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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_codib/codi_bcont_minimal.clif
(cl-imports http://colore.oor.net/multidim_space_codi/codi.clif)
(cl-imports http://colore.oor.net/multidim_space_dim/definitions/covers.clif)
(cl-imports http://colore.oor.net/multidim_space_codi/definitions/po.clif)
(cl-imports http://colore.oor.net/multidim_space_codi/definitions/sc.clif)
(cl-imports http://colore.oor.net/multidim_space_codi/definitions/min_max_in_dim.clif)
(cl-comment 'BC-A1: entities in the boundary are at least of a dimension lower than the bounded entity')
(forall (x y)
(if
(BCont x y)
(and
(Cont x y)
(not (EqDim x y))
)
)
)
(cl-comment 'BC-A2: if z is contained in two superficially connected entities x and y embedded in an entity v of the dimension of x, that is x has locally a codimension of zero, then z is contained in the boundary of x')
(forall (x y v z)
(if
(and
(SC x y)
(Min x)
(P x v)
(Cont y v)
(Cont z x)
(Cont z y)
)
(BCont z x)
)
)
(cl-comment 'BC-A3: any z contained in two superficially connected parts x and y of v that is exactly of one dimension lower than v is not in the boundary of v')
(forall (x y z v)
(if
(and
(SC x y)
(P x v)
(P y v)
(Cont z x)
(Cont z y)
(Covers v z)
)
(not (BCont z v))
)
)
(cl-comment 'BC-A4')
(forall (x y z)
(if
(and
(BCont x y)
(P y z)
(forall (v w)
(if
(and
(P v z)
(not (PO v y))
(P w x)
)
(not (Cont w v))
)
)
)
(BCont x z)
)
)
(cl-comment 'BC-A5: transitivity with respect to Cont')
(forall (x y z)
(if
(and
(BCont x y)
(Cont z x)
)
(BCont z y)
)
)
)
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