| Some definitions of interest. |
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delete_fenum_value | Def Replace value k by f(m) in f == Replace values x s.t. x= k by f(m) in f |
| | Thm* Inj({k: | P(k) }; {k: | Q(k) }; f)
Thm* 
Thm* ( m:{u: | P(u) }, k:{v: | Q(v) }.
Thm* ((Replace value k by f(m) in f)
Thm* ( {u: | P(u) & u = m } {v: | Q(v) & v = k }) |
| | Thm* Inj( (m+1); (k+1); f)  (Replace value k by f(m) in f) m  k |
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list_to_function | Def seq:l(i) == l[i] |
| | Thm* l:A List. seq:l ||l|| A |
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listify | Def f{m..n } == if n m nil else f(m).f{(m+1)..n } fi (recursive) |
| | Thm* T:Type, m,n: , f:({m..n } T). f{m..n } T List |
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le_int | Def i j ==  j< i |
| | Thm* i,j: . (i j)  |
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length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | Thm* A:Type, l:A List. ||l||  |
| | Thm* ||nil||  |
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let | Def let x = a in b(x) == ( x.b(x))(a) |
| | Thm* A,B:Type, a:A, b:(A B). let x = a in b(x) B |