/
ig.clif
172 lines (152 loc) · 2.29 KB
/
ig.clif
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/*******************************************************************************
* Copyright (c) University of Toronto and others. All rights reserved.
* The content of this file is licensed under the Creative Commons Attribution-
* ShareAlike 4.0 Unported license. The legal text of this license can be
* found at http://creativecommons.org/licenses/by-sa/4.0/legalcode.
*
* Contributors:
* Torsten Hahmann - initial implementation
*******************************************************************************/
(cl-text http://colore.oor.net/incidence_geometry/ig.clif
(cl-imports http://colore.oor.net/incidence_geometry/ig_2d_lin.clif)
(cl-comment '(linear) incidence geometry')
(cl-comment 'I.0b')
(forall (x)
(if
(Pt x)
(and
(not (L x))
(not (Pl x))
)
)
)
(forall (x)
(if
(L x)
(and
(not (Pt x))
(not (Pl x))
)
)
)
(forall (x)
(if
(Pl x)
(and
(not (Pt x))
(not (L x))
)
)
)
(cl-comment 'I.3')
(forall (x)
(if
(Pl x)
(exists (p q r)
(and
(not (= p q))
(not (= p r))
(not (= q r))
(Pt p)
(Pt q)
(Pt r)
(on p x)
(on q x)
(on r x)
(forall (l)
(if
(L l)
(or
(not (on p l))
(not (on q l))
(not (on r l))
)
)
)
)
)
)
)
(cl-comment 'I.4a')
(forall (p q r)
(if
(and
(Pt p)
(Pt q)
(Pt r)
(forall (l)
(if
(L l)
(or
(not (on p l))
(not (on q l))
(not (on r l))
)
)
)
)
(exists (x)
(and
(Pl x)
(on p x)
(on q x)
(on r x)
)
)
)
)
(cl-comment 'I.4b')
(forall (p q r x y)
(if
(and
(Pt p)
(Pt q)
(Pt r)
(forall (l)
(if
(L l)
(or
(not (on p l))
(not (on q l))
(not (on r l))
)
)
)
(Pl x)
(on p x)
(on q x)
(on r x)
(Pl y)
(on p y)
(on q y)
(on r y)
)
(= x y)
)
)
(cl-comment 'I.5')
(forall (p q l x)
(if
(and
(Pt p)
(Pt q)
(not (= p q))
(L l)
(on p l)
(on q l)
(Pl x)
(on p x)
(on q x)
)
(forall (r)
(if
(and
(Pt r)
(on r l)
)
(on r x)
)
)
)
)
)