(* This file was automatically generated: do not edit *********************)
+include "LambdaDelta-1/pc3/props.ma".
-
-include "pc3/props.ma".
-
-include "wcpr0/getl.ma".
+include "LambdaDelta-1/wcpr0/getl.ma".
theorem pc3_wcpr0__pc3_wcpr0_t_aux:
\forall (c1: C).(\forall (c2: C).((wcpr0 c1 c2) \to (\forall (k: K).(\forall
K).(\lambda (u: T).(\lambda (t1: T).(\lambda (t2: T).(\lambda (H0: (pr3
(CHead c1 k u) t1 t2)).(pr3_ind (CHead c1 k u) (\lambda (t: T).(\lambda (t0:
T).(pc3 (CHead c2 k u) t t0))) (\lambda (t: T).(pc3_refl (CHead c2 k u) t))
-(\lambda (t0: T).(\lambda (t3: T).(\lambda (H1: (pr2 (CHead c1 k u) t3
-t0)).(\lambda (t4: T).(\lambda (_: (pr3 (CHead c1 k u) t0 t4)).(\lambda (H3:
-(pc3 (CHead c2 k u) t0 t4)).(pc3_t t0 (CHead c2 k u) t3 (let H4 \def (match
-H1 in pr2 return (\lambda (c: C).(\lambda (t: T).(\lambda (t5: T).(\lambda
-(_: (pr2 c t t5)).((eq C c (CHead c1 k u)) \to ((eq T t t3) \to ((eq T t5 t0)
-\to (pc3 (CHead c2 k u) t3 t0)))))))) with [(pr2_free c t5 t6 H4) \Rightarrow
-(\lambda (H5: (eq C c (CHead c1 k u))).(\lambda (H6: (eq T t5 t3)).(\lambda
-(H7: (eq T t6 t0)).(eq_ind C (CHead c1 k u) (\lambda (_: C).((eq T t5 t3) \to
-((eq T t6 t0) \to ((pr0 t5 t6) \to (pc3 (CHead c2 k u) t3 t0))))) (\lambda
-(H8: (eq T t5 t3)).(eq_ind T t3 (\lambda (t: T).((eq T t6 t0) \to ((pr0 t t6)
-\to (pc3 (CHead c2 k u) t3 t0)))) (\lambda (H9: (eq T t6 t0)).(eq_ind T t0
-(\lambda (t: T).((pr0 t3 t) \to (pc3 (CHead c2 k u) t3 t0))) (\lambda (H10:
-(pr0 t3 t0)).(pc3_pr2_r (CHead c2 k u) t3 t0 (pr2_free (CHead c2 k u) t3 t0
-H10))) t6 (sym_eq T t6 t0 H9))) t5 (sym_eq T t5 t3 H8))) c (sym_eq C c (CHead
-c1 k u) H5) H6 H7 H4)))) | (pr2_delta c d u0 i H4 t5 t6 H5 t H6) \Rightarrow
-(\lambda (H7: (eq C c (CHead c1 k u))).(\lambda (H8: (eq T t5 t3)).(\lambda
-(H9: (eq T t t0)).(eq_ind C (CHead c1 k u) (\lambda (c0: C).((eq T t5 t3) \to
-((eq T t t0) \to ((getl i c0 (CHead d (Bind Abbr) u0)) \to ((pr0 t5 t6) \to
-((subst0 i u0 t6 t) \to (pc3 (CHead c2 k u) t3 t0))))))) (\lambda (H10: (eq T
-t5 t3)).(eq_ind T t3 (\lambda (t7: T).((eq T t t0) \to ((getl i (CHead c1 k
-u) (CHead d (Bind Abbr) u0)) \to ((pr0 t7 t6) \to ((subst0 i u0 t6 t) \to
-(pc3 (CHead c2 k u) t3 t0)))))) (\lambda (H11: (eq T t t0)).(eq_ind T t0
-(\lambda (t7: T).((getl i (CHead c1 k u) (CHead d (Bind Abbr) u0)) \to ((pr0
-t3 t6) \to ((subst0 i u0 t6 t7) \to (pc3 (CHead c2 k u) t3 t0))))) (\lambda
-(H12: (getl i (CHead c1 k u) (CHead d (Bind Abbr) u0))).(\lambda (H13: (pr0
-t3 t6)).(\lambda (H14: (subst0 i u0 t6 t0)).(ex3_2_ind C T (\lambda (e2:
+(\lambda (t3: T).(\lambda (t4: T).(\lambda (H1: (pr2 (CHead c1 k u) t4
+t3)).(\lambda (t5: T).(\lambda (_: (pr3 (CHead c1 k u) t3 t5)).(\lambda (H3:
+(pc3 (CHead c2 k u) t3 t5)).(pc3_t t3 (CHead c2 k u) t4 (insert_eq C (CHead
+c1 k u) (\lambda (c: C).(pr2 c t4 t3)) (\lambda (_: C).(pc3 (CHead c2 k u) t4
+t3)) (\lambda (y: C).(\lambda (H4: (pr2 y t4 t3)).(pr2_ind (\lambda (c:
+C).(\lambda (t: T).(\lambda (t0: T).((eq C c (CHead c1 k u)) \to (pc3 (CHead
+c2 k u) t t0))))) (\lambda (c: C).(\lambda (t6: T).(\lambda (t0: T).(\lambda
+(H5: (pr0 t6 t0)).(\lambda (_: (eq C c (CHead c1 k u))).(pc3_pr2_r (CHead c2
+k u) t6 t0 (pr2_free (CHead c2 k u) t6 t0 H5))))))) (\lambda (c: C).(\lambda
+(d: C).(\lambda (u0: T).(\lambda (i: nat).(\lambda (H5: (getl i c (CHead d
+(Bind Abbr) u0))).(\lambda (t6: T).(\lambda (t0: T).(\lambda (H6: (pr0 t6
+t0)).(\lambda (t: T).(\lambda (H7: (subst0 i u0 t0 t)).(\lambda (H8: (eq C c
+(CHead c1 k u))).(let H9 \def (eq_ind C c (\lambda (c0: C).(getl i c0 (CHead
+d (Bind Abbr) u0))) H5 (CHead c1 k u) H8) in (ex3_2_ind C T (\lambda (e2:
C).(\lambda (u2: T).(getl i (CHead c2 k u) (CHead e2 (Bind Abbr) u2))))
(\lambda (e2: C).(\lambda (_: T).(wcpr0 d e2))) (\lambda (_: C).(\lambda (u2:
-T).(pr0 u0 u2))) (pc3 (CHead c2 k u) t3 t0) (\lambda (x0: C).(\lambda (x1:
-T).(\lambda (H15: (getl i (CHead c2 k u) (CHead x0 (Bind Abbr) x1))).(\lambda
-(_: (wcpr0 d x0)).(\lambda (H17: (pr0 u0 x1)).(ex2_ind T (\lambda (t7:
-T).(subst0 i x1 t6 t7)) (\lambda (t7: T).(pr0 t0 t7)) (pc3 (CHead c2 k u) t3
-t0) (\lambda (x: T).(\lambda (H18: (subst0 i x1 t6 x)).(\lambda (H19: (pr0 t0
-x)).(pc3_pr2_u (CHead c2 k u) x t3 (pr2_delta (CHead c2 k u) x0 x1 i H15 t3
-t6 H13 x H18) t0 (pc3_pr2_x (CHead c2 k u) x t0 (pr2_free (CHead c2 k u) t0 x
-H19)))))) (pr0_subst0_fwd u0 t6 t0 i H14 x1 H17))))))) (wcpr0_getl (CHead c1
-k u) (CHead c2 k u) (wcpr0_comp c1 c2 H u u (pr0_refl u) k) i d u0 (Bind
-Abbr) H12))))) t (sym_eq T t t0 H11))) t5 (sym_eq T t5 t3 H10))) c (sym_eq C
-c (CHead c1 k u) H7) H8 H9 H4 H5 H6))))]) in (H4 (refl_equal C (CHead c1 k
-u)) (refl_equal T t3) (refl_equal T t0))) t4 H3))))))) t1 t2 H0)))))))).
+T).(pr0 u0 u2))) (pc3 (CHead c2 k u) t6 t) (\lambda (x0: C).(\lambda (x1:
+T).(\lambda (H10: (getl i (CHead c2 k u) (CHead x0 (Bind Abbr) x1))).(\lambda
+(_: (wcpr0 d x0)).(\lambda (H12: (pr0 u0 x1)).(ex2_ind T (\lambda (t7:
+T).(subst0 i x1 t0 t7)) (\lambda (t7: T).(pr0 t t7)) (pc3 (CHead c2 k u) t6
+t) (\lambda (x: T).(\lambda (H13: (subst0 i x1 t0 x)).(\lambda (H14: (pr0 t
+x)).(pc3_pr2_u (CHead c2 k u) x t6 (pr2_delta (CHead c2 k u) x0 x1 i H10 t6
+t0 H6 x H13) t (pc3_pr2_x (CHead c2 k u) x t (pr2_free (CHead c2 k u) t x
+H14)))))) (pr0_subst0_fwd u0 t0 t i H7 x1 H12))))))) (wcpr0_getl (CHead c1 k
+u) (CHead c2 k u) (wcpr0_comp c1 c2 H u u (pr0_refl u) k) i d u0 (Bind Abbr)
+H9)))))))))))))) y t4 t3 H4))) H1) t5 H3))))))) t1 t2 H0)))))))).
theorem pc3_wcpr0_t:
\forall (c1: C).(\forall (c2: C).((wcpr0 c1 c2) \to (\forall (t1:
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