(* This file was automatically generated: do not edit *********************)
-
+set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/pr0/fwd".
include "pr0/props.ma".
\def
\lambda (t1: T).(\lambda (x: T).(\lambda (h: nat).(\lambda (d: nat).(\lambda
(H: (pr0 (lift h d t1) x)).(insert_eq T (lift h d t1) (\lambda (t: T).(pr0 t
-x)) (ex2 T (\lambda (t2: T).(eq T x (lift h d t2))) (\lambda (t2: T).(pr0 t1
-t2))) (\lambda (y: T).(\lambda (H0: (pr0 y x)).(unintro nat d (\lambda (n:
-nat).((eq T y (lift h n t1)) \to (ex2 T (\lambda (t2: T).(eq T x (lift h n
-t2))) (\lambda (t2: T).(pr0 t1 t2))))) (unintro T t1 (\lambda (t: T).(\forall
-(x0: nat).((eq T y (lift h x0 t)) \to (ex2 T (\lambda (t2: T).(eq T x (lift h
-x0 t2))) (\lambda (t2: T).(pr0 t t2)))))) (pr0_ind (\lambda (t: T).(\lambda
-(t0: T).(\forall (x0: T).(\forall (x1: nat).((eq T t (lift h x1 x0)) \to (ex2
-T (\lambda (t2: T).(eq T t0 (lift h x1 t2))) (\lambda (t2: T).(pr0 x0
-t2)))))))) (\lambda (t: T).(\lambda (x0: T).(\lambda (x1: nat).(\lambda (H1:
-(eq T t (lift h x1 x0))).(ex_intro2 T (\lambda (t2: T).(eq T t (lift h x1
-t2))) (\lambda (t2: T).(pr0 x0 t2)) x0 H1 (pr0_refl x0)))))) (\lambda (u1:
-T).(\lambda (u2: T).(\lambda (_: (pr0 u1 u2)).(\lambda (H2: ((\forall (x0:
-T).(\forall (x1: nat).((eq T u1 (lift h x1 x0)) \to (ex2 T (\lambda (t2:
-T).(eq T u2 (lift h x1 t2))) (\lambda (t2: T).(pr0 x0 t2)))))))).(\lambda
-(t2: T).(\lambda (t3: T).(\lambda (_: (pr0 t2 t3)).(\lambda (H4: ((\forall
-(x0: T).(\forall (x1: nat).((eq T t2 (lift h x1 x0)) \to (ex2 T (\lambda (t4:
-T).(eq T t3 (lift h x1 t4))) (\lambda (t4: T).(pr0 x0 t4)))))))).(\lambda (k:
-K).(\lambda (x0: T).(\lambda (x1: nat).(\lambda (H5: (eq T (THead k u1 t2)
-(lift h x1 x0))).(K_ind (\lambda (k0: K).((eq T (THead k0 u1 t2) (lift h x1
-x0)) \to (ex2 T (\lambda (t4: T).(eq T (THead k0 u2 t3) (lift h x1 t4)))
-(\lambda (t4: T).(pr0 x0 t4))))) (\lambda (b: B).(\lambda (H6: (eq T (THead
-(Bind b) u1 t2) (lift h x1 x0))).(ex3_2_ind T T (\lambda (y0: T).(\lambda (z:
-T).(eq T x0 (THead (Bind b) y0 z)))) (\lambda (y0: T).(\lambda (_: T).(eq T
-u1 (lift h x1 y0)))) (\lambda (_: T).(\lambda (z: T).(eq T t2 (lift h (S x1)
-z)))) (ex2 T (\lambda (t4: T).(eq T (THead (Bind b) u2 t3) (lift h x1 t4)))
-(\lambda (t4: T).(pr0 x0 t4))) (\lambda (x2: T).(\lambda (x3: T).(\lambda
-(H7: (eq T x0 (THead (Bind b) x2 x3))).(\lambda (H8: (eq T u1 (lift h x1
-x2))).(\lambda (H9: (eq T t2 (lift h (S x1) x3))).(eq_ind_r T (THead (Bind b)
-x2 x3) (\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T (THead (Bind b) u2 t3)
-(lift h x1 t4))) (\lambda (t4: T).(pr0 t t4)))) (ex2_ind T (\lambda (t4:
-T).(eq T t3 (lift h (S x1) t4))) (\lambda (t4: T).(pr0 x3 t4)) (ex2 T
-(\lambda (t4: T).(eq T (THead (Bind b) u2 t3) (lift h x1 t4))) (\lambda (t4:
-T).(pr0 (THead (Bind b) x2 x3) t4))) (\lambda (x4: T).(\lambda (H_x: (eq T t3
-(lift h (S x1) x4))).(\lambda (H10: (pr0 x3 x4)).(eq_ind_r T (lift h (S x1)
-x4) (\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T (THead (Bind b) u2 t) (lift
-h x1 t4))) (\lambda (t4: T).(pr0 (THead (Bind b) x2 x3) t4)))) (ex2_ind T
-(\lambda (t4: T).(eq T u2 (lift h x1 t4))) (\lambda (t4: T).(pr0 x2 t4)) (ex2
-T (\lambda (t4: T).(eq T (THead (Bind b) u2 (lift h (S x1) x4)) (lift h x1
-t4))) (\lambda (t4: T).(pr0 (THead (Bind b) x2 x3) t4))) (\lambda (x5:
-T).(\lambda (H_x0: (eq T u2 (lift h x1 x5))).(\lambda (H11: (pr0 x2
-x5)).(eq_ind_r T (lift h x1 x5) (\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T
-(THead (Bind b) t (lift h (S x1) x4)) (lift h x1 t4))) (\lambda (t4: T).(pr0
-(THead (Bind b) x2 x3) t4)))) (ex_intro2 T (\lambda (t4: T).(eq T (THead
-(Bind b) (lift h x1 x5) (lift h (S x1) x4)) (lift h x1 t4))) (\lambda (t4:
-T).(pr0 (THead (Bind b) x2 x3) t4)) (THead (Bind b) x5 x4) (sym_eq T (lift h
-x1 (THead (Bind b) x5 x4)) (THead (Bind b) (lift h x1 x5) (lift h (S x1) x4))
-(lift_bind b x5 x4 h x1)) (pr0_comp x2 x5 H11 x3 x4 H10 (Bind b))) u2
-H_x0)))) (H2 x2 x1 H8)) t3 H_x)))) (H4 x3 (S x1) H9)) x0 H7))))))
-(lift_gen_bind b u1 t2 x0 h x1 H6)))) (\lambda (f: F).(\lambda (H6: (eq T
-(THead (Flat f) u1 t2) (lift h x1 x0))).(ex3_2_ind T T (\lambda (y0:
-T).(\lambda (z: T).(eq T x0 (THead (Flat f) y0 z)))) (\lambda (y0:
-T).(\lambda (_: T).(eq T u1 (lift h x1 y0)))) (\lambda (_: T).(\lambda (z:
-T).(eq T t2 (lift h x1 z)))) (ex2 T (\lambda (t4: T).(eq T (THead (Flat f) u2
-t3) (lift h x1 t4))) (\lambda (t4: T).(pr0 x0 t4))) (\lambda (x2: T).(\lambda
-(x3: T).(\lambda (H7: (eq T x0 (THead (Flat f) x2 x3))).(\lambda (H8: (eq T
-u1 (lift h x1 x2))).(\lambda (H9: (eq T t2 (lift h x1 x3))).(eq_ind_r T
-(THead (Flat f) x2 x3) (\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T (THead
-(Flat f) u2 t3) (lift h x1 t4))) (\lambda (t4: T).(pr0 t t4)))) (ex2_ind T
-(\lambda (t4: T).(eq T t3 (lift h x1 t4))) (\lambda (t4: T).(pr0 x3 t4)) (ex2
-T (\lambda (t4: T).(eq T (THead (Flat f) u2 t3) (lift h x1 t4))) (\lambda
-(t4: T).(pr0 (THead (Flat f) x2 x3) t4))) (\lambda (x4: T).(\lambda (H_x: (eq
-T t3 (lift h x1 x4))).(\lambda (H10: (pr0 x3 x4)).(eq_ind_r T (lift h x1 x4)
-(\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T (THead (Flat f) u2 t) (lift h
-x1 t4))) (\lambda (t4: T).(pr0 (THead (Flat f) x2 x3) t4)))) (ex2_ind T
-(\lambda (t4: T).(eq T u2 (lift h x1 t4))) (\lambda (t4: T).(pr0 x2 t4)) (ex2
-T (\lambda (t4: T).(eq T (THead (Flat f) u2 (lift h x1 x4)) (lift h x1 t4)))
-(\lambda (t4: T).(pr0 (THead (Flat f) x2 x3) t4))) (\lambda (x5: T).(\lambda
+x)) (\lambda (_: T).(ex2 T (\lambda (t2: T).(eq T x (lift h d t2))) (\lambda
+(t2: T).(pr0 t1 t2)))) (\lambda (y: T).(\lambda (H0: (pr0 y x)).(unintro nat
+d (\lambda (n: nat).((eq T y (lift h n t1)) \to (ex2 T (\lambda (t2: T).(eq T
+x (lift h n t2))) (\lambda (t2: T).(pr0 t1 t2))))) (unintro T t1 (\lambda (t:
+T).(\forall (x0: nat).((eq T y (lift h x0 t)) \to (ex2 T (\lambda (t2: T).(eq
+T x (lift h x0 t2))) (\lambda (t2: T).(pr0 t t2)))))) (pr0_ind (\lambda (t:
+T).(\lambda (t0: T).(\forall (x0: T).(\forall (x1: nat).((eq T t (lift h x1
+x0)) \to (ex2 T (\lambda (t2: T).(eq T t0 (lift h x1 t2))) (\lambda (t2:
+T).(pr0 x0 t2)))))))) (\lambda (t: T).(\lambda (x0: T).(\lambda (x1:
+nat).(\lambda (H1: (eq T t (lift h x1 x0))).(ex_intro2 T (\lambda (t2: T).(eq
+T t (lift h x1 t2))) (\lambda (t2: T).(pr0 x0 t2)) x0 H1 (pr0_refl x0))))))
+(\lambda (u1: T).(\lambda (u2: T).(\lambda (_: (pr0 u1 u2)).(\lambda (H2:
+((\forall (x0: T).(\forall (x1: nat).((eq T u1 (lift h x1 x0)) \to (ex2 T
+(\lambda (t2: T).(eq T u2 (lift h x1 t2))) (\lambda (t2: T).(pr0 x0
+t2)))))))).(\lambda (t2: T).(\lambda (t3: T).(\lambda (_: (pr0 t2
+t3)).(\lambda (H4: ((\forall (x0: T).(\forall (x1: nat).((eq T t2 (lift h x1
+x0)) \to (ex2 T (\lambda (t4: T).(eq T t3 (lift h x1 t4))) (\lambda (t4:
+T).(pr0 x0 t4)))))))).(\lambda (k: K).(\lambda (x0: T).(\lambda (x1:
+nat).(\lambda (H5: (eq T (THead k u1 t2) (lift h x1 x0))).(K_ind (\lambda
+(k0: K).((eq T (THead k0 u1 t2) (lift h x1 x0)) \to (ex2 T (\lambda (t4:
+T).(eq T (THead k0 u2 t3) (lift h x1 t4))) (\lambda (t4: T).(pr0 x0 t4)))))
+(\lambda (b: B).(\lambda (H6: (eq T (THead (Bind b) u1 t2) (lift h x1
+x0))).(ex3_2_ind T T (\lambda (y0: T).(\lambda (z: T).(eq T x0 (THead (Bind
+b) y0 z)))) (\lambda (y0: T).(\lambda (_: T).(eq T u1 (lift h x1 y0))))
+(\lambda (_: T).(\lambda (z: T).(eq T t2 (lift h (S x1) z)))) (ex2 T (\lambda
+(t4: T).(eq T (THead (Bind b) u2 t3) (lift h x1 t4))) (\lambda (t4: T).(pr0
+x0 t4))) (\lambda (x2: T).(\lambda (x3: T).(\lambda (H7: (eq T x0 (THead
+(Bind b) x2 x3))).(\lambda (H8: (eq T u1 (lift h x1 x2))).(\lambda (H9: (eq T
+t2 (lift h (S x1) x3))).(eq_ind_r T (THead (Bind b) x2 x3) (\lambda (t:
+T).(ex2 T (\lambda (t4: T).(eq T (THead (Bind b) u2 t3) (lift h x1 t4)))
+(\lambda (t4: T).(pr0 t t4)))) (ex2_ind T (\lambda (t4: T).(eq T t3 (lift h
+(S x1) t4))) (\lambda (t4: T).(pr0 x3 t4)) (ex2 T (\lambda (t4: T).(eq T
+(THead (Bind b) u2 t3) (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead (Bind b)
+x2 x3) t4))) (\lambda (x4: T).(\lambda (H_x: (eq T t3 (lift h (S x1)
+x4))).(\lambda (H10: (pr0 x3 x4)).(eq_ind_r T (lift h (S x1) x4) (\lambda (t:
+T).(ex2 T (\lambda (t4: T).(eq T (THead (Bind b) u2 t) (lift h x1 t4)))
+(\lambda (t4: T).(pr0 (THead (Bind b) x2 x3) t4)))) (ex2_ind T (\lambda (t4:
+T).(eq T u2 (lift h x1 t4))) (\lambda (t4: T).(pr0 x2 t4)) (ex2 T (\lambda
+(t4: T).(eq T (THead (Bind b) u2 (lift h (S x1) x4)) (lift h x1 t4)))
+(\lambda (t4: T).(pr0 (THead (Bind b) x2 x3) t4))) (\lambda (x5: T).(\lambda
(H_x0: (eq T u2 (lift h x1 x5))).(\lambda (H11: (pr0 x2 x5)).(eq_ind_r T
-(lift h x1 x5) (\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T (THead (Flat f)
-t (lift h x1 x4)) (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead (Flat f) x2
-x3) t4)))) (ex_intro2 T (\lambda (t4: T).(eq T (THead (Flat f) (lift h x1 x5)
-(lift h x1 x4)) (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead (Flat f) x2 x3)
-t4)) (THead (Flat f) x5 x4) (sym_eq T (lift h x1 (THead (Flat f) x5 x4))
-(THead (Flat f) (lift h x1 x5) (lift h x1 x4)) (lift_flat f x5 x4 h x1))
-(pr0_comp x2 x5 H11 x3 x4 H10 (Flat f))) u2 H_x0)))) (H2 x2 x1 H8)) t3
-H_x)))) (H4 x3 x1 H9)) x0 H7)))))) (lift_gen_flat f u1 t2 x0 h x1 H6)))) k
-H5))))))))))))) (\lambda (u: T).(\lambda (v1: T).(\lambda (v2: T).(\lambda
-(_: (pr0 v1 v2)).(\lambda (H2: ((\forall (x0: T).(\forall (x1: nat).((eq T v1
-(lift h x1 x0)) \to (ex2 T (\lambda (t2: T).(eq T v2 (lift h x1 t2)))
-(\lambda (t2: T).(pr0 x0 t2)))))))).(\lambda (t2: T).(\lambda (t3:
-T).(\lambda (_: (pr0 t2 t3)).(\lambda (H4: ((\forall (x0: T).(\forall (x1:
-nat).((eq T t2 (lift h x1 x0)) \to (ex2 T (\lambda (t4: T).(eq T t3 (lift h
-x1 t4))) (\lambda (t4: T).(pr0 x0 t4)))))))).(\lambda (x0: T).(\lambda (x1:
-nat).(\lambda (H5: (eq T (THead (Flat Appl) v1 (THead (Bind Abst) u t2))
-(lift h x1 x0))).(ex3_2_ind T T (\lambda (y0: T).(\lambda (z: T).(eq T x0
-(THead (Flat Appl) y0 z)))) (\lambda (y0: T).(\lambda (_: T).(eq T v1 (lift h
-x1 y0)))) (\lambda (_: T).(\lambda (z: T).(eq T (THead (Bind Abst) u t2)
-(lift h x1 z)))) (ex2 T (\lambda (t4: T).(eq T (THead (Bind Abbr) v2 t3)
-(lift h x1 t4))) (\lambda (t4: T).(pr0 x0 t4))) (\lambda (x2: T).(\lambda
-(x3: T).(\lambda (H6: (eq T x0 (THead (Flat Appl) x2 x3))).(\lambda (H7: (eq
-T v1 (lift h x1 x2))).(\lambda (H8: (eq T (THead (Bind Abst) u t2) (lift h x1
-x3))).(eq_ind_r T (THead (Flat Appl) x2 x3) (\lambda (t: T).(ex2 T (\lambda
-(t4: T).(eq T (THead (Bind Abbr) v2 t3) (lift h x1 t4))) (\lambda (t4:
-T).(pr0 t t4)))) (ex3_2_ind T T (\lambda (y0: T).(\lambda (z: T).(eq T x3
-(THead (Bind Abst) y0 z)))) (\lambda (y0: T).(\lambda (_: T).(eq T u (lift h
-x1 y0)))) (\lambda (_: T).(\lambda (z: T).(eq T t2 (lift h (S x1) z)))) (ex2
-T (\lambda (t4: T).(eq T (THead (Bind Abbr) v2 t3) (lift h x1 t4))) (\lambda
-(t4: T).(pr0 (THead (Flat Appl) x2 x3) t4))) (\lambda (x4: T).(\lambda (x5:
-T).(\lambda (H9: (eq T x3 (THead (Bind Abst) x4 x5))).(\lambda (_: (eq T u
-(lift h x1 x4))).(\lambda (H11: (eq T t2 (lift h (S x1) x5))).(eq_ind_r T
-(THead (Bind Abst) x4 x5) (\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T
-(THead (Bind Abbr) v2 t3) (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead (Flat
-Appl) x2 t) t4)))) (ex2_ind T (\lambda (t4: T).(eq T t3 (lift h (S x1) t4)))
-(\lambda (t4: T).(pr0 x5 t4)) (ex2 T (\lambda (t4: T).(eq T (THead (Bind
-Abbr) v2 t3) (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead (Flat Appl) x2
-(THead (Bind Abst) x4 x5)) t4))) (\lambda (x6: T).(\lambda (H_x: (eq T t3
-(lift h (S x1) x6))).(\lambda (H12: (pr0 x5 x6)).(eq_ind_r T (lift h (S x1)
-x6) (\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T (THead (Bind Abbr) v2 t)
-(lift h x1 t4))) (\lambda (t4: T).(pr0 (THead (Flat Appl) x2 (THead (Bind
-Abst) x4 x5)) t4)))) (ex2_ind T (\lambda (t4: T).(eq T v2 (lift h x1 t4)))
-(\lambda (t4: T).(pr0 x2 t4)) (ex2 T (\lambda (t4: T).(eq T (THead (Bind
-Abbr) v2 (lift h (S x1) x6)) (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead
-(Flat Appl) x2 (THead (Bind Abst) x4 x5)) t4))) (\lambda (x7: T).(\lambda
-(H_x0: (eq T v2 (lift h x1 x7))).(\lambda (H13: (pr0 x2 x7)).(eq_ind_r T
-(lift h x1 x7) (\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T (THead (Bind
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-(Flat Appl) x2 (THead (Bind Abst) x4 x5)) t4)))) (ex_intro2 T (\lambda (t4:
-T).(eq T (THead (Bind Abbr) (lift h x1 x7) (lift h (S x1) x6)) (lift h x1
-t4))) (\lambda (t4: T).(pr0 (THead (Flat Appl) x2 (THead (Bind Abst) x4 x5))
-t4)) (THead (Bind Abbr) x7 x6) (sym_eq T (lift h x1 (THead (Bind Abbr) x7
-x6)) (THead (Bind Abbr) (lift h x1 x7) (lift h (S x1) x6)) (lift_bind Abbr x7
-x6 h x1)) (pr0_beta x4 x2 x7 H13 x5 x6 H12)) v2 H_x0)))) (H2 x2 x1 H7)) t3
-H_x)))) (H4 x5 (S x1) H11)) x3 H9)))))) (lift_gen_bind Abst u t2 x3 h x1 H8))
-x0 H6)))))) (lift_gen_flat Appl v1 (THead (Bind Abst) u t2) x0 h x1
-H5)))))))))))))) (\lambda (b: B).(\lambda (H1: (not (eq B b Abst))).(\lambda
-(v1: T).(\lambda (v2: T).(\lambda (_: (pr0 v1 v2)).(\lambda (H3: ((\forall
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+(lift h x1 x5) (\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T (THead (Bind b)
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+x2 x3) t4)))) (ex_intro2 T (\lambda (t4: T).(eq T (THead (Bind b) (lift h x1
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+x1)) (pr0_comp x2 x5 H11 x3 x4 H10 (Bind b))) u2 H_x0)))) (H2 x2 x1 H8)) t3
+H_x)))) (H4 x3 (S x1) H9)) x0 H7)))))) (lift_gen_bind b u1 t2 x0 h x1 H6))))
+(\lambda (f: F).(\lambda (H6: (eq T (THead (Flat f) u1 t2) (lift h x1
+x0))).(ex3_2_ind T T (\lambda (y0: T).(\lambda (z: T).(eq T x0 (THead (Flat
+f) y0 z)))) (\lambda (y0: T).(\lambda (_: T).(eq T u1 (lift h x1 y0))))
+(\lambda (_: T).(\lambda (z: T).(eq T t2 (lift h x1 z)))) (ex2 T (\lambda
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+(\lambda (t4: T).(pr0 x3 t4)) (ex2 T (\lambda (t4: T).(eq T (THead (Flat f)
+u2 t3) (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead (Flat f) x2 x3) t4)))
+(\lambda (x4: T).(\lambda (H_x: (eq T t3 (lift h x1 x4))).(\lambda (H10: (pr0
+x3 x4)).(eq_ind_r T (lift h x1 x4) (\lambda (t: T).(ex2 T (\lambda (t4:
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+(Flat f) x2 x3) t4)))) (ex2_ind T (\lambda (t4: T).(eq T u2 (lift h x1 t4)))
+(\lambda (t4: T).(pr0 x2 t4)) (ex2 T (\lambda (t4: T).(eq T (THead (Flat f)
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+(H11: (pr0 x2 x5)).(eq_ind_r T (lift h x1 x5) (\lambda (t: T).(ex2 T (\lambda
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+(t4: T).(pr0 (THead (Flat f) x2 x3) t4)))) (ex_intro2 T (\lambda (t4: T).(eq
+T (THead (Flat f) (lift h x1 x5) (lift h x1 x4)) (lift h x1 t4))) (\lambda
+(t4: T).(pr0 (THead (Flat f) x2 x3) t4)) (THead (Flat f) x5 x4) (sym_eq T
+(lift h x1 (THead (Flat f) x5 x4)) (THead (Flat f) (lift h x1 x5) (lift h x1
+x4)) (lift_flat f x5 x4 h x1)) (pr0_comp x2 x5 H11 x3 x4 H10 (Flat f))) u2
+H_x0)))) (H2 x2 x1 H8)) t3 H_x)))) (H4 x3 x1 H9)) x0 H7)))))) (lift_gen_flat
+f u1 t2 x0 h x1 H6)))) k H5))))))))))))) (\lambda (u: T).(\lambda (v1:
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+(t4: T).(eq T (THead (Bind Abbr) t (lift h (S x1) x6)) (lift h x1 t4)))
+(\lambda (t4: T).(pr0 (THead (Flat Appl) x2 (THead (Bind Abst) x4 x5)) t4))))
+(ex_intro2 T (\lambda (t4: T).(eq T (THead (Bind Abbr) (lift h x1 x7) (lift h
+(S x1) x6)) (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead (Flat Appl) x2
+(THead (Bind Abst) x4 x5)) t4)) (THead (Bind Abbr) x7 x6) (sym_eq T (lift h
+x1 (THead (Bind Abbr) x7 x6)) (THead (Bind Abbr) (lift h x1 x7) (lift h (S
+x1) x6)) (lift_bind Abbr x7 x6 h x1)) (pr0_beta x4 x2 x7 H13 x5 x6 H12)) v2
+H_x0)))) (H2 x2 x1 H7)) t3 H_x)))) (H4 x5 (S x1) H11)) x3 H9))))))
+(lift_gen_bind Abst u t2 x3 h x1 H8)) x0 H6)))))) (lift_gen_flat Appl v1
+(THead (Bind Abst) u t2) x0 h x1 H5)))))))))))))) (\lambda (b: B).(\lambda
+(H1: (not (eq B b Abst))).(\lambda (v1: T).(\lambda (v2: T).(\lambda (_: (pr0
+v1 v2)).(\lambda (H3: ((\forall (x0: T).(\forall (x1: nat).((eq T v1 (lift h
+x1 x0)) \to (ex2 T (\lambda (t2: T).(eq T v2 (lift h x1 t2))) (\lambda (t2:
+T).(pr0 x0 t2)))))))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (_: (pr0 u1
+u2)).(\lambda (H5: ((\forall (x0: T).(\forall (x1: nat).((eq T u1 (lift h x1
x0)) \to (ex2 T (\lambda (t2: T).(eq T u2 (lift h x1 t2))) (\lambda (t2:
T).(pr0 x0 t2)))))))).(\lambda (t2: T).(\lambda (t3: T).(\lambda (_: (pr0 t2
-t3)).(\lambda (H4: ((\forall (x0: T).(\forall (x1: nat).((eq T t2 (lift h x1
+t3)).(\lambda (H7: ((\forall (x0: T).(\forall (x1: nat).((eq T t2 (lift h x1
x0)) \to (ex2 T (\lambda (t4: T).(eq T t3 (lift h x1 t4))) (\lambda (t4:
-T).(pr0 x0 t4)))))))).(\lambda (w: T).(\lambda (H5: (subst0 O u2 t3
-w)).(\lambda (x0: T).(\lambda (x1: nat).(\lambda (H6: (eq T (THead (Bind
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-T).(eq T x0 (THead (Bind Abbr) y0 z)))) (\lambda (y0: T).(\lambda (_: T).(eq
-T u1 (lift h x1 y0)))) (\lambda (_: T).(\lambda (z: T).(eq T t2 (lift h (S
-x1) z)))) (ex2 T (\lambda (t4: T).(eq T (THead (Bind Abbr) u2 w) (lift h x1
-t4))) (\lambda (t4: T).(pr0 x0 t4))) (\lambda (x2: T).(\lambda (x3:
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-(lift h x1 x2))).(\lambda (H9: (eq T t2 (lift h (S x1) x3))).(eq_ind_r T
-(THead (Bind Abbr) x2 x3) (\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T
-(THead (Bind Abbr) u2 w) (lift h x1 t4))) (\lambda (t4: T).(pr0 t t4))))
-(ex2_ind T (\lambda (t4: T).(eq T t3 (lift h (S x1) t4))) (\lambda (t4:
-T).(pr0 x3 t4)) (ex2 T (\lambda (t4: T).(eq T (THead (Bind Abbr) u2 w) (lift
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-(x4: T).(\lambda (H_x: (eq T t3 (lift h (S x1) x4))).(\lambda (H10: (pr0 x3
-x4)).(let H11 \def (eq_ind T t3 (\lambda (t: T).(subst0 O u2 t w)) H5 (lift h
-(S x1) x4) H_x) in (ex2_ind T (\lambda (t4: T).(eq T u2 (lift h x1 t4)))
-(\lambda (t4: T).(pr0 x2 t4)) (ex2 T (\lambda (t4: T).(eq T (THead (Bind
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-(t4: T).(eq T (THead (Bind Abbr) t w) (lift h x1 t4))) (\lambda (t4: T).(pr0
-(THead (Bind Abbr) x2 x3) t4)))) (let H13 \def (eq_ind T u2 (\lambda (t:
-T).(subst0 O t (lift h (S x1) x4) w)) H11 (lift h x1 x5) H_x0) in (let H14
-\def (refl_equal nat (S (plus O x1))) in (let H15 \def (eq_ind nat (S x1)
-(\lambda (n: nat).(subst0 O (lift h x1 x5) (lift h n x4) w)) H13 (S (plus O
-x1)) H14) in (ex2_ind T (\lambda (t4: T).(eq T w (lift h (S (plus O x1))
-t4))) (\lambda (t4: T).(subst0 O x5 x4 t4)) (ex2 T (\lambda (t4: T).(eq T
-(THead (Bind Abbr) (lift h x1 x5) w) (lift h x1 t4))) (\lambda (t4: T).(pr0
-(THead (Bind Abbr) x2 x3) t4))) (\lambda (x6: T).(\lambda (H16: (eq T w (lift
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-h (S (plus O x1)) x6) (\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T (THead
-(Bind Abbr) (lift h x1 x5) t) (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead
-(Bind Abbr) x2 x3) t4)))) (ex_intro2 T (\lambda (t4: T).(eq T (THead (Bind
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-(t4: T).(pr0 (THead (Bind Abbr) x2 x3) t4)) (THead (Bind Abbr) x5 x6) (sym_eq
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-(lift h (S (plus O x1)) x6)) (lift_bind Abbr x5 x6 h (plus O x1))) (pr0_delta
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-(lift_gen_bind Abbr u1 t2 x0 h x1 H6))))))))))))))) (\lambda (b: B).(\lambda
-(H1: (not (eq B b Abst))).(\lambda (t2: T).(\lambda (t3: T).(\lambda (_: (pr0
-t2 t3)).(\lambda (H3: ((\forall (x0: T).(\forall (x1: nat).((eq T t2 (lift h
-x1 x0)) \to (ex2 T (\lambda (t4: T).(eq T t3 (lift h x1 t4))) (\lambda (t4:
-T).(pr0 x0 t4)))))))).(\lambda (u: T).(\lambda (x0: T).(\lambda (x1:
-nat).(\lambda (H4: (eq T (THead (Bind b) u (lift (S O) O t2)) (lift h x1
+T).(pr0 x0 t4)))))))).(\lambda (x0: T).(\lambda (x1: nat).(\lambda (H8: (eq T
+(THead (Flat Appl) v1 (THead (Bind b) u1 t2)) (lift h x1 x0))).(ex3_2_ind T T
+(\lambda (y0: T).(\lambda (z: T).(eq T x0 (THead (Flat Appl) y0 z))))
+(\lambda (y0: T).(\lambda (_: T).(eq T v1 (lift h x1 y0)))) (\lambda (_:
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+(\lambda (t4: T).(eq T (THead (Bind b) u2 (THead (Flat Appl) (lift (S O) O
+v2) t3)) (lift h x1 t4))) (\lambda (t4: T).(pr0 x0 t4))) (\lambda (x2:
+T).(\lambda (x3: T).(\lambda (H9: (eq T x0 (THead (Flat Appl) x2
+x3))).(\lambda (H10: (eq T v1 (lift h x1 x2))).(\lambda (H11: (eq T (THead
+(Bind b) u1 t2) (lift h x1 x3))).(eq_ind_r T (THead (Flat Appl) x2 x3)
+(\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T (THead (Bind b) u2 (THead (Flat
+Appl) (lift (S O) O v2) t3)) (lift h x1 t4))) (\lambda (t4: T).(pr0 t t4))))
+(ex3_2_ind T T (\lambda (y0: T).(\lambda (z: T).(eq T x3 (THead (Bind b) y0
+z)))) (\lambda (y0: T).(\lambda (_: T).(eq T u1 (lift h x1 y0)))) (\lambda
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+T).(eq T (THead (Bind b) u2 (THead (Flat Appl) (lift (S O) O v2) t3)) (lift h
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+x5))).(eq_ind_r T (THead (Bind b) x4 x5) (\lambda (t: T).(ex2 T (\lambda (t4:
+T).(eq T (THead (Bind b) u2 (THead (Flat Appl) (lift (S O) O v2) t3)) (lift h
+x1 t4))) (\lambda (t4: T).(pr0 (THead (Flat Appl) x2 t) t4)))) (ex2_ind T
+(\lambda (t4: T).(eq T t3 (lift h (S x1) t4))) (\lambda (t4: T).(pr0 x5 t4))
+(ex2 T (\lambda (t4: T).(eq T (THead (Bind b) u2 (THead (Flat Appl) (lift (S
+O) O v2) t3)) (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead (Flat Appl) x2
+(THead (Bind b) x4 x5)) t4))) (\lambda (x6: T).(\lambda (H_x: (eq T t3 (lift
+h (S x1) x6))).(\lambda (H15: (pr0 x5 x6)).(eq_ind_r T (lift h (S x1) x6)
+(\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T (THead (Bind b) u2 (THead (Flat
+Appl) (lift (S O) O v2) t)) (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead
+(Flat Appl) x2 (THead (Bind b) x4 x5)) t4)))) (ex2_ind T (\lambda (t4: T).(eq
+T u2 (lift h x1 t4))) (\lambda (t4: T).(pr0 x4 t4)) (ex2 T (\lambda (t4:
+T).(eq T (THead (Bind b) u2 (THead (Flat Appl) (lift (S O) O v2) (lift h (S
+x1) x6))) (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead (Flat Appl) x2 (THead
+(Bind b) x4 x5)) t4))) (\lambda (x7: T).(\lambda (H_x0: (eq T u2 (lift h x1
+x7))).(\lambda (H16: (pr0 x4 x7)).(eq_ind_r T (lift h x1 x7) (\lambda (t:
+T).(ex2 T (\lambda (t4: T).(eq T (THead (Bind b) t (THead (Flat Appl) (lift
+(S O) O v2) (lift h (S x1) x6))) (lift h x1 t4))) (\lambda (t4: T).(pr0
+(THead (Flat Appl) x2 (THead (Bind b) x4 x5)) t4)))) (ex2_ind T (\lambda (t4:
+T).(eq T v2 (lift h x1 t4))) (\lambda (t4: T).(pr0 x2 t4)) (ex2 T (\lambda
+(t4: T).(eq T (THead (Bind b) (lift h x1 x7) (THead (Flat Appl) (lift (S O) O
+v2) (lift h (S x1) x6))) (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead (Flat
+Appl) x2 (THead (Bind b) x4 x5)) t4))) (\lambda (x8: T).(\lambda (H_x1: (eq T
+v2 (lift h x1 x8))).(\lambda (H17: (pr0 x2 x8)).(eq_ind_r T (lift h x1 x8)
+(\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T (THead (Bind b) (lift h x1 x7)
+(THead (Flat Appl) (lift (S O) O t) (lift h (S x1) x6))) (lift h x1 t4)))
+(\lambda (t4: T).(pr0 (THead (Flat Appl) x2 (THead (Bind b) x4 x5)) t4))))
+(eq_ind T (lift h (plus (S O) x1) (lift (S O) O x8)) (\lambda (t: T).(ex2 T
+(\lambda (t4: T).(eq T (THead (Bind b) (lift h x1 x7) (THead (Flat Appl) t
+(lift h (S x1) x6))) (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead (Flat
+Appl) x2 (THead (Bind b) x4 x5)) t4)))) (eq_ind T (lift h (S x1) (THead (Flat
+Appl) (lift (S O) O x8) x6)) (\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T
+(THead (Bind b) (lift h x1 x7) t) (lift h x1 t4))) (\lambda (t4: T).(pr0
+(THead (Flat Appl) x2 (THead (Bind b) x4 x5)) t4)))) (ex_intro2 T (\lambda
+(t4: T).(eq T (THead (Bind b) (lift h x1 x7) (lift h (S x1) (THead (Flat
+Appl) (lift (S O) O x8) x6))) (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead
+(Flat Appl) x2 (THead (Bind b) x4 x5)) t4)) (THead (Bind b) x7 (THead (Flat
+Appl) (lift (S O) O x8) x6)) (sym_eq T (lift h x1 (THead (Bind b) x7 (THead
+(Flat Appl) (lift (S O) O x8) x6))) (THead (Bind b) (lift h x1 x7) (lift h (S
+x1) (THead (Flat Appl) (lift (S O) O x8) x6))) (lift_bind b x7 (THead (Flat
+Appl) (lift (S O) O x8) x6) h x1)) (pr0_upsilon b H1 x2 x8 H17 x4 x7 H16 x5
+x6 H15)) (THead (Flat Appl) (lift h (S x1) (lift (S O) O x8)) (lift h (S x1)
+x6)) (lift_flat Appl (lift (S O) O x8) x6 h (S x1))) (lift (S O) O (lift h x1
+x8)) (lift_d x8 h (S O) x1 O (le_O_n x1))) v2 H_x1)))) (H3 x2 x1 H10)) u2
+H_x0)))) (H5 x4 x1 H13)) t3 H_x)))) (H7 x5 (S x1) H14)) x3 H12))))))
+(lift_gen_bind b u1 t2 x3 h x1 H11)) x0 H9)))))) (lift_gen_flat Appl v1
+(THead (Bind b) u1 t2) x0 h x1 H8))))))))))))))))))) (\lambda (u1:
+T).(\lambda (u2: T).(\lambda (_: (pr0 u1 u2)).(\lambda (H2: ((\forall (x0:
+T).(\forall (x1: nat).((eq T u1 (lift h x1 x0)) \to (ex2 T (\lambda (t2:
+T).(eq T u2 (lift h x1 t2))) (\lambda (t2: T).(pr0 x0 t2)))))))).(\lambda
+(t2: T).(\lambda (t3: T).(\lambda (_: (pr0 t2 t3)).(\lambda (H4: ((\forall
+(x0: T).(\forall (x1: nat).((eq T t2 (lift h x1 x0)) \to (ex2 T (\lambda (t4:
+T).(eq T t3 (lift h x1 t4))) (\lambda (t4: T).(pr0 x0 t4)))))))).(\lambda (w:
+T).(\lambda (H5: (subst0 O u2 t3 w)).(\lambda (x0: T).(\lambda (x1:
+nat).(\lambda (H6: (eq T (THead (Bind Abbr) u1 t2) (lift h x1
x0))).(ex3_2_ind T T (\lambda (y0: T).(\lambda (z: T).(eq T x0 (THead (Bind
-b) y0 z)))) (\lambda (y0: T).(\lambda (_: T).(eq T u (lift h x1 y0))))
-(\lambda (_: T).(\lambda (z: T).(eq T (lift (S O) O t2) (lift h (S x1) z))))
-(ex2 T (\lambda (t4: T).(eq T t3 (lift h x1 t4))) (\lambda (t4: T).(pr0 x0
-t4))) (\lambda (x2: T).(\lambda (x3: T).(\lambda (H5: (eq T x0 (THead (Bind
-b) x2 x3))).(\lambda (_: (eq T u (lift h x1 x2))).(\lambda (H7: (eq T (lift
-(S O) O t2) (lift h (S x1) x3))).(eq_ind_r T (THead (Bind b) x2 x3) (\lambda
-(t: T).(ex2 T (\lambda (t4: T).(eq T t3 (lift h x1 t4))) (\lambda (t4:
-T).(pr0 t t4)))) (let H8 \def (eq_ind_r nat (plus (S O) x1) (\lambda (n:
-nat).(eq nat (S x1) n)) (refl_equal nat (plus (S O) x1)) (plus x1 (S O))
-(plus_comm x1 (S O))) in (let H9 \def (eq_ind nat (S x1) (\lambda (n:
-nat).(eq T (lift (S O) O t2) (lift h n x3))) H7 (plus x1 (S O)) H8) in
-(ex2_ind T (\lambda (t4: T).(eq T x3 (lift (S O) O t4))) (\lambda (t4: T).(eq
-T t2 (lift h x1 t4))) (ex2 T (\lambda (t4: T).(eq T t3 (lift h x1 t4)))
-(\lambda (t4: T).(pr0 (THead (Bind b) x2 x3) t4))) (\lambda (x4: T).(\lambda
-(H10: (eq T x3 (lift (S O) O x4))).(\lambda (H11: (eq T t2 (lift h x1
-x4))).(eq_ind_r T (lift (S O) O x4) (\lambda (t: T).(ex2 T (\lambda (t4:
+Abbr) y0 z)))) (\lambda (y0: T).(\lambda (_: T).(eq T u1 (lift h x1 y0))))
+(\lambda (_: T).(\lambda (z: T).(eq T t2 (lift h (S x1) z)))) (ex2 T (\lambda
+(t4: T).(eq T (THead (Bind Abbr) u2 w) (lift h x1 t4))) (\lambda (t4: T).(pr0
+x0 t4))) (\lambda (x2: T).(\lambda (x3: T).(\lambda (H7: (eq T x0 (THead
+(Bind Abbr) x2 x3))).(\lambda (H8: (eq T u1 (lift h x1 x2))).(\lambda (H9:
+(eq T t2 (lift h (S x1) x3))).(eq_ind_r T (THead (Bind Abbr) x2 x3) (\lambda
+(t: T).(ex2 T (\lambda (t4: T).(eq T (THead (Bind Abbr) u2 w) (lift h x1
+t4))) (\lambda (t4: T).(pr0 t t4)))) (ex2_ind T (\lambda (t4: T).(eq T t3
+(lift h (S x1) t4))) (\lambda (t4: T).(pr0 x3 t4)) (ex2 T (\lambda (t4:
+T).(eq T (THead (Bind Abbr) u2 w) (lift h x1 t4))) (\lambda (t4: T).(pr0
+(THead (Bind Abbr) x2 x3) t4))) (\lambda (x4: T).(\lambda (H_x: (eq T t3
+(lift h (S x1) x4))).(\lambda (H10: (pr0 x3 x4)).(let H11 \def (eq_ind T t3
+(\lambda (t: T).(subst0 O u2 t w)) H5 (lift h (S x1) x4) H_x) in (ex2_ind T
+(\lambda (t4: T).(eq T u2 (lift h x1 t4))) (\lambda (t4: T).(pr0 x2 t4)) (ex2
+T (\lambda (t4: T).(eq T (THead (Bind Abbr) u2 w) (lift h x1 t4))) (\lambda
+(t4: T).(pr0 (THead (Bind Abbr) x2 x3) t4))) (\lambda (x5: T).(\lambda (H_x0:
+(eq T u2 (lift h x1 x5))).(\lambda (H12: (pr0 x2 x5)).(eq_ind_r T (lift h x1
+x5) (\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T (THead (Bind Abbr) t w)
+(lift h x1 t4))) (\lambda (t4: T).(pr0 (THead (Bind Abbr) x2 x3) t4)))) (let
+H13 \def (eq_ind T u2 (\lambda (t: T).(subst0 O t (lift h (S x1) x4) w)) H11
+(lift h x1 x5) H_x0) in (let H14 \def (refl_equal nat (S (plus O x1))) in
+(let H15 \def (eq_ind nat (S x1) (\lambda (n: nat).(subst0 O (lift h x1 x5)
+(lift h n x4) w)) H13 (S (plus O x1)) H14) in (ex2_ind T (\lambda (t4: T).(eq
+T w (lift h (S (plus O x1)) t4))) (\lambda (t4: T).(subst0 O x5 x4 t4)) (ex2
+T (\lambda (t4: T).(eq T (THead (Bind Abbr) (lift h x1 x5) w) (lift h x1
+t4))) (\lambda (t4: T).(pr0 (THead (Bind Abbr) x2 x3) t4))) (\lambda (x6:
+T).(\lambda (H16: (eq T w (lift h (S (plus O x1)) x6))).(\lambda (H17:
+(subst0 O x5 x4 x6)).(eq_ind_r T (lift h (S (plus O x1)) x6) (\lambda (t:
+T).(ex2 T (\lambda (t4: T).(eq T (THead (Bind Abbr) (lift h x1 x5) t) (lift h
+x1 t4))) (\lambda (t4: T).(pr0 (THead (Bind Abbr) x2 x3) t4)))) (ex_intro2 T
+(\lambda (t4: T).(eq T (THead (Bind Abbr) (lift h x1 x5) (lift h (S (plus O
+x1)) x6)) (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead (Bind Abbr) x2 x3)
+t4)) (THead (Bind Abbr) x5 x6) (sym_eq T (lift h x1 (THead (Bind Abbr) x5
+x6)) (THead (Bind Abbr) (lift h x1 x5) (lift h (S (plus O x1)) x6))
+(lift_bind Abbr x5 x6 h (plus O x1))) (pr0_delta x2 x5 H12 x3 x4 H10 x6 H17))
+w H16)))) (subst0_gen_lift_lt x5 x4 w O h x1 H15))))) u2 H_x0)))) (H2 x2 x1
+H8)))))) (H4 x3 (S x1) H9)) x0 H7)))))) (lift_gen_bind Abbr u1 t2 x0 h x1
+H6))))))))))))))) (\lambda (b: B).(\lambda (H1: (not (eq B b Abst))).(\lambda
+(t2: T).(\lambda (t3: T).(\lambda (_: (pr0 t2 t3)).(\lambda (H3: ((\forall
+(x0: T).(\forall (x1: nat).((eq T t2 (lift h x1 x0)) \to (ex2 T (\lambda (t4:
+T).(eq T t3 (lift h x1 t4))) (\lambda (t4: T).(pr0 x0 t4)))))))).(\lambda (u:
+T).(\lambda (x0: T).(\lambda (x1: nat).(\lambda (H4: (eq T (THead (Bind b) u
+(lift (S O) O t2)) (lift h x1 x0))).(ex3_2_ind T T (\lambda (y0: T).(\lambda
+(z: T).(eq T x0 (THead (Bind b) y0 z)))) (\lambda (y0: T).(\lambda (_: T).(eq
+T u (lift h x1 y0)))) (\lambda (_: T).(\lambda (z: T).(eq T (lift (S O) O t2)
+(lift h (S x1) z)))) (ex2 T (\lambda (t4: T).(eq T t3 (lift h x1 t4)))
+(\lambda (t4: T).(pr0 x0 t4))) (\lambda (x2: T).(\lambda (x3: T).(\lambda
+(H5: (eq T x0 (THead (Bind b) x2 x3))).(\lambda (_: (eq T u (lift h x1
+x2))).(\lambda (H7: (eq T (lift (S O) O t2) (lift h (S x1) x3))).(eq_ind_r T
+(THead (Bind b) x2 x3) (\lambda (t: T).(ex2 T (\lambda (t4: T).(eq T t3 (lift
+h x1 t4))) (\lambda (t4: T).(pr0 t t4)))) (let H8 \def (eq_ind_r nat (plus (S
+O) x1) (\lambda (n: nat).(eq nat (S x1) n)) (refl_equal nat (plus (S O) x1))
+(plus x1 (S O)) (plus_comm x1 (S O))) in (let H9 \def (eq_ind nat (S x1)
+(\lambda (n: nat).(eq T (lift (S O) O t2) (lift h n x3))) H7 (plus x1 (S O))
+H8) in (ex2_ind T (\lambda (t4: T).(eq T x3 (lift (S O) O t4))) (\lambda (t4:
+T).(eq T t2 (lift h x1 t4))) (ex2 T (\lambda (t4: T).(eq T t3 (lift h x1
+t4))) (\lambda (t4: T).(pr0 (THead (Bind b) x2 x3) t4))) (\lambda (x4:
+T).(\lambda (H10: (eq T x3 (lift (S O) O x4))).(\lambda (H11: (eq T t2 (lift
+h x1 x4))).(eq_ind_r T (lift (S O) O x4) (\lambda (t: T).(ex2 T (\lambda (t4:
T).(eq T t3 (lift h x1 t4))) (\lambda (t4: T).(pr0 (THead (Bind b) x2 t)
t4)))) (ex2_ind T (\lambda (t4: T).(eq T t3 (lift h x1 t4))) (\lambda (t4:
T).(pr0 x4 t4)) (ex2 T (\lambda (t4: T).(eq T t3 (lift h x1 t4))) (\lambda
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