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Def AB == B<A

is mentioned by

Thm* f:(TT), m:(T).
Thm* (x:Tm(f(x))m(x) & (m(f(x)) = m(x f(x) = x))
Thm* 
Thm* (x:Tn:f(f^n(x)) = f^n(x))
[iteration_terminates]
Thm* n,m:f:(nm). Inj(nmf nm[pigeon-hole]
Thm* k,b:f:(k). (x:kbf(x))  bksum(f(x) | x < k)[sum_lower_bound]
Thm* k,b:f:(k). (x:kf(x)b sum(f(x) | x < k)bk[sum_bound]
Thm* k:f,g:(k).
Thm* (x:kf(x)g(x))  sum(f(x) | x < k)sum(g(x) | x < k)
[sum_le]
Thm* n:f:(n). (x:n. 0f(x))  0sum(f(x) | x < n)[non_neg_sum]
Thm* k,m:. (f:(km). Inj(kmf))  km[injection_le]
Thm* k:f:(k), x:k. increasing(f;k f(0)+xf(x)[increasing_lower_bound]
Thm* k,m:. (f:(km). increasing(f;k))  km[increasing_le]
Def nondecreasing(f;k) == i:(k-1). f(i)f(i+1)[nondecreasing]

In prior sections: int 1 bool 1 int 2 list 1 core

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