is mentioned by
Thm* ((i:k. P(i)) 0<search(k;P)) Thm* & (0<search(k;P) P(search(k;P)-1) & (j:k. j<search(k;P)-1 P(j))) | [search_property] |
Thm* (x:T. m(f(x))m(x) & (m(f(x)) = m(x) f(x) = x)) Thm* Thm* (x:T. n:. f(f^n(x)) = f^n(x)) | [iteration_terminates] |
Thm* x1 = x2 y1 = y2 Thm* Thm* (x:n, y:m. (x = x1 & y = y1) (x = x2 & y = y2) f(x,y) = 0) Thm* Thm* sum(f(x,y) | x < n; y < m) = f(x1,y1)+f(x2,y2) | [pair_support_double_sum] |
Thm* p:(k( List)). Thm* sum(||p(j)|| | j < k) = n Thm* & (j:k, x,y:||p(j)||. x<y (p(j))[x]>(p(j))[y]) Thm* & (j:k, x:||p(j)||. (p(j))[x]<n & c((p(j))[x]) = j) | [finite-partition] |
Thm* (i:m. Dec(P(i))) Thm* Thm* (n,k:, f:(nm), g:(km). Thm* (increasing(f;n) Thm* (& increasing(g;k) Thm* (& (i:n. P(f(i))) Thm* (& (j:k. P(g(j))) Thm* (& (i:m. (j:n. i = f(j)) (j:k. i = g(j)))) | [increasing_split] |
Thm* 0<k Thm* Thm* Bij(k; k; f) Thm* Thm* f(k-1) = k-1 f (k-1)(k-1) & Bij((k-1); (k-1); f) | [bijection_restriction] |
[prop_and] | |
Def (recursive) | [rel_exp] |
In prior sections: core int 1 bool 1 int 2 fun 1 rel 1
Try larger context:
MarkB generic
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