int_seg	Def {i..j} == {k:| i k < j } Thm* m,n:. {m..n} Type
length	Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) Thm* A:Type, l:A*. ||l|| Thm* ||nil||
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
select	Def l[i] == hd(nth_tl(i;l)) Thm* A:Type, l:A*, n:. 0n n < ||l|| l[n] A
lelt	Def i j < k == ij & j < k
nth_tl	Def nth_tl(n;as) == if n0 as else nth_tl(n-1;tl(as)) fi (recursive) Thm* A:Type, as:A*, i:. nth_tl(i;as) A*
hd	Def hd(l) == Case of l; nil "?" ; h.t h Thm* A:Type, l:A*. ||l||1 hd(l) A
le	Def AB == B < A Thm* i,j:. ij Prop
tl	Def tl(l) == Case of l; nil nil ; h.t t Thm* A:Type, l:A*. tl(l) A*
le_int	Def ij == j < i Thm* i,j:. ij
not	Def A == A False Thm* A:Prop. (A) Prop
lt_int	Def i < j == if i < j true ; false fi Thm* i,j:. i < j
bnot	Def b == if b false else true fi Thm* b:. b

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