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(^ ThingsAndFeatures ^)

[- Amalgamation -]

({ The thing whose features are all the features of features of +a will be represented by +am/ +a. })

+Df +Am [a [b = +ft// +b +am/ +a ]c ( +ft// +b +c +ft// +c +a
+Am1 +Pr ) - +Am = +ft// +b +am/ +a ]c ( +ft// +b +c +ft// +c +a
+Am2 +Pr ) - +Am = +ft// +b +am/ +a ]e ( +ft// +b +e +ft// +e +a
+Am3 +Pr ) - +Am = +ft// +b +am/ +a ]d ( +ft// +b +d +ft// +d +a

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

+Am4 +Pr ) - ( +Am +sm// +a +b +sm// +am/ +a +am/ +b
+Am5 +Pr ) - +Am ) - ( +ft// +c +b +ft// +b +a +ft// +c +am/ +a

[- Union -]

+Df +un// +a +b +am/ +th// +a +b

({ The features of +un// +a +b are the combined features of +a and +b. })

+Un1 +Pr ) - +Th ) - +Am ) - ( +ft/ +a +ft/ +b = +ft// +c +un// +a +b ) +ft// +c +a +ft// +c +b

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

+Un2 +Pr ) - ( +Th ( +Am ( +ft/ +a +ft/ +b +sm// +un// +a +b +un// +b +a
+Un3 +Pr ) - ( +Th ( +Am +ft/ +a +sm// +un// +a +a +a

({ The proof of the following Fact about amalgamations uses +Un3. })

+Am6 +Pr ) - ( +Th ( +Am +ft/ +a +sm// +am/ +th/ +a +a

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

+Un4 +Pr ) - ( +Th ( +Am ( +ft/ +a +ft/ +b ) - +sm// +a +g +sm// +un// +a +b +un// +g +b
+Un5 +Pr ) - ( +Th ( +Am ( +ft/ +a +ft/ +b ) - +sm// +a +g +sm// +un// +b +a +un// +b +g

[- Division -]

({ For any thing +a, the thing whose features are all the things that have exactly one feature, and are such that their one and only feature is a feature of +a, will be called the division of +a, and represented by +dv/ +a. })

+Df +Dv [a [b = +ft// +b +dv/ +a ]c ( +ft// +c +a +sm// +b +th/ +c
+Dv1 +Pr ) - +Dv = +ft// +b +dv/ +a ]c ( +ft// +c +a +sm// +b +th/ +c

({ The Adverb can be changed as in the following example. })

+Dv2 +Pr ) - +Dv = +ft// +b +dv/ +a ]g ( +ft// +g +a +sm// +b +th/ +g
+Dv3 +Pr ) - +Dv ) - +ft// +g +a +ft// +th/ +g +dv/ +a

({ If +a is a feature, then +th/ +a is a feature. })

+Th18 +Pr ) - ( +Th +Dv ) - +ft/ +a +ft/ +th/ +a
+Th19 +Pr ) - ( +Th ( +Am ( +Dv ( +ft/ +a +ft/ +b +sm// +un// +th/ +a +th/ +b +th// +a +b
+Th20 +Pr ) - ( +Nf ( +Th ( +Dv ( +ft/ +b +ft/ +c - +sm// +th// +0 +th/ +b +th/ +c

(_ CrossUnion _)

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