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Def
sum(f(x) | x < k) == primrec(k;0;
x,n. n+f(x))
is mentioned by
Thm*
L:
List. sum(L[i]-1 | i < ||L||)+1- > L^1
[Ramsey-base-case]
Thm*
n,k:
, c:(
n
k).
p:(
k
(
List)). sum(||p(j)|| | j < k) = n & (
j:
k, x,y:
||p(j)||. x < y
(p(j))[x] > (p(j))[y]) & (
j:
k, x:
||p(j)||. (p(j))[x] < n & c((p(j))[x]) = j)
[finite-partition]
Def
array-count(v.P(v);a) == sum(if P(a[i])
1 else 0 fi | i < |a|)
[array-count]
In prior sections:
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