Some definitions of interest.
assert	Def b == if b True else False fi
	Thm* b:. b  Prop
hnum	Def hnum ==
	Thm* hnum  S
hrep_num	Def rep_num == n:. ncompose(suc_rep;n;zero_rep)
	Thm* rep_num  (hnum  hind)
hzero_rep	Def zero_rep == @x:. (y:. x = suc_rep(y)  )
	Thm* zero_rep  hind
hsuc_rep	Def suc_rep == x:. (@f:. (one_one(;;f) & onto(;;f)))(x)
	Thm* suc_rep  (hind  hind)
nat	Def  == {i:| 0i }
	Thm*   Type
	Thm*   S
prop_to_bool	Def P == InjCase(lem(P) ; true; false)
	Thm* P:Prop. (P)
tlambda	Def (x:T. b(x))(x) == b(x)

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