22 t1 x0 H8 x2 H25) (pr2_delta c d u i H22 t2
-x1 H11 x2 H24))))) H23)) (\lambda (H23: (subst0 i u x1 x0)).(ex_intro2 T
-(\lambda (t: T).(pr2 c t1 t)) (\lambda (t: T).(pr2 c t2 t)) x0 (pr2_free c t1
-x0 H8) (pr2_delta c d u i H22 t2 x1 H11 x0 H23))) (\lambda (H23: (subst0 i u
-x0 x1)).(ex_intro2 T (\lambda (t: T).(pr2 c t1 t)) (\lambda (t: T).(pr2 c t2
-t)) x1 (pr2_delta c d u i H22 t1 x0 H8 x1 H23) (pr2_free c t2 x1 H11)))
-(subst0_confluence_eq x x1 u i H20 x0 H9))))))) H17)))))))))) H10))
-(pr0_subst0 t4 x H5 u0 t2 i0 H4 u0 (pr0_refl u0)))))) H7)) (pr0_subst0 t3 x
-H6 u t1 i H1 u (pr0_refl u)))))) (pr0_confluence t0 t4 H3 t3
-H0))))))))))))))))))).
-(* COMMENTS
-Initial nodes: 1901
-END *)
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow d | (CHead c0 _ _)
+\Rightarrow c0])) (CHead d (Bind Abbr) u) (CHead d0 (Bind Abbr) u0)
+(getl_mono c (CHead d (Bind Abbr) u) i H (CHead d0 (Bind Abbr) u0) H15)) in
+((let H18 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow u | (CHead _ _ t) \Rightarrow t])) (CHead d (Bind Abbr) u) (CHead
+d0 (Bind Abbr) u0) (getl_mono c (CHead d (Bind Abbr) u) i H (CHead d0 (Bind
+Abbr) u0) H15)) in (\lambda (H19: (eq C d d0)).(let H20 \def (eq_ind_r T u0
+(\lambda (t: T).(subst0 i t x x1)) H14 u H18) in (let H21 \def (eq_ind_r T u0
+(\lambda (t: T).(getl i c (CHead d0 (Bind Abbr) t))) H16 u H18) in (let H22
+\def (eq_ind_r C d0 (\lambda (c0: C).(getl i c (CHead c0 (Bind Abbr) u))) H21
+d H19) in (or4_ind (eq T x1 x0) (ex2 T (\lambda (t: T).(subst0 i u x1 t))
+(\lambda (t: T).(subst0 i u x0 t))) (subst0 i u x1 x0) (subst0 i u x0 x1)
+(ex2 T (\lambda (t: T).(pr2 c t1 t)) (\lambda (t: T).(pr2 c t2 t))) (\lambda
+(H23: (eq T x1 x0)).(let H24 \def (eq_ind T x1 (\lambda (t: T).(pr0 t2 t))
+H11 x0 H23) in (ex_intro2 T (\lambda (t: T).(pr2 c t1 t)) (\lambda (t:
+T).(pr2 c t2 t)) x0 (pr2_free c t1 x0 H8) (pr2_free c t2 x0 H24)))) (\lambda
+(H23: (ex2 T (\lambda (t: T).(subst0 i u x1 t)) (\lambda (t: T).(subst0 i u
+x0 t)))).(ex2_ind T (\lambda (t: T).(subst0 i u x1 t)) (\lambda (t:
+T).(subst0 i u x0 t)) (ex2 T (\lambda (t: T).(pr2 c t1 t)) (\lambda (t:
+T).(pr2 c t2 t))) (\lambda (x2: T).(\lambda (H24: (subst0 i u x1
+x2)).(\lambda (H25: (subst0 i u x0 x2)).(ex_intro2 T (\lambda (t: T).(pr2 c
+t1 t)) (\lambda (t: T).(pr2 c t2 t)) x2 (pr2_delta c d u i H22 t1 x0 H8 x2
+H25) (pr2_delta c d u i H22 t2 x1 H11 x2 H24))))) H23)) (\lambda (H23:
+(subst0 i u x1 x0)).(ex_intro2 T (\lambda (t: T).(pr2 c t1 t)) (\lambda (t:
+T).(pr2 c t2 t)) x0 (pr2_free c t1 x0 H8) (pr2_delta c d u i H22 t2 x1 H11 x0
+H23))) (\lambda (H23: (subst0 i u x0 x1)).(ex_intro2 T (\lambda (t: T).(pr2 c
+t1 t)) (\lambda (t: T).(pr2 c t2 t)) x1 (pr2_delta c d u i H22 t1 x0 H8 x1
+H23) (pr2_free c t2 x1 H11))) (subst0_confluence_eq x x1 u i H20 x0 H9)))))))
+H17)))))))))) H10)) (pr0_subst0 t4 x H5 u0 t2 i0 H4 u0 (pr0_refl u0))))))
+H7)) (pr0_subst0 t3 x H6 u t1 i H1 u (pr0_refl u)))))) (pr0_confluence t0 t4
+H3 t3 H0))))))))))))))))))).
theorem pr2_confluence:
\forall (c: C).(\forall (t0: T).(\forall (t1: T).((pr2 c t0 t1) \to (\forall
T).(pr2 c t2 t))))))))
\def
\lambda (c: C).(\lambda (t0: T).(\lambda (t1: T).(\lambda (H: (pr2 c t0
-t1)).(\lambda (t2: T).(\lambda (H0: (pr2 c t0 t2)).(let H1 \def (match H in
-pr2 return (\lambda (c0: C).(\lambda (t: T).(\lambda (t3: T).(\lambda (_:
-(pr2 c0 t t3)).((eq C c0 c) \to ((eq T t t0) \to ((eq T t3 t1) \to (ex2 T
-(\lambda (t4: T).(pr2 c t1 t4)) (\lambda (t4: T).(pr2 c t2 t4)))))))))) with
+t1)).(\lambda (t2: T).(\lambda (H0: (pr2 c t0 t2)).(let H1 \def (match H with
[(pr2_free c0 t3 t4 H1) \Rightarrow (\lambda (H2: (eq C c0 c)).(\lambda (H3:
(eq T t3 t0)).(\lambda (H4: (eq T t4 t1)).(eq_ind C c (\lambda (_: C).((eq T
t3 t0) \to ((eq T t4 t1) \to ((pr0 t3 t4) \to (ex2 T (\lambda (t: T).(pr2 c
T).(pr2 c t1 t5)) (\lambda (t5: T).(pr2 c t2 t5)))))) (\lambda (H6: (eq T t4
t1)).(eq_ind T t1 (\lambda (t: T).((pr0 t0 t) \to (ex2 T (\lambda (t5:
T).(pr2 c t1 t5)) (\lambda (t5: T).(pr2 c t2 t5))))) (\lambda (H7: (pr0 t0
-t1)).(let H8 \def (match H0 in pr2 return (\lambda (c1: C).(\lambda (t:
-T).(\lambda (t5: T).(\lambda (_: (pr2 c1 t t5)).((eq C c1 c) \to ((eq T t t0)
-\to ((eq T t5 t2) \to (ex2 T (\lambda (t6: T).(pr2 c t1 t6)) (\lambda (t6:
-T).(pr2 c t2 t6)))))))))) with [(pr2_free c1 t5 t6 H8) \Rightarrow (\lambda
+t1)).(let H8 \def (match H0 with [(pr2_free c1 t5 t6 H8) \Rightarrow (\lambda
(H9: (eq C c1 c)).(\lambda (H10: (eq T t5 t0)).(\lambda (H11: (eq T t6
t2)).(eq_ind C c (\lambda (_: C).((eq T t5 t0) \to ((eq T t6 t2) \to ((pr0 t5
t6) \to (ex2 T (\lambda (t: T).(pr2 c t1 t)) (\lambda (t: T).(pr2 c t2
\to ((subst0 i u t4 t5) \to (ex2 T (\lambda (t6: T).(pr2 c t1 t6)) (\lambda
(t6: T).(pr2 c t2 t6))))))) (\lambda (H9: (getl i c (CHead d (Bind Abbr)
u))).(\lambda (H10: (pr0 t0 t4)).(\lambda (H11: (subst0 i u t4 t1)).(let H12
-\def (match H0 in pr2 return (\lambda (c1: C).(\lambda (t5: T).(\lambda (t6:
-T).(\lambda (_: (pr2 c1 t5 t6)).((eq C c1 c) \to ((eq T t5 t0) \to ((eq T t6
-t2) \to (ex2 T (\lambda (t7: T).(pr2 c t1 t7)) (\lambda (t7: T).(pr2 c t2
-t7)))))))))) with [(pr2_free c1 t5 t6 H12) \Rightarrow (\lambda (H13: (eq C
+\def (match H0 with [(pr2_free c1 t5 t6 H12) \Rightarrow (\lambda (H13: (eq C
c1 c)).(\lambda (H14: (eq T t5 t0)).(\lambda (H15: (eq T t6 t2)).(eq_ind C c
(\lambda (_: C).((eq T t5 t0) \to ((eq T t6 t2) \to ((pr0 t5 t6) \to (ex2 T
(\lambda (t7: T).(pr2 c t1 t7)) (\lambda (t7: T).(pr2 c t2 t7))))))) (\lambda
(refl_equal T t0) (refl_equal T t2)))))) t (sym_eq T t t1 H8))) t3 (sym_eq T
t3 t0 H7))) c0 (sym_eq C c0 c H4) H5 H6 H1 H2 H3))))]) in (H1 (refl_equal C
c) (refl_equal T t0) (refl_equal T t1)))))))).
-(* COMMENTS
-Initial nodes: 2087
-END *)