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 "formal_topology/saturations.ma".
16 include "formal_topology/o-saturations.ma".
17 include "formal_topology/relations_to_o-algebra.ma".
19 (* These are only conversions :-) *)
21 definition o_operator_of_operator: ∀C:REL. (Ω^C ⇒_1 Ω^C) → ((POW C) ⇒_1 (POW C)) ≝ λC,t.t.
23 definition is_o_saturation_of_is_saturation:
24 ∀C:REL.∀R: Ω^C ⇒_1 Ω^C. is_saturation ? R → is_o_saturation ? (o_operator_of_operator ? R).
25 intros (C R i); apply i; qed.
27 definition is_o_reduction_of_is_reduction:
28 ∀C:REL.∀R: Ω^C ⇒_1 Ω^C.is_reduction ? R → is_o_reduction ? (o_operator_of_operator ? R).
29 intros (C R i); apply i; qed.