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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "delayed_updating/syntax/path.ma".
16 include "delayed_updating/notation/functions/class_i_0.ma".
17 include "ground/lib/subset.ma".
19 (* INNER CONDITION FOR PATH *************************************************)
21 definition pic: predicate path ā
22 Ī»p. āq,k. qāš±k = p ā ā„
26 "inner condition (path)"
29 (* Basic constructions ******************************************************)
56 (* Basic inversions ********************************************************)
58 lemma pic_inv_d_dx (p) (k):
59 pāš±k Ļµ š ā ā„.
63 (* Constructions with path_lcons ********************************************)
66 p Ļµ š ā šŗāp Ļµ š.
67 * [| * [ #k ] #p #Hp <list_cons_shift ] //
68 [ #_ <list_cons_comm //
69 | elim (pic_inv_d_dx ā¦ Hp)
74 p Ļµ š ā šāp Ļµ š.
75 * [| * [ #k ] #p #Hp <list_cons_shift ] //
76 [ #_ <list_cons_comm //
77 | elim (pic_inv_d_dx ā¦ Hp)
82 p Ļµ š ā šāp Ļµ š.
83 * [| * [ #k ] #p #Hp <list_cons_shift ] //
84 [ #_ <list_cons_comm //
85 | elim (pic_inv_d_dx ā¦ Hp)
90 p Ļµ š ā š¦āp Ļµ š.
91 * [| * [ #k ] #p #Hp <list_cons_shift ] //
92 [ #_ <list_cons_comm //
93 | elim (pic_inv_d_dx ā¦ Hp)