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(^ CrossUnion ^)

[- Partial difference -]

({ Part of the difference between a thing +a and a thing +b is the thing whose features are all the features of +a that are not features of +b. This will be called the partial difference of +a and +b, and represented by +pd// +a +b. })

+Df +Pd [a [b [c = +ft// +c +pd// +a +b ( +ft// +c +a - +ft// +c +b
+Pd1 +Pr ) - +Pd = +ft// +c +pd// +a +b ( +ft// +c +a - +ft// +c +b

({ The relation of being the same is transmitted for the partial difference. })

+Pd2 +Pr ) - +Pd ) - +sm// +a +g +sm// +pd// +a +b +pd// +g +b
+Pd3 +Pr ) - +Pd ) - +sm// +b +g +sm// +pd// +a +b +pd// +a +g

({ The partial difference between a thing and itself is +0. })

+Pd4 +Pr ) - ( +Nf +Pd +sm// +pd// +a +a +0

[- Intersection -]

+Df +in// +a +b +pd// +a +pd// +a +b

({ The features of +in// +a +b are the common features of +a and +b. })

+In1 +Pr ) - +Pd = +ft// +c +in// +a +b ( +ft// +c +a +ft// +c +b

({ +in// +a +b is symmetrical. })

+In2 +Pr ) - +Pd +sm// +in// +a +b +in// +b +a

({ The relation of being the same is transmitted for intersections. })

+In3 +Pr ) - +Pd ) - +sm// +a +d +sm// +in// +a +b +in// +d +b
+In4 +Pr ) - +Pd ) - +sm// +b +d +sm// +in// +a +b +in// +a +d

[- Being a part -]

({ The statement that +a is part of +b is an abbreviation of the statement that every feature of +a is a feature of +b. })

+Df +pt// +a +b [c ) - +ft// +c +a +ft// +c +b

({ A thing is part of itself. })

+Pt1 +Pr +pt// +a +a
+Pt2 +Pr ) - +pt// +a +b ) - +ft// +c +a +ft// +c +b

({ The relation of being a part is transmitted. })

+Pt3 +Pr ) - ( +pt// +a +b +sm// +a +d +pt// +d +b
+Pt4 +Pr ) - ( +pt// +a +b +sm// +b +d +pt// +a +d

({ If two things are parts of each other, then they are the same. })

+Pt5 +Pr ) - ( +pt// +a +b +pt// +b +a +sm// +a +b

({ A part of a part of a thing is part of that thing. })

+Pt6 +Pr ) - ( +pt// +a +b +pt// +b +d +pt// +a +d
+Pt7 +Pr ) - ( +Th ( +Am ( +ft/ +a +ft/ +b +pt// +a +un// +a +b
+Pt8 +Pr ) - ( +Th ( +Am ( +ft/ +a +ft/ +b +pt// +b +un// +a +b
+Pt9 +Pr ) - +Pd +pt// +in// +a +b +a
+Pt10 +Pr ) - +Pd +pt// +in// +a +b +b
+Pt11 +Pr ) - ( +Th ( +Am ( +Pd ( +ft/ +a +ft/ +b +pt// +in// +a +b +un// +a +b
+Pt12 +Pr ) - ( +Th ( +Am ( +ft/ +a +ft/ +b ) - +pt// +a +b +sm// +un// +a +b +b
+Pt13 +Pr ) - ( +Th ( +Am ( +ft/ +a +ft/ +b ) - +pt// +a +b +sm// +un// +b +a +b
+Pt14 +Pr ) - +Pd ) - +pt// +a +b +sm// +in// +a +b +a
+Pt15 +Pr ) - +Pd ) - +pt// +a +b +sm// +in// +b +a +a
+Pt16 +Pr ) - +Nf +pt// +0 +a
+Un8 +Pr ) - ( +Nf ( +Th ( +Am +ft/ +a +sm// +un// +0 +a +a
+Un9 +Pr ) - ( +Nf ( +Th ( +Am +ft/ +a +sm// +un// +a +0 +a
+In5 +Pr ) - ( +Nf +Pd +sm// +in// +0 +a +0
+In6 +Pr ) - ( +Nf +Pd +sm// +in// +a +0 +0

[- Proper part -]

({ The statement that +a is a proper part of +b is an abbreviation of the statement that +a is part of +b, and not the same as +b. })

+Df +pp// +a +b ( +pt// +a +b - +sm// +a +b

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