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updated comments in Ordered Geometry Hierarchies with single quotes

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carmenchui committed Jun 20, 2018
1 parent 0e638aa commit 3c7d314fe71a991bcb7c1c632505530db395903e
@@ -2,17 +2,17 @@

(cl-imports http://colore.oor.net/bipartite_incidence/hilbert_incidence.clif)

(cl-comment "If a point p2 is between points p1 and p3, then p2 is also
between p3 and p1, and there exists a line containing the points.")
(cl-comment 'If a point p2 is between points p1 and p3, then p2 is also
between p3 and p1, and there exists a line containing the points.')
(forall (p1 p2 p3)
(if (and (point p1)
(point p2)
(point p3)
(between p1 p2 p3))
(between p3 p2 p1)))

(cl-comment "If a point p2 is between points p1 and p3, then
there exists a line containing the points.")
(cl-comment 'If a point p2 is between points p1 and p3, then
there exists a line containing the points.')
(forall (p1 p2 p3)
(if (and (point p1)
(point p2)
@@ -24,8 +24,8 @@ there exists a line containing the points.")
(in p2 l)
(in p3 l)))))

(cl-comment "If p1 and p3 are two points of a straight line,
then there exists at least one point p2 lying between p1 and p3.")
(cl-comment 'If p1 and p3 are two points of a straight line,
then there exists at least one point p2 lying between p1 and p3.')
(forall (p1 p3 l)
(if (and (point p1)
(point p3)
@@ -36,8 +36,8 @@ then there exists at least one point p2 lying between p1 and p3.")
(and (point p2)
(between p1 p2 p3)))))

(cl-comment "Of any three points situated on a straight line,
there is always one which lies between the other two.")
(cl-comment 'Of any three points situated on a straight line,
there is always one which lies between the other two.')

(forall (p1 p2 p3 l)
(if (and (point p1)
@@ -51,8 +51,8 @@ there is always one which lies between the other two.")
(between p2 p1 p3)
(between p1 p3 p2))))

(cl-comment "Of any three points situated on a straight line,
there is only one which lies between the other two.")
(cl-comment 'Of any three points situated on a straight line,
there is only one which lies between the other two.')

(forall (p1 p2 p3 l)
(if (and (point p1)
@@ -62,7 +62,7 @@ there is only one which lies between the other two.")
(between p1 p2 p3))
(not (between p1 p3 p2))))

(cl-comment "Paschs Axiom:Let A, B, C be three points not lying in the same straight line and let a be a straight line lying in the plane ABC and not passing through any of the points A, B, C. Then, if the straight line a passes through a point of the segment AB, it will also pass through either a point of the segment BC or a point of the segment AC.")
(cl-comment 'Paschs Axiom:Let A, B, C be three points not lying in the same straight line and let a be a straight line lying in the plane ABC and not passing through any of the points A, B, C. Then, if the straight line a passes through a point of the segment AB, it will also pass through either a point of the segment BC or a point of the segment AC.')
(forall (p1 p2 p3 p4 l1)
(if (and (point p1)
(point p2)
@@ -10,9 +10,9 @@

(cl-text http://colore.oor.net/ordered_incidence_geometry/b_2d

(cl-comment "basic axioms of betweenness in 2D incidence geometry")
(cl-comment 'basic axioms of betweenness in 2D incidence geometry')

(cl-comment "incidence")
(cl-comment 'incidence')

(forall (x y)
(if
@@ -25,7 +25,7 @@
)


(cl-comment "B1: outer symmetry")
(cl-comment 'B1: outer symmetry')

(forall (a b c)
(if
@@ -35,7 +35,7 @@
)


(cl-comment "B2: strict, i.e. acyclic")
(cl-comment 'B2: strict, i.e. acyclic')

(forall (a b c)
(if
@@ -44,7 +44,7 @@
)
)

(cl-comment "B3: linear coherence")
(cl-comment 'B3: linear coherence')

(forall (a b c p)
(iff
@@ -69,7 +69,7 @@
)


(cl-comment "B4: Separation")
(cl-comment 'B4: Separation')

(forall (a b c p l)
(if
@@ -10,12 +10,12 @@

(cl-text http://colore.oor.net/ordered_incidence_geometry/b_3d

(cl-comment "basic axioms of betweenness in 3D incidence geometry")
(cl-comment 'basic axioms of betweenness in 3D incidence geometry')

(cl-comment "sets of points, lines, and planes")
(cl-comment 'sets of points, lines, and planes')


(cl-comment "I.0b")
(cl-comment 'I.0b')

(forall (x)
(if
@@ -48,7 +48,7 @@
)


(cl-comment "I.0c")
(cl-comment 'I.0c')

(forall (x y)
(if
@@ -61,7 +61,7 @@
)


(cl-comment "O.1: outer symmetry")
(cl-comment 'O.1: outer symmetry')

(forall (a b c)
(if
@@ -71,7 +71,7 @@
)


(cl-comment "O.2: strict, i.e. acyclic")
(cl-comment 'O.2: strict, i.e. acyclic')

(forall (a b c)
(if
@@ -80,7 +80,7 @@
)
)

(cl-comment "O.3: linear coherence")
(cl-comment 'O.3: linear coherence')

(forall (a b c p)
(iff
@@ -106,7 +106,7 @@
)


(cl-comment "B4: Separation")
(cl-comment 'B4: Separation')

(forall (a b c p l)
(if
@@ -13,7 +13,7 @@
(cl-imports http://colore.oor.net/ordered_incidence_geometry/b_2d)


(cl-comment "separation property")
(cl-comment 'separation property')

(forall (a b c x)
(if
@@ -26,7 +26,7 @@
)


(cl-comment "no more than one of three distinct elements is in the middle position")
(cl-comment 'no more than one of three distinct elements is in the middle position')

(forall (a b c)
(if
@@ -39,7 +39,7 @@
)


(cl-comment "4")
(cl-comment '4')

(forall (a b x y)
(if
@@ -56,7 +56,7 @@
)


(cl-comment "6")
(cl-comment '6')

(forall (a b x y)
(if
@@ -73,7 +73,7 @@
)


(cl-comment "outer transitivity")
(cl-comment 'outer transitivity')

(forall (a b x y)
(if
@@ -86,7 +86,7 @@
)


(cl-comment "inner transitivity")
(cl-comment 'inner transitivity')

(forall (a b x y)
(if
@@ -13,7 +13,7 @@
(cl-imports http://colore.oor.net/ordered_incidence_geometry/b_3d)


(cl-comment "separation property")
(cl-comment 'separation property')

(forall (a b c x)
(if
@@ -26,7 +26,7 @@
)


(cl-comment "no more than one of three distinct elements is in the middle position")
(cl-comment 'no more than one of three distinct elements is in the middle position')

(forall (a b c)
(if
@@ -39,7 +39,7 @@
)


(cl-comment "4")
(cl-comment '4')

(forall (a b x y)
(if
@@ -56,7 +56,7 @@
)


(cl-comment "6")
(cl-comment '6')

(forall (a b x y)
(if
@@ -73,7 +73,7 @@
)


(cl-comment "outer transitivity")
(cl-comment 'outer transitivity')

(forall (a b x y)
(if
@@ -86,7 +86,7 @@
)


(cl-comment "inner transitivity")
(cl-comment 'inner transitivity')

(forall (a b x y)
(if
@@ -33,7 +33,7 @@
)
)

(cl-comment "separation property")
(cl-comment 'separation property')

(forall (a b c x)
(if
@@ -46,7 +46,7 @@
)


(cl-comment "no more than one of three distinct elements is in the middle position")
(cl-comment 'no more than one of three distinct elements is in the middle position')

(forall (a b c)
(if
@@ -59,7 +59,7 @@
)


(cl-comment "4")
(cl-comment '4')

(forall (a b x y)
(if
@@ -76,7 +76,7 @@
)


(cl-comment "6")
(cl-comment '6')

(forall (a b x y)
(if
@@ -93,7 +93,7 @@
)


(cl-comment "outer transitivity")
(cl-comment 'outer transitivity')

(forall (a b x y)
(if
@@ -106,7 +106,7 @@
)


(cl-comment "inner transitivity")
(cl-comment 'inner transitivity')

(forall (a b x y)
(if
@@ -13,7 +13,7 @@
(cl-imports http://colore.oor.net/ordered_incidence_geometry/woig)


(cl-comment "O.7: outer transitivity")
(cl-comment 'O.7: outer transitivity')

(forall (a b x y l)
(if
@@ -31,7 +31,7 @@
)


(cl-comment "O.8: inner transitivity")
(cl-comment 'O.8: inner transitivity')

(forall (a b x y l)
(if
@@ -49,7 +49,7 @@
)


(cl-comment "separation property")
(cl-comment 'separation property')

(forall (a b c x l)
(if
@@ -67,7 +67,7 @@
)


(cl-comment "no more than one of three distinct elements is in the middle position")
(cl-comment 'no more than one of three distinct elements is in the middle position')

(forall (a b c)
(if
@@ -80,7 +80,7 @@
)


(cl-comment "4")
(cl-comment '4')

(forall (a b x y l)
(if
@@ -102,7 +102,7 @@
)


(cl-comment "6")
(cl-comment '6')

(forall (a b x y l)
(if
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