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14
15 include "ground_2/notation/relations/isuniform_1.ma".
16 include "ground_2/relocation/trace_isid.ma".
17
18 (* RELOCATION TRACE *********************************************************)
19
20 inductive isun: predicate trace ≝
21 | isun_id   : ∀t. 𝐈⦃t⦄ → isun t
22 | isun_false: ∀t. isun t → isun (Ⓕ@t)
23 .
24
25 interpretation "test for uniformity (trace)"
26    'IsUniform t = (isun t).
27
28 (* Basic inversion lennas ***************************************************)
29
30 fact isun_inv_true_aux: ∀t. 𝐔⦃t⦄ → ∀u. t = Ⓣ@u → 𝐈⦃u⦄.
31 #t * -t
32 [ #t #Ht #u #H destruct /2 width=1 by isid_inv_true/
33 | #t #_ #u #H destruct
34 ]
35 qed-.
36
37 lemma isun_inv_true: ∀t. 𝐔⦃Ⓣ@t⦄ → 𝐈⦃t⦄.
38 /2 width=3 by isun_inv_true_aux/ qed-.
39
40 fact isun_inv_false_aux: ∀t. 𝐔⦃t⦄ → ∀u. t = Ⓕ@u → 𝐔⦃u⦄.
41 #t * -t 
42 [ #t #Ht #u #H destruct elim (isid_inv_false … Ht)
43 | #t #Ht #u #H destruct //
44 ]
45 qed-.
46
47 lemma isun_inv_false: ∀t. 𝐔⦃Ⓕ@t⦄ → 𝐔⦃t⦄.
48 /2 width=3 by isun_inv_false_aux/ qed-.