Some definitions of interest.
nat	Def   == {i:| 0i }
	Thm*    Type
le	Def  AB == B<A
	Thm*  i,j:. (ij)  Prop
nat_plus	Def   == {i:| 0<i }
	Thm*    Type
not	Def  A == A  False
	Thm*  A:Prop. (A)  Prop

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