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15 (* This file was automatically generated: do not edit *********************)
17 include "basic_1A/T/defs.ma".
19 implied rec lemma T_rect (P: (T \to Type[0])) (f: (\forall (n: nat).(P (TSort
20 n)))) (f0: (\forall (n: nat).(P (TLRef n)))) (f1: (\forall (k: K).(\forall
21 (t: T).((P t) \to (\forall (t0: T).((P t0) \to (P (THead k t t0)))))))) (t:
22 T) on t: P t \def match t with [(TSort n) \Rightarrow (f n) | (TLRef n)
23 \Rightarrow (f0 n) | (THead k t0 t1) \Rightarrow (f1 k t0 ((T_rect P f f0 f1)
24 t0) t1 ((T_rect P f f0 f1) t1))].
27 \forall (P: ((T \to Prop))).(((\forall (n: nat).(P (TSort n)))) \to
28 (((\forall (n: nat).(P (TLRef n)))) \to (((\forall (k: K).(\forall (t: T).((P
29 t) \to (\forall (t0: T).((P t0) \to (P (THead k t t0)))))))) \to (\forall (t:
32 \lambda (P: ((T \to Prop))).(T_rect P).
35 \forall (k: K).(\forall (v: T).(\forall (t: T).((eq T (THead k v t) t) \to
36 (\forall (P: Prop).P))))
38 \lambda (k: K).(\lambda (v: T).(\lambda (t: T).(T_ind (\lambda (t0: T).((eq
39 T (THead k v t0) t0) \to (\forall (P: Prop).P))) (\lambda (n: nat).(\lambda
40 (H: (eq T (THead k v (TSort n)) (TSort n))).(\lambda (P: Prop).(let H0 \def
41 (eq_ind T (THead k v (TSort n)) (\lambda (ee: T).(match ee with [(TSort _)
42 \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow
43 True])) I (TSort n) H) in (False_ind P H0))))) (\lambda (n: nat).(\lambda (H:
44 (eq T (THead k v (TLRef n)) (TLRef n))).(\lambda (P: Prop).(let H0 \def
45 (eq_ind T (THead k v (TLRef n)) (\lambda (ee: T).(match ee with [(TSort _)
46 \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow
47 True])) I (TLRef n) H) in (False_ind P H0))))) (\lambda (k0: K).(\lambda (t0:
48 T).(\lambda (_: (((eq T (THead k v t0) t0) \to (\forall (P:
49 Prop).P)))).(\lambda (t1: T).(\lambda (H0: (((eq T (THead k v t1) t1) \to
50 (\forall (P: Prop).P)))).(\lambda (H1: (eq T (THead k v (THead k0 t0 t1))
51 (THead k0 t0 t1))).(\lambda (P: Prop).(let H2 \def (f_equal T K (\lambda (e:
52 T).(match e with [(TSort _) \Rightarrow k | (TLRef _) \Rightarrow k | (THead
53 k1 _ _) \Rightarrow k1])) (THead k v (THead k0 t0 t1)) (THead k0 t0 t1) H1)
54 in ((let H3 \def (f_equal T T (\lambda (e: T).(match e with [(TSort _)
55 \Rightarrow v | (TLRef _) \Rightarrow v | (THead _ t2 _) \Rightarrow t2]))
56 (THead k v (THead k0 t0 t1)) (THead k0 t0 t1) H1) in ((let H4 \def (f_equal T
57 T (\lambda (e: T).(match e with [(TSort _) \Rightarrow (THead k0 t0 t1) |
58 (TLRef _) \Rightarrow (THead k0 t0 t1) | (THead _ _ t2) \Rightarrow t2]))
59 (THead k v (THead k0 t0 t1)) (THead k0 t0 t1) H1) in (\lambda (H5: (eq T v
60 t0)).(\lambda (H6: (eq K k k0)).(let H7 \def (eq_ind T v (\lambda (t2:
61 T).((eq T (THead k t2 t1) t1) \to (\forall (P0: Prop).P0))) H0 t0 H5) in (let
62 H8 \def (eq_ind K k (\lambda (k1: K).((eq T (THead k1 t0 t1) t1) \to (\forall
63 (P0: Prop).P0))) H7 k0 H6) in (H8 H4 P)))))) H3)) H2))))))))) t))).