Some definitions of interest.
inv_funs_2	Def  InvFuns(A;B;f;g) == (x:A. g(f(x)) = x) & (y:B. f(g(y)) = y)
	Thm*  f:(AB), g:(BA). InvFuns(A;B;f;g)  Prop
nat	Def   == {i:| 0i }
	Thm*    Type
next_nat_pair	Def  next_nat_pair(xy) == xy/x,y. if y=0 <0,x+1> else <x+1,y-1> fi
	Thm*  next_nat_pair
not	Def  A == A  False
	Thm*  A:Prop. (A)  Prop
prev_nat_pair	Def  prev_nat_pair(xy) == xy/x,y. if x=0 <y-1,0> else <x-1,y+1> fi
	Thm*  prev_nat_pair  {xy:()| xy = <0,0>   }

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