assert	Def b == if b True else False fi Thm* b:. b Prop
biject	Def Bij(A; B; f) == Inj(A; B; f) & Surj(A; B; f) Thm* A,B:Type, f:(AB). Bij(A; B; f) Prop
iff	Def P Q == (P Q) & (P Q) Thm* A,B:Prop. (A B) Prop
int_seg	Def {i..j} == {k:| i k < j } Thm* m,n:. {m..n} Type
nat	Def == {i:| 0i } Thm* Type
lelt	Def i j < k == ij & j < k
le	Def AB == B < A Thm* i,j:. ij Prop
mem_f	Def mem_f(T;a;bs) == Case of bs; nil False ; b.bs' b = a T mem_f(T;a;bs') (recursive) Thm* T:Type, a:T, bs:T*. mem_f(T;a;bs) Prop
surject	Def Surj(A; B; f) == b:B. a:A. f(a) = b Thm* A,B:Type, f:(AB). Surj(A; B; f) Prop
inject	Def Inj(A; B; f) == a1,a2:A. f(a1) = f(a2) B a1 = a2 Thm* A,B:Type, f:(AB). Inj(A; B; f) Prop
rev_implies	Def P Q == Q P Thm* A,B:Prop. (A B) Prop
not	Def A == A False Thm* A:Prop. (A) Prop

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