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* 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* m = k Thm* Thm* (x:n. x = m x = k f(x) = 0) sum(f(x) | x < n) = f(m)+f(k) | [pair_support] |
Thm* (x:n. x = m f(x) = 0) sum(f(x) | x < n) = f(m) | [singleton_support_sum] |
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* increasing(f;n) Thm* Thm* increasing(g;k) Thm* Thm* (i:m. (j:n. i = f(j)) (j:k. i = g(j))) Thm* Thm* (j1:n, j2:k. f(j1) = g(j2)) m = n+k | [disjoint_increasing_onto] |
In prior sections: core bool 1 int 2 list 1 rel 1 sqequal 1
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MarkB generic
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