1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "ground/lib/list.ma".
16 include "static_2/notation/functions/snapplvector_2.ma".
17 include "static_2/syntax/term_simple.ma".
19 (* TERMS ********************************************************************)
21 rec definition applv Vs T on Vs ≝
24 | list_cons hd tl ⇒ ⓐhd. (applv tl T)
27 interpretation "application to vector (term)"
28 'SnApplVector Vs T = (applv Vs T).
30 (* Basic properties *********************************************************)
32 lemma applv_nil: ∀T. Ⓐⓔ.T = T.
35 lemma applv_cons: ∀V,Vs,T. ⒶV⨮Vs.T = ⓐV.ⒶVs.T.
38 (* Properties with simple terms *********************************************)
40 lemma applv_simple: ∀T,Vs. 𝐒❨T❩ → 𝐒❨ⒶVs.T❩.