--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/ty3/dec".
+
+include "ty3/pr3_props.ma".
+
+include "pc3/dec.ma".
+
+include "getl/flt.ma".
+
+include "getl/dec.ma".
+
+theorem ty3_inference:
+ \forall (g: G).(\forall (c: C).(\forall (t1: T).(or (ex T (\lambda (t2:
+T).(ty3 g c t1 t2))) (\forall (t2: T).((ty3 g c t1 t2) \to (\forall (P:
+Prop).P))))))
+\def
+ \lambda (g: G).(\lambda (c: C).(\lambda (t1: T).(flt_wf_ind (\lambda (c0:
+C).(\lambda (t: T).(or (ex T (\lambda (t2: T).(ty3 g c0 t t2))) (\forall (t2:
+T).((ty3 g c0 t t2) \to (\forall (P: Prop).P)))))) (\lambda (c2: C).(\lambda
+(t2: T).(T_ind (\lambda (t: T).(((\forall (c1: C).(\forall (t3: T).((flt c1
+t3 c2 t) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4:
+T).((ty3 g c1 t3 t4) \to (\forall (P: Prop).P)))))))) \to (or (ex T (\lambda
+(t3: T).(ty3 g c2 t t3))) (\forall (t3: T).((ty3 g c2 t t3) \to (\forall (P:
+Prop).P)))))) (\lambda (n: nat).(\lambda (_: ((\forall (c1: C).(\forall (t3:
+T).((flt c1 t3 c2 (TSort n)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3
+t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to (\forall (P:
+Prop).P))))))))).(or_introl (ex T (\lambda (t3: T).(ty3 g c2 (TSort n) t3)))
+(\forall (t3: T).((ty3 g c2 (TSort n) t3) \to (\forall (P: Prop).P)))
+(ex_intro T (\lambda (t3: T).(ty3 g c2 (TSort n) t3)) (TSort (next g n))
+(ty3_sort g c2 n))))) (\lambda (n: nat).(\lambda (H: ((\forall (c1:
+C).(\forall (t3: T).((flt c1 t3 c2 (TLRef n)) \to (or (ex T (\lambda (t4:
+T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to (\forall (P:
+Prop).P))))))))).(let H_x \def (getl_dec c2 n) in (let H0 \def H_x in (or_ind
+(ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl n c2 (CHead
+e (Bind b) v)))))) (\forall (d: C).((getl n c2 d) \to (\forall (P: Prop).P)))
+(or (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g
+c2 (TLRef n) t3) \to (\forall (P: Prop).P)))) (\lambda (H1: (ex_3 C B T
+(\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl n c2 (CHead e (Bind b)
+v))))))).(ex_3_ind C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v:
+T).(getl n c2 (CHead e (Bind b) v))))) (or (ex T (\lambda (t3: T).(ty3 g c2
+(TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to (\forall (P:
+Prop).P)))) (\lambda (x0: C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H2:
+(getl n c2 (CHead x0 (Bind x1) x2))).(let H3 \def (H x0 x2 (getl_flt x1 c2 x0
+x2 n H2)) in (or_ind (ex T (\lambda (t3: T).(ty3 g x0 x2 t3))) (\forall (t3:
+T).((ty3 g x0 x2 t3) \to (\forall (P: Prop).P))) (or (ex T (\lambda (t3:
+T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to
+(\forall (P: Prop).P)))) (\lambda (H4: (ex T (\lambda (t3: T).(ty3 g x0 x2
+t3)))).(ex_ind T (\lambda (t3: T).(ty3 g x0 x2 t3)) (or (ex T (\lambda (t3:
+T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to
+(\forall (P: Prop).P)))) (\lambda (x: T).(\lambda (H5: (ty3 g x0 x2
+x)).(B_ind (\lambda (b: B).((getl n c2 (CHead x0 (Bind b) x2)) \to (or (ex T
+(\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef
+n) t3) \to (\forall (P: Prop).P)))))) (\lambda (H6: (getl n c2 (CHead x0
+(Bind Abbr) x2))).(or_introl (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3)))
+(\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to (\forall (P: Prop).P)))
+(ex_intro T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3)) (lift (S n) O x)
+(ty3_abbr g n c2 x0 x2 H6 x H5)))) (\lambda (H6: (getl n c2 (CHead x0 (Bind
+Abst) x2))).(or_introl (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3)))
+(\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to (\forall (P: Prop).P)))
+(ex_intro T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3)) (lift (S n) O x2)
+(ty3_abst g n c2 x0 x2 H6 x H5)))) (\lambda (H6: (getl n c2 (CHead x0 (Bind
+Void) x2))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3)))
+(\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to (\forall (P: Prop).P)))
+(\lambda (t3: T).(\lambda (H7: (ty3 g c2 (TLRef n) t3)).(\lambda (P:
+Prop).(or_ind (ex3_3 C T T (\lambda (_: C).(\lambda (_: T).(\lambda (t:
+T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda
+(_: T).(getl n c2 (CHead e (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u:
+T).(\lambda (t: T).(ty3 g e u t))))) (ex3_3 C T T (\lambda (_: C).(\lambda
+(u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3)))) (\lambda (e:
+C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abst) u)))))
+(\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t))))) P (\lambda
+(H8: (ex3_3 C T T (\lambda (_: C).(\lambda (_: T).(\lambda (t: T).(pc3 c2
+(lift (S n) O t) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl
+n c2 (CHead e (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t:
+T).(ty3 g e u t)))))).(ex3_3_ind C T T (\lambda (_: C).(\lambda (_:
+T).(\lambda (t: T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda
+(u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abbr) u))))) (\lambda (e:
+C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))) P (\lambda (x3:
+C).(\lambda (x4: T).(\lambda (x5: T).(\lambda (_: (pc3 c2 (lift (S n) O x5)
+t3)).(\lambda (H10: (getl n c2 (CHead x3 (Bind Abbr) x4))).(\lambda (_: (ty3
+g x3 x4 x5)).(let H12 \def (eq_ind C (CHead x0 (Bind Void) x2) (\lambda (c0:
+C).(getl n c2 c0)) H6 (CHead x3 (Bind Abbr) x4) (getl_mono c2 (CHead x0 (Bind
+Void) x2) n H6 (CHead x3 (Bind Abbr) x4) H10)) in (let H13 \def (eq_ind C
+(CHead x0 (Bind Void) x2) (\lambda (ee: C).(match ee in C return (\lambda (_:
+C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match
+k in K return (\lambda (_: K).Prop) with [(Bind b) \Rightarrow (match b in B
+return (\lambda (_: B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow
+False | Void \Rightarrow True]) | (Flat _) \Rightarrow False])])) I (CHead x3
+(Bind Abbr) x4) (getl_mono c2 (CHead x0 (Bind Void) x2) n H6 (CHead x3 (Bind
+Abbr) x4) H10)) in (False_ind P H13))))))))) H8)) (\lambda (H8: (ex3_3 C T T
+(\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u)
+t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
+(Bind Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
+t)))))).(ex3_3_ind C T T (\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3
+c2 (lift (S n) O u) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_:
+T).(getl n c2 (CHead e (Bind Abst) u))))) (\lambda (e: C).(\lambda (u:
+T).(\lambda (t: T).(ty3 g e u t)))) P (\lambda (x3: C).(\lambda (x4:
+T).(\lambda (x5: T).(\lambda (_: (pc3 c2 (lift (S n) O x4) t3)).(\lambda
+(H10: (getl n c2 (CHead x3 (Bind Abst) x4))).(\lambda (_: (ty3 g x3 x4
+x5)).(let H12 \def (eq_ind C (CHead x0 (Bind Void) x2) (\lambda (c0: C).(getl
+n c2 c0)) H6 (CHead x3 (Bind Abst) x4) (getl_mono c2 (CHead x0 (Bind Void)
+x2) n H6 (CHead x3 (Bind Abst) x4) H10)) in (let H13 \def (eq_ind C (CHead x0
+(Bind Void) x2) (\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop)
+with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match k in K
+return (\lambda (_: K).Prop) with [(Bind b) \Rightarrow (match b in B return
+(\lambda (_: B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow False |
+Void \Rightarrow True]) | (Flat _) \Rightarrow False])])) I (CHead x3 (Bind
+Abst) x4) (getl_mono c2 (CHead x0 (Bind Void) x2) n H6 (CHead x3 (Bind Abst)
+x4) H10)) in (False_ind P H13))))))))) H8)) (ty3_gen_lref g c2 t3 n H7)))))))
+x1 H2))) H4)) (\lambda (H4: ((\forall (t3: T).((ty3 g x0 x2 t3) \to (\forall
+(P: Prop).P))))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3)))
+(\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to (\forall (P: Prop).P)))
+(\lambda (t3: T).(\lambda (H5: (ty3 g c2 (TLRef n) t3)).(\lambda (P:
+Prop).(or_ind (ex3_3 C T T (\lambda (_: C).(\lambda (_: T).(\lambda (t:
+T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda
+(_: T).(getl n c2 (CHead e (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u:
+T).(\lambda (t: T).(ty3 g e u t))))) (ex3_3 C T T (\lambda (_: C).(\lambda
+(u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3)))) (\lambda (e:
+C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abst) u)))))
+(\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t))))) P (\lambda
+(H6: (ex3_3 C T T (\lambda (_: C).(\lambda (_: T).(\lambda (t: T).(pc3 c2
+(lift (S n) O t) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl
+n c2 (CHead e (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t:
+T).(ty3 g e u t)))))).(ex3_3_ind C T T (\lambda (_: C).(\lambda (_:
+T).(\lambda (t: T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda
+(u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abbr) u))))) (\lambda (e:
+C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))) P (\lambda (x3:
+C).(\lambda (x4: T).(\lambda (x5: T).(\lambda (_: (pc3 c2 (lift (S n) O x5)
+t3)).(\lambda (H8: (getl n c2 (CHead x3 (Bind Abbr) x4))).(\lambda (H9: (ty3
+g x3 x4 x5)).(let H10 \def (eq_ind C (CHead x0 (Bind x1) x2) (\lambda (c0:
+C).(getl n c2 c0)) H2 (CHead x3 (Bind Abbr) x4) (getl_mono c2 (CHead x0 (Bind
+x1) x2) n H2 (CHead x3 (Bind Abbr) x4) H8)) in (let H11 \def (f_equal C C
+(\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
+\Rightarrow x0 | (CHead c0 _ _) \Rightarrow c0])) (CHead x0 (Bind x1) x2)
+(CHead x3 (Bind Abbr) x4) (getl_mono c2 (CHead x0 (Bind x1) x2) n H2 (CHead
+x3 (Bind Abbr) x4) H8)) in ((let H12 \def (f_equal C B (\lambda (e: C).(match
+e in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow x1 | (CHead _ k
+_) \Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind b)
+\Rightarrow b | (Flat _) \Rightarrow x1])])) (CHead x0 (Bind x1) x2) (CHead
+x3 (Bind Abbr) x4) (getl_mono c2 (CHead x0 (Bind x1) x2) n H2 (CHead x3 (Bind
+Abbr) x4) H8)) in ((let H13 \def (f_equal C T (\lambda (e: C).(match e in C
+return (\lambda (_: C).T) with [(CSort _) \Rightarrow x2 | (CHead _ _ t)
+\Rightarrow t])) (CHead x0 (Bind x1) x2) (CHead x3 (Bind Abbr) x4) (getl_mono
+c2 (CHead x0 (Bind x1) x2) n H2 (CHead x3 (Bind Abbr) x4) H8)) in (\lambda
+(_: (eq B x1 Abbr)).(\lambda (H15: (eq C x0 x3)).(let H16 \def (eq_ind_r T x4
+(\lambda (t: T).(getl n c2 (CHead x3 (Bind Abbr) t))) H10 x2 H13) in (let H17
+\def (eq_ind_r T x4 (\lambda (t: T).(ty3 g x3 t x5)) H9 x2 H13) in (let H18
+\def (eq_ind_r C x3 (\lambda (c0: C).(getl n c2 (CHead c0 (Bind Abbr) x2)))
+H16 x0 H15) in (let H19 \def (eq_ind_r C x3 (\lambda (c0: C).(ty3 g c0 x2
+x5)) H17 x0 H15) in (H4 x5 H19 P)))))))) H12)) H11))))))))) H6)) (\lambda
+(H6: (ex3_3 C T T (\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2
+(lift (S n) O u) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl
+n c2 (CHead e (Bind Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t:
+T).(ty3 g e u t)))))).(ex3_3_ind C T T (\lambda (_: C).(\lambda (u:
+T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3)))) (\lambda (e: C).(\lambda
+(u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abst) u))))) (\lambda (e:
+C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))) P (\lambda (x3:
+C).(\lambda (x4: T).(\lambda (x5: T).(\lambda (H7: (pc3 c2 (lift (S n) O x4)
+t3)).(\lambda (H8: (getl n c2 (CHead x3 (Bind Abst) x4))).(\lambda (H9: (ty3
+g x3 x4 x5)).(let H10 \def (eq_ind C (CHead x0 (Bind x1) x2) (\lambda (c0:
+C).(getl n c2 c0)) H2 (CHead x3 (Bind Abst) x4) (getl_mono c2 (CHead x0 (Bind
+x1) x2) n H2 (CHead x3 (Bind Abst) x4) H8)) in (let H11 \def (f_equal C C
+(\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
+\Rightarrow x0 | (CHead c0 _ _) \Rightarrow c0])) (CHead x0 (Bind x1) x2)
+(CHead x3 (Bind Abst) x4) (getl_mono c2 (CHead x0 (Bind x1) x2) n H2 (CHead
+x3 (Bind Abst) x4) H8)) in ((let H12 \def (f_equal C B (\lambda (e: C).(match
+e in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow x1 | (CHead _ k
+_) \Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind b)
+\Rightarrow b | (Flat _) \Rightarrow x1])])) (CHead x0 (Bind x1) x2) (CHead
+x3 (Bind Abst) x4) (getl_mono c2 (CHead x0 (Bind x1) x2) n H2 (CHead x3 (Bind
+Abst) x4) H8)) in ((let H13 \def (f_equal C T (\lambda (e: C).(match e in C
+return (\lambda (_: C).T) with [(CSort _) \Rightarrow x2 | (CHead _ _ t)
+\Rightarrow t])) (CHead x0 (Bind x1) x2) (CHead x3 (Bind Abst) x4) (getl_mono
+c2 (CHead x0 (Bind x1) x2) n H2 (CHead x3 (Bind Abst) x4) H8)) in (\lambda
+(_: (eq B x1 Abst)).(\lambda (H15: (eq C x0 x3)).(let H16 \def (eq_ind_r T x4
+(\lambda (t: T).(getl n c2 (CHead x3 (Bind Abst) t))) H10 x2 H13) in (let H17
+\def (eq_ind_r T x4 (\lambda (t: T).(ty3 g x3 t x5)) H9 x2 H13) in (let H18
+\def (eq_ind_r T x4 (\lambda (t: T).(pc3 c2 (lift (S n) O t) t3)) H7 x2 H13)
+in (let H19 \def (eq_ind_r C x3 (\lambda (c0: C).(getl n c2 (CHead c0 (Bind
+Abst) x2))) H16 x0 H15) in (let H20 \def (eq_ind_r C x3 (\lambda (c0: C).(ty3
+g c0 x2 x5)) H17 x0 H15) in (H4 x5 H20 P))))))))) H12)) H11))))))))) H6))
+(ty3_gen_lref g c2 t3 n H5))))))) H3)))))) H1)) (\lambda (H1: ((\forall (d:
+C).((getl n c2 d) \to (\forall (P: Prop).P))))).(or_intror (ex T (\lambda
+(t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef n) t3)
+\to (\forall (P: Prop).P))) (\lambda (t3: T).(\lambda (H2: (ty3 g c2 (TLRef
+n) t3)).(\lambda (P: Prop).(or_ind (ex3_3 C T T (\lambda (_: C).(\lambda (_:
+T).(\lambda (t: T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda
+(u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abbr) u))))) (\lambda (e:
+C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t))))) (ex3_3 C T T (\lambda
+(_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3))))
+(\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind
+Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
+t))))) P (\lambda (H3: (ex3_3 C T T (\lambda (_: C).(\lambda (_: T).(\lambda
+(t: T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda (u:
+T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abbr) u))))) (\lambda (e:
+C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind C T T
+(\lambda (_: C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O t)
+t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
+(Bind Abbr) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
+t)))) P (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: T).(\lambda (_: (pc3
+c2 (lift (S n) O x2) t3)).(\lambda (H5: (getl n c2 (CHead x0 (Bind Abbr)
+x1))).(\lambda (_: (ty3 g x0 x1 x2)).(H1 (CHead x0 (Bind Abbr) x1) H5
+P))))))) H3)) (\lambda (H3: (ex3_3 C T T (\lambda (_: C).(\lambda (u:
+T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3)))) (\lambda (e: C).(\lambda
+(u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abst) u))))) (\lambda (e:
+C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind C T T
+(\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u)
+t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
+(Bind Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
+t)))) P (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: T).(\lambda (_: (pc3
+c2 (lift (S n) O x1) t3)).(\lambda (H5: (getl n c2 (CHead x0 (Bind Abst)
+x1))).(\lambda (_: (ty3 g x0 x1 x2)).(H1 (CHead x0 (Bind Abst) x1) H5
+P))))))) H3)) (ty3_gen_lref g c2 t3 n H2))))))) H0))))) (\lambda (k:
+K).(\lambda (t: T).(\lambda (_: ((((\forall (c1: C).(\forall (t3: T).((flt c1
+t3 c2 t) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4:
+T).((ty3 g c1 t3 t4) \to (\forall (P: Prop).P)))))))) \to (or (ex T (\lambda
+(t3: T).(ty3 g c2 t t3))) (\forall (t3: T).((ty3 g c2 t t3) \to (\forall (P:
+Prop).P))))))).(\lambda (t0: T).(\lambda (_: ((((\forall (c1: C).(\forall
+(t3: T).((flt c1 t3 c2 t0) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4)))
+(\forall (t4: T).((ty3 g c1 t3 t4) \to (\forall (P: Prop).P)))))))) \to (or
+(ex T (\lambda (t3: T).(ty3 g c2 t0 t3))) (\forall (t3: T).((ty3 g c2 t0 t3)
+\to (\forall (P: Prop).P))))))).(\lambda (H1: ((\forall (c1: C).(\forall (t3:
+T).((flt c1 t3 c2 (THead k t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3
+t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to (\forall (P:
+Prop).P))))))))).(K_ind (\lambda (k0: K).(((\forall (c1: C).(\forall (t3:
+T).((flt c1 t3 c2 (THead k0 t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1
+t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to (\forall (P: Prop).P))))))))
+\to (or (ex T (\lambda (t3: T).(ty3 g c2 (THead k0 t t0) t3))) (\forall (t3:
+T).((ty3 g c2 (THead k0 t t0) t3) \to (\forall (P: Prop).P)))))) (\lambda (b:
+B).(\lambda (H2: ((\forall (c1: C).(\forall (t3: T).((flt c1 t3 c2 (THead
+(Bind b) t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall
+(t4: T).((ty3 g c1 t3 t4) \to (\forall (P: Prop).P))))))))).(let H3 \def (H2
+c2 t (flt_thead_sx (Bind b) c2 t t0)) in (or_ind (ex T (\lambda (t3: T).(ty3
+g c2 t t3))) (\forall (t3: T).((ty3 g c2 t t3) \to (\forall (P: Prop).P)))
+(or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t t0) t3))) (\forall
+(t3: T).((ty3 g c2 (THead (Bind b) t t0) t3) \to (\forall (P: Prop).P))))
+(\lambda (H4: (ex T (\lambda (t3: T).(ty3 g c2 t t3)))).(ex_ind T (\lambda
+(t3: T).(ty3 g c2 t t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Bind b)
+t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3) \to
+(\forall (P: Prop).P)))) (\lambda (x: T).(\lambda (H5: (ty3 g c2 t x)).(let
+H6 \def (H2 (CHead c2 (Bind b) t) t0 (flt_shift (Bind b) c2 t t0)) in (or_ind
+(ex T (\lambda (t3: T).(ty3 g (CHead c2 (Bind b) t) t0 t3))) (\forall (t3:
+T).((ty3 g (CHead c2 (Bind b) t) t0 t3) \to (\forall (P: Prop).P))) (or (ex T
+(\lambda (t3: T).(ty3 g c2 (THead (Bind b) t t0) t3))) (\forall (t3: T).((ty3
+g c2 (THead (Bind b) t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (H7: (ex
+T (\lambda (t3: T).(ty3 g (CHead c2 (Bind b) t) t0 t3)))).(ex_ind T (\lambda
+(t3: T).(ty3 g (CHead c2 (Bind b) t) t0 t3)) (or (ex T (\lambda (t3: T).(ty3
+g c2 (THead (Bind b) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b)
+t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (x0: T).(\lambda (H8: (ty3 g
+(CHead c2 (Bind b) t) t0 x0)).(ex_ind T (\lambda (t3: T).(ty3 g (CHead c2
+(Bind b) t) x0 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t
+t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3) \to (\forall
+(P: Prop).P)))) (\lambda (x1: T).(\lambda (H9: (ty3 g (CHead c2 (Bind b) t)
+x0 x1)).(or_introl (ex T (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t t0)
+t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3) \to (\forall (P:
+Prop).P))) (ex_intro T (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t t0) t3))
+(THead (Bind b) t x0) (ty3_bind g c2 t x H5 b t0 x0 H8 x1 H9)))))
+(ty3_correct g (CHead c2 (Bind b) t) t0 x0 H8)))) H7)) (\lambda (H7:
+((\forall (t3: T).((ty3 g (CHead c2 (Bind b) t) t0 t3) \to (\forall (P:
+Prop).P))))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t
+t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3) \to (\forall
+(P: Prop).P))) (\lambda (t3: T).(\lambda (H8: (ty3 g c2 (THead (Bind b) t t0)
+t3)).(\lambda (P: Prop).(ex4_3_ind T T T (\lambda (t4: T).(\lambda (_:
+T).(\lambda (_: T).(pc3 c2 (THead (Bind b) t t4) t3)))) (\lambda (_:
+T).(\lambda (t5: T).(\lambda (_: T).(ty3 g c2 t t5)))) (\lambda (t4:
+T).(\lambda (_: T).(\lambda (_: T).(ty3 g (CHead c2 (Bind b) t) t0 t4))))
+(\lambda (t4: T).(\lambda (_: T).(\lambda (t6: T).(ty3 g (CHead c2 (Bind b)
+t) t4 t6)))) P (\lambda (x0: T).(\lambda (x1: T).(\lambda (x2: T).(\lambda
+(_: (pc3 c2 (THead (Bind b) t x0) t3)).(\lambda (_: (ty3 g c2 t x1)).(\lambda
+(H11: (ty3 g (CHead c2 (Bind b) t) t0 x0)).(\lambda (_: (ty3 g (CHead c2
+(Bind b) t) x0 x2)).(H7 x0 H11 P)))))))) (ty3_gen_bind g b c2 t t0 t3
+H8))))))) H6)))) H4)) (\lambda (H4: ((\forall (t3: T).((ty3 g c2 t t3) \to
+(\forall (P: Prop).P))))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead
+(Bind b) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3)
+\to (\forall (P: Prop).P))) (\lambda (t3: T).(\lambda (H5: (ty3 g c2 (THead
+(Bind b) t t0) t3)).(\lambda (P: Prop).(ex4_3_ind T T T (\lambda (t4:
+T).(\lambda (_: T).(\lambda (_: T).(pc3 c2 (THead (Bind b) t t4) t3))))
+(\lambda (_: T).(\lambda (t5: T).(\lambda (_: T).(ty3 g c2 t t5)))) (\lambda
+(t4: T).(\lambda (_: T).(\lambda (_: T).(ty3 g (CHead c2 (Bind b) t) t0
+t4)))) (\lambda (t4: T).(\lambda (_: T).(\lambda (t6: T).(ty3 g (CHead c2
+(Bind b) t) t4 t6)))) P (\lambda (x0: T).(\lambda (x1: T).(\lambda (x2:
+T).(\lambda (_: (pc3 c2 (THead (Bind b) t x0) t3)).(\lambda (H7: (ty3 g c2 t
+x1)).(\lambda (_: (ty3 g (CHead c2 (Bind b) t) t0 x0)).(\lambda (_: (ty3 g
+(CHead c2 (Bind b) t) x0 x2)).(H4 x1 H7 P)))))))) (ty3_gen_bind g b c2 t t0
+t3 H5))))))) H3)))) (\lambda (f: F).(\lambda (H2: ((\forall (c1: C).(\forall
+(t3: T).((flt c1 t3 c2 (THead (Flat f) t t0)) \to (or (ex T (\lambda (t4:
+T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to (\forall (P:
+Prop).P))))))))).(F_ind (\lambda (f0: F).(((\forall (c1: C).(\forall (t3:
+T).((flt c1 t3 c2 (THead (Flat f0) t t0)) \to (or (ex T (\lambda (t4: T).(ty3
+g c1 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to (\forall (P:
+Prop).P)))))))) \to (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat f0) t
+t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat f0) t t0) t3) \to (\forall
+(P: Prop).P)))))) (\lambda (H3: ((\forall (c1: C).(\forall (t3: T).((flt c1
+t3 c2 (THead (Flat Appl) t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3
+t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to (\forall (P:
+Prop).P))))))))).(let H4 \def (H3 c2 t (flt_thead_sx (Flat Appl) c2 t t0)) in
+(or_ind (ex T (\lambda (t3: T).(ty3 g c2 t t3))) (\forall (t3: T).((ty3 g c2
+t t3) \to (\forall (P: Prop).P))) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead
+(Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0)
+t3) \to (\forall (P: Prop).P)))) (\lambda (H5: (ex T (\lambda (t3: T).(ty3 g
+c2 t t3)))).(ex_ind T (\lambda (t3: T).(ty3 g c2 t t3)) (or (ex T (\lambda
+(t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2
+(THead (Flat Appl) t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (x:
+T).(\lambda (H6: (ty3 g c2 t x)).(let H7 \def (H3 c2 t0 (flt_thead_dx (Flat
+Appl) c2 t t0)) in (or_ind (ex T (\lambda (t3: T).(ty3 g c2 t0 t3))) (\forall
+(t3: T).((ty3 g c2 t0 t3) \to (\forall (P: Prop).P))) (or (ex T (\lambda (t3:
+T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2
+(THead (Flat Appl) t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (H8: (ex T
+(\lambda (t3: T).(ty3 g c2 t0 t3)))).(ex_ind T (\lambda (t3: T).(ty3 g c2 t0
+t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3)))
+(\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to (\forall (P:
+Prop).P)))) (\lambda (x0: T).(\lambda (H9: (ty3 g c2 t0 x0)).(ex_ind T
+(\lambda (t3: T).(ty3 g c2 x0 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2
+(THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl)
+t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (x1: T).(\lambda (H10: (ty3 g
+c2 x0 x1)).(ex_ind T (\lambda (t3: T).(ty3 g c2 x t3)) (or (ex T (\lambda
+(t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2
+(THead (Flat Appl) t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (x2:
+T).(\lambda (H11: (ty3 g c2 x x2)).(let H12 \def (ty3_sn3 g c2 x x2 H11) in
+(let H_x \def (nf2_sn3 c2 x H12) in (let H13 \def H_x in (ex2_ind T (\lambda
+(u: T).(pr3 c2 x u)) (\lambda (u: T).(nf2 c2 u)) (or (ex T (\lambda (t3:
+T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2
+(THead (Flat Appl) t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (x3:
+T).(\lambda (H14: (pr3 c2 x x3)).(\lambda (H15: (nf2 c2 x3)).(let H16 \def
+(ty3_sred_pr3 c2 x x3 H14 g x2 H11) in (let H_x0 \def (pc3_abst_dec g c2 x0
+x1 H10 x3 x2 H16) in (let H17 \def H_x0 in (or_ind (ex4_2 T T (\lambda (u:
+T).(\lambda (_: T).(pc3 c2 x0 (THead (Bind Abst) x3 u)))) (\lambda (u:
+T).(\lambda (v2: T).(ty3 g c2 (THead (Bind Abst) v2 u) x1))) (\lambda (_:
+T).(\lambda (v2: T).(pr3 c2 x3 v2))) (\lambda (_: T).(\lambda (v2: T).(nf2 c2
+v2)))) (\forall (u: T).((pc3 c2 x0 (THead (Bind Abst) x3 u)) \to (\forall (P:
+Prop).P))) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0)
+t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to (\forall
+(P: Prop).P)))) (\lambda (H18: (ex4_2 T T (\lambda (u: T).(\lambda (_:
+T).(pc3 c2 x0 (THead (Bind Abst) x3 u)))) (\lambda (u: T).(\lambda (v2:
+T).(ty3 g c2 (THead (Bind Abst) v2 u) x1))) (\lambda (_: T).(\lambda (v2:
+T).(pr3 c2 x3 v2))) (\lambda (_: T).(\lambda (v2: T).(nf2 c2
+v2))))).(ex4_2_ind T T (\lambda (u: T).(\lambda (_: T).(pc3 c2 x0 (THead
+(Bind Abst) x3 u)))) (\lambda (u: T).(\lambda (v2: T).(ty3 g c2 (THead (Bind
+Abst) v2 u) x1))) (\lambda (_: T).(\lambda (v2: T).(pr3 c2 x3 v2))) (\lambda
+(_: T).(\lambda (v2: T).(nf2 c2 v2))) (or (ex T (\lambda (t3: T).(ty3 g c2
+(THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl)
+t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (x4: T).(\lambda (x5:
+T).(\lambda (H19: (pc3 c2 x0 (THead (Bind Abst) x3 x4))).(\lambda (H20: (ty3
+g c2 (THead (Bind Abst) x5 x4) x1)).(\lambda (H21: (pr3 c2 x3 x5)).(\lambda
+(_: (nf2 c2 x5)).(let H_y \def (nf2_pr3_unfold c2 x3 x5 H21 H15) in (let H23
+\def (eq_ind_r T x5 (\lambda (t3: T).(pr3 c2 x3 t3)) H21 x3 H_y) in (let H24
+\def (eq_ind_r T x5 (\lambda (t3: T).(ty3 g c2 (THead (Bind Abst) t3 x4) x1))
+H20 x3 H_y) in (or_introl (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl)
+t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to
+(\forall (P: Prop).P))) (ex_intro T (\lambda (t3: T).(ty3 g c2 (THead (Flat
+Appl) t t0) t3)) (THead (Flat Appl) t (THead (Bind Abst) x3 x4)) (ty3_appl g
+c2 t x3 (ty3_tred g c2 t x H6 x3 H14) t0 x4 (ty3_conv g c2 (THead (Bind Abst)
+x3 x4) x1 H24 t0 x0 H9 H19))))))))))))) H18)) (\lambda (H18: ((\forall (u:
+T).((pc3 c2 x0 (THead (Bind Abst) x3 u)) \to (\forall (P:
+Prop).P))))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t
+t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to
+(\forall (P: Prop).P))) (\lambda (t3: T).(\lambda (H19: (ty3 g c2 (THead
+(Flat Appl) t t0) t3)).(\lambda (P: Prop).(ex3_2_ind T T (\lambda (u:
+T).(\lambda (t4: T).(pc3 c2 (THead (Flat Appl) t (THead (Bind Abst) u t4))
+t3))) (\lambda (u: T).(\lambda (t4: T).(ty3 g c2 t0 (THead (Bind Abst) u
+t4)))) (\lambda (u: T).(\lambda (_: T).(ty3 g c2 t u))) P (\lambda (x4:
+T).(\lambda (x5: T).(\lambda (_: (pc3 c2 (THead (Flat Appl) t (THead (Bind
+Abst) x4 x5)) t3)).(\lambda (H21: (ty3 g c2 t0 (THead (Bind Abst) x4
+x5))).(\lambda (H22: (ty3 g c2 t x4)).(let H_y \def (ty3_unique g c2 t x4 H22
+x H6) in (let H_y0 \def (ty3_unique g c2 t0 (THead (Bind Abst) x4 x5) H21 x0
+H9) in (H18 x5 (pc3_t (THead (Bind Abst) x4 x5) c2 x0 (pc3_s c2 x0 (THead
+(Bind Abst) x4 x5) H_y0) (THead (Bind Abst) x3 x5) (pc3_head_1 c2 x4 x3
+(pc3_t x c2 x4 H_y x3 (pc3_pr3_r c2 x x3 H14)) (Bind Abst) x5)) P))))))))
+(ty3_gen_appl g c2 t t0 t3 H19))))))) H17))))))) H13)))))) (ty3_correct g c2
+t x H6)))) (ty3_correct g c2 t0 x0 H9)))) H8)) (\lambda (H8: ((\forall (t3:
+T).((ty3 g c2 t0 t3) \to (\forall (P: Prop).P))))).(or_intror (ex T (\lambda
+(t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2
+(THead (Flat Appl) t t0) t3) \to (\forall (P: Prop).P))) (\lambda (t3:
+T).(\lambda (H9: (ty3 g c2 (THead (Flat Appl) t t0) t3)).(\lambda (P:
+Prop).(ex3_2_ind T T (\lambda (u: T).(\lambda (t4: T).(pc3 c2 (THead (Flat
+Appl) t (THead (Bind Abst) u t4)) t3))) (\lambda (u: T).(\lambda (t4: T).(ty3
+g c2 t0 (THead (Bind Abst) u t4)))) (\lambda (u: T).(\lambda (_: T).(ty3 g c2
+t u))) P (\lambda (x0: T).(\lambda (x1: T).(\lambda (_: (pc3 c2 (THead (Flat
+Appl) t (THead (Bind Abst) x0 x1)) t3)).(\lambda (H11: (ty3 g c2 t0 (THead
+(Bind Abst) x0 x1))).(\lambda (_: (ty3 g c2 t x0)).(H8 (THead (Bind Abst) x0
+x1) H11 P)))))) (ty3_gen_appl g c2 t t0 t3 H9))))))) H7)))) H5)) (\lambda
+(H5: ((\forall (t3: T).((ty3 g c2 t t3) \to (\forall (P:
+Prop).P))))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t
+t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to
+(\forall (P: Prop).P))) (\lambda (t3: T).(\lambda (H6: (ty3 g c2 (THead (Flat
+Appl) t t0) t3)).(\lambda (P: Prop).(ex3_2_ind T T (\lambda (u: T).(\lambda
+(t4: T).(pc3 c2 (THead (Flat Appl) t (THead (Bind Abst) u t4)) t3))) (\lambda
+(u: T).(\lambda (t4: T).(ty3 g c2 t0 (THead (Bind Abst) u t4)))) (\lambda (u:
+T).(\lambda (_: T).(ty3 g c2 t u))) P (\lambda (x0: T).(\lambda (x1:
+T).(\lambda (_: (pc3 c2 (THead (Flat Appl) t (THead (Bind Abst) x0 x1))
+t3)).(\lambda (_: (ty3 g c2 t0 (THead (Bind Abst) x0 x1))).(\lambda (H9: (ty3
+g c2 t x0)).(H5 x0 H9 P)))))) (ty3_gen_appl g c2 t t0 t3 H6))))))) H4)))
+(\lambda (H3: ((\forall (c1: C).(\forall (t3: T).((flt c1 t3 c2 (THead (Flat
+Cast) t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4:
+T).((ty3 g c1 t3 t4) \to (\forall (P: Prop).P))))))))).(let H4 \def (H3 c2 t
+(flt_thead_sx (Flat Cast) c2 t t0)) in (or_ind (ex T (\lambda (t3: T).(ty3 g
+c2 t t3))) (\forall (t3: T).((ty3 g c2 t t3) \to (\forall (P: Prop).P))) (or
+(ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3:
+T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to (\forall (P: Prop).P))))
+(\lambda (H5: (ex T (\lambda (t3: T).(ty3 g c2 t t3)))).(ex_ind T (\lambda
+(t3: T).(ty3 g c2 t t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat
+Cast) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3)
+\to (\forall (P: Prop).P)))) (\lambda (x: T).(\lambda (H6: (ty3 g c2 t
+x)).(let H7 \def (H3 c2 t0 (flt_thead_dx (Flat Cast) c2 t t0)) in (or_ind (ex
+T (\lambda (t3: T).(ty3 g c2 t0 t3))) (\forall (t3: T).((ty3 g c2 t0 t3) \to
+(\forall (P: Prop).P))) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat
+Cast) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3)
+\to (\forall (P: Prop).P)))) (\lambda (H8: (ex T (\lambda (t3: T).(ty3 g c2
+t0 t3)))).(ex_ind T (\lambda (t3: T).(ty3 g c2 t0 t3)) (or (ex T (\lambda
+(t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3: T).((ty3 g c2
+(THead (Flat Cast) t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (x0:
+T).(\lambda (H9: (ty3 g c2 t0 x0)).(ex_ind T (\lambda (t3: T).(ty3 g c2 x0
+t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3)))
+(\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to (\forall (P:
+Prop).P)))) (\lambda (x1: T).(\lambda (H10: (ty3 g c2 x0 x1)).(let H_x \def
+(pc3_dec g c2 x0 x1 H10 t x H6) in (let H11 \def H_x in (or_ind (pc3 c2 x0 t)
+((pc3 c2 x0 t) \to (\forall (P: Prop).P)) (or (ex T (\lambda (t3: T).(ty3 g
+c2 (THead (Flat Cast) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat
+Cast) t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (H12: (pc3 c2 x0
+t)).(or_introl (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0)
+t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to (\forall
+(P: Prop).P))) (ex_intro T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t
+t0) t3)) t (ty3_cast g c2 t0 t (ty3_conv g c2 t x H6 t0 x0 H9 H12) x H6))))
+(\lambda (H12: (((pc3 c2 x0 t) \to (\forall (P: Prop).P)))).(or_intror (ex T
+(\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3:
+T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to (\forall (P: Prop).P)))
+(\lambda (t3: T).(\lambda (H13: (ty3 g c2 (THead (Flat Cast) t t0)
+t3)).(\lambda (P: Prop).(and_ind (pc3 c2 t t3) (ty3 g c2 t0 t) P (\lambda (_:
+(pc3 c2 t t3)).(\lambda (H15: (ty3 g c2 t0 t)).(let H_y \def (ty3_unique g c2
+t0 t H15 x0 H9) in (H12 (pc3_s c2 x0 t H_y) P)))) (ty3_gen_cast g c2 t0 t t3
+H13))))))) H11))))) (ty3_correct g c2 t0 x0 H9)))) H8)) (\lambda (H8:
+((\forall (t3: T).((ty3 g c2 t0 t3) \to (\forall (P: Prop).P))))).(or_intror
+(ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3:
+T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to (\forall (P: Prop).P)))
+(\lambda (t3: T).(\lambda (H9: (ty3 g c2 (THead (Flat Cast) t t0)
+t3)).(\lambda (P: Prop).(and_ind (pc3 c2 t t3) (ty3 g c2 t0 t) P (\lambda (_:
+(pc3 c2 t t3)).(\lambda (H11: (ty3 g c2 t0 t)).(H8 t H11 P))) (ty3_gen_cast g
+c2 t0 t t3 H9))))))) H7)))) H5)) (\lambda (H5: ((\forall (t3: T).((ty3 g c2 t
+t3) \to (\forall (P: Prop).P))))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2
+(THead (Flat Cast) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast)
+t t0) t3) \to (\forall (P: Prop).P))) (\lambda (t3: T).(\lambda (H6: (ty3 g
+c2 (THead (Flat Cast) t t0) t3)).(\lambda (P: Prop).(and_ind (pc3 c2 t t3)
+(ty3 g c2 t0 t) P (\lambda (_: (pc3 c2 t t3)).(\lambda (H8: (ty3 g c2 t0
+t)).(ex_ind T (\lambda (t4: T).(ty3 g c2 t t4)) P (\lambda (x: T).(\lambda
+(H9: (ty3 g c2 t x)).(H5 x H9 P))) (ty3_correct g c2 t0 t H8))))
+(ty3_gen_cast g c2 t0 t t3 H6))))))) H4))) f H2))) k H1))))))) t2))) c t1))).
+
projects / helm.git / blobdiff