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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/multidim_space_dim/dim_prime_linear_unbounded.clif
(cl-comment 'compact axioms for linear relative dimension')
(cl-comment 'greater or equal dimension (<=) as well as ZEX relation only apply to space regions.')
(forall (x y)
(if
(<= x y)
(S x)
)
)
(forall (x y)
(if
(<= x y)
(S y)
)
)
(forall (x)
(if
(ZEX x)
(S x)
)
)
(cl-comment 'D-A1: reflexive')
(forall (x)
(if
(S x)
(<= x x)
)
)
(cl-comment 'D-A3: transitive')
(forall (x y z)
(if
(and
(<= x y)
(<= y z)
)
(<= x z)
)
)
(cl-comment 'D-A4: unique ZEX')
(forall (x y)
(if
(and (ZEX x) (ZEX y))
(= x y)
)
)
(cl-comment 'D-A5: ZEX has dimension lower than any other region')
(forall (x y)
(if
(and
(ZEX x)
(S y)
)
(<= x y)
)
)
)
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