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15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/fsubst0/fwd".
19 include "fsubst0/defs.ma".
21 theorem fsubst0_gen_base:
22 \forall (c1: C).(\forall (c2: C).(\forall (t1: T).(\forall (t2: T).(\forall
23 (v: T).(\forall (i: nat).((fsubst0 i v c1 t1 c2 t2) \to (or3 (land (eq C c1
24 c2) (subst0 i v t1 t2)) (land (eq T t1 t2) (csubst0 i v c1 c2)) (land (subst0
25 i v t1 t2) (csubst0 i v c1 c2)))))))))
27 \lambda (c1: C).(\lambda (c2: C).(\lambda (t1: T).(\lambda (t2: T).(\lambda
28 (v: T).(\lambda (i: nat).(\lambda (H: (fsubst0 i v c1 t1 c2 t2)).(let H0 \def
29 (match H in fsubst0 return (\lambda (c: C).(\lambda (t: T).(\lambda (_:
30 (fsubst0 ? ? ? ? c t)).((eq C c c2) \to ((eq T t t2) \to (or3 (land (eq C c1
31 c2) (subst0 i v t1 t2)) (land (eq T t1 t2) (csubst0 i v c1 c2)) (land (subst0
32 i v t1 t2) (csubst0 i v c1 c2)))))))) with [(fsubst0_snd t0 H0) \Rightarrow
33 (\lambda (H1: (eq C c1 c2)).(\lambda (H2: (eq T t0 t2)).(eq_ind C c2 (\lambda
34 (c: C).((eq T t0 t2) \to ((subst0 i v t1 t0) \to (or3 (land (eq C c c2)
35 (subst0 i v t1 t2)) (land (eq T t1 t2) (csubst0 i v c c2)) (land (subst0 i v
36 t1 t2) (csubst0 i v c c2)))))) (\lambda (H3: (eq T t0 t2)).(eq_ind T t2
37 (\lambda (t: T).((subst0 i v t1 t) \to (or3 (land (eq C c2 c2) (subst0 i v t1
38 t2)) (land (eq T t1 t2) (csubst0 i v c2 c2)) (land (subst0 i v t1 t2)
39 (csubst0 i v c2 c2))))) (\lambda (H4: (subst0 i v t1 t2)).(or3_intro0 (land
40 (eq C c2 c2) (subst0 i v t1 t2)) (land (eq T t1 t2) (csubst0 i v c2 c2))
41 (land (subst0 i v t1 t2) (csubst0 i v c2 c2)) (conj (eq C c2 c2) (subst0 i v
42 t1 t2) (refl_equal C c2) H4))) t0 (sym_eq T t0 t2 H3))) c1 (sym_eq C c1 c2
43 H1) H2 H0))) | (fsubst0_fst c0 H0) \Rightarrow (\lambda (H1: (eq C c0
44 c2)).(\lambda (H2: (eq T t1 t2)).(eq_ind C c2 (\lambda (c: C).((eq T t1 t2)
45 \to ((csubst0 i v c1 c) \to (or3 (land (eq C c1 c2) (subst0 i v t1 t2)) (land
46 (eq T t1 t2) (csubst0 i v c1 c2)) (land (subst0 i v t1 t2) (csubst0 i v c1
47 c2)))))) (\lambda (H3: (eq T t1 t2)).(eq_ind T t2 (\lambda (t: T).((csubst0 i
48 v c1 c2) \to (or3 (land (eq C c1 c2) (subst0 i v t t2)) (land (eq T t t2)
49 (csubst0 i v c1 c2)) (land (subst0 i v t t2) (csubst0 i v c1 c2))))) (\lambda
50 (H4: (csubst0 i v c1 c2)).(or3_intro1 (land (eq C c1 c2) (subst0 i v t2 t2))
51 (land (eq T t2 t2) (csubst0 i v c1 c2)) (land (subst0 i v t2 t2) (csubst0 i v
52 c1 c2)) (conj (eq T t2 t2) (csubst0 i v c1 c2) (refl_equal T t2) H4))) t1
53 (sym_eq T t1 t2 H3))) c0 (sym_eq C c0 c2 H1) H2 H0))) | (fsubst0_both t0 H0
54 c0 H1) \Rightarrow (\lambda (H2: (eq C c0 c2)).(\lambda (H3: (eq T t0
55 t2)).(eq_ind C c2 (\lambda (c: C).((eq T t0 t2) \to ((subst0 i v t1 t0) \to
56 ((csubst0 i v c1 c) \to (or3 (land (eq C c1 c2) (subst0 i v t1 t2)) (land (eq
57 T t1 t2) (csubst0 i v c1 c2)) (land (subst0 i v t1 t2) (csubst0 i v c1
58 c2))))))) (\lambda (H4: (eq T t0 t2)).(eq_ind T t2 (\lambda (t: T).((subst0 i
59 v t1 t) \to ((csubst0 i v c1 c2) \to (or3 (land (eq C c1 c2) (subst0 i v t1
60 t2)) (land (eq T t1 t2) (csubst0 i v c1 c2)) (land (subst0 i v t1 t2)
61 (csubst0 i v c1 c2)))))) (\lambda (H5: (subst0 i v t1 t2)).(\lambda (H6:
62 (csubst0 i v c1 c2)).(or3_intro2 (land (eq C c1 c2) (subst0 i v t1 t2)) (land
63 (eq T t1 t2) (csubst0 i v c1 c2)) (land (subst0 i v t1 t2) (csubst0 i v c1
64 c2)) (conj (subst0 i v t1 t2) (csubst0 i v c1 c2) H5 H6)))) t0 (sym_eq T t0
65 t2 H4))) c0 (sym_eq C c0 c2 H2) H3 H0 H1)))]) in (H0 (refl_equal C c2)
66 (refl_equal T t2))))))))).