| 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) mk |
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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 nm 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 ij == j<i |
| | Thm* i,j:. (ij) |
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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:(AB). let x = a in b(x) B |