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Def P & Q == PQ

is mentioned by

Thm* k:P:(k).
Thm* ((i:kP(i))  0<search(k;P))
Thm* & (0<search(k;P P(search(k;P)-1) & (j:kj<search(k;P)-1  P(j)))
[search_property]
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), x1,x2:ny1,y2:m.
Thm* x1 = x2  y1 = y2
Thm* 
Thm* (x:ny:m(x = x1 & y = y1 (x = x2 & y = y2 f(x,y) = 0)
Thm* 
Thm* sum(f(x,y) | x < ny < m) = f(x1,y1)+f(x2,y2)
[pair_support_double_sum]
Thm* n,k:c:(nk).
Thm* p:(k( List)). 
Thm* sum(||p(j)|| | j < k) = n
Thm* & (j:kx,y:||p(j)||. x<y  (p(j))[x]>(p(j))[y])
Thm* & (j:kx:||p(j)||. (p(j))[x]<n & c((p(j))[x]) = j)
[finite-partition]
Thm* m:P:(mProp).
Thm* (i:m. Dec(P(i)))
Thm* 
Thm* (n,k:f:(nm), g:(km).
Thm* (increasing(f;n)
Thm* (& increasing(g;k)
Thm* (& (i:nP(f(i)))
Thm* (& (j:kP(g(j)))
Thm* (& (i:m. (j:ni = f(j))  (j:ki = g(j))))
[increasing_split]
Thm* k:f:(kk).
Thm* 0<k
Thm* 
Thm* Bij(kkf)
Thm* 
Thm* f(k-1) = k-1  f  (k-1)(k-1) & Bij((k-1); (k-1); f)
[bijection_restriction]
Def (P  Q)(L) == P(L) & Q(L)[prop_and]
Def R^n == if n=0 x,yx = y  T else x,yz:T. (x R z) & (z R^n-1 y) fi
Def (recursive)
[rel_exp]

In prior sections: core int 1 bool 1 int 2 fun 1 rel 1

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mb nat Sections MarkB generic Doc