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4 (* ||A|| A project by Andrea Asperti *)
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15 include "delayed_updating/syntax/path.ma".
16 include "delayed_updating/notation/functions/class_p_0.ma".
17 include "ground/lib/subset.ma".
18 include "ground/xoa/ex_1_2.ma".
20 (* PROPER CONDITION FOR PATH ************************************************)
22 definition ppc: predicate path ā
27 "proper condition (path)"
30 (* Basic constructions ******************************************************)
32 lemma ppc_lcons (l) (q): lāq Ļµ š.
36 lemma ppc_rcons (l) (q): qāl Ļµ š.
38 elim (eq_inv_list_empty_rcons ??? H)
41 (* Basic inversions ********************************************************)
44 (š) Ļµ š ā ā„.
48 lemma ppc_inv_lcons (p):
49 p Ļµ š ā āāl,q. lāq = p.
51 [ #H0 elim (ppc_inv_empty ā¦ H0)
52 | #l #q #_ /2 width=3 by ex1_2_intro/
56 lemma ppc_inv_rcons (p):
57 p Ļµ š ā āāq,l. qāl = p.
58 #p @(list_ind_rcons ā¦ p) -p
59 [ #H0 elim (ppc_inv_empty ā¦ H0)
60 | #q #l #_ #_ /2 width=3 by ex1_2_intro/