Who Cites ball?
ball	Def x:T. P(x) == (x:T. P(x))
	Thm* T:Type, P:(T). (x:T. P(x))
assert	Def b == if b True else False fi
	Thm* b:. b  Prop
prop_to_bool	Def P == InjCase(lem(P) ; true; false)
	Thm* P:Prop. (P)
ifthenelse	Def if b t else f fi == InjCase(b ; t; f)
	Thm* b:, A:Type, p,q:A. if b p else q fi  A
bfalse	Def false == inr()
	Thm* false
btrue	Def true == inl()
	Thm* true

Syntax:

x:T. P(x)

has structure:

ball(T; x.P(x))

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