assert	Def b == if b True else False fi Thm* b:. b Prop
iff	Def P Q == (P Q) & (P Q) Thm* A,B:Prop. (A B) Prop
int_iseg	Def {i...j} == {k:| ik & kj } Thm* i,j:. {i...j} Type
length	Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) Thm* A:Type, l:A*. ||l|| Thm* ||nil||
null	Def null(as) == Case of as; nil true ; a.as' false Thm* T:Type, as:T*. null(as) Thm* null(nil)
segment	Def as[m..n] == firstn(n-m;nth_tl(m;as)) Thm* T:Type, as:T*, m,n:. (as[m..n]) T*
rev_implies	Def P Q == Q P Thm* A,B:Prop. (A B) Prop
le	Def AB == B < A Thm* i,j:. ij Prop
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*
firstn	Def firstn(n;as) == Case of as; nil nil ; a.as' if 0 < n a.firstn(n-1;as') else nil fi (recursive) Thm* A:Type, as:A*, n:. firstn(n;as) A*
not	Def A == A False Thm* A:Prop. (A) 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
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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