1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| A.Asperti, C.Sacerdoti Coen, *)
8 (* ||A|| E.Tassi, S.Zacchiroli *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU Lesser General Public License Version 2.1 *)
13 (**************************************************************************)
15 include "logic/pts.ma".
17 ninductive True: CProp ≝
20 ninductive False: CProp ≝.
21 (* elimination principle *)
22 ndefinition False_rect ≝ λP: False → Type.λp: False.
23 match p in False return λp. P p with [].
25 ndefinition Not: CProp → CProp ≝
28 interpretation "logical not" 'not x = (Not x).
30 ninductive And (A,B:CProp) : CProp ≝
31 conj : A → B → And A B.
33 interpretation "logical and" 'and x y = (And x y).
35 ninductive Or (A,B:CProp) : CProp ≝
36 or_introl : A → Or A B
37 | or_intror : B → Or A B.
39 interpretation "logical or" 'or x y = (Or x y).
41 ninductive Ex (A:Type) (P:A → CProp) : CProp ≝
42 ex_intro: ∀x:A. P x → Ex A P.
44 interpretation "exists" 'exists x = (Ex ? x).