(26steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc

At: finite-partition 2 1 2 1 1

1. n:
2. 0 < n
3. k:
4. c: nk
5. p: k( List)
6. sum(||p(j)|| | j < k) = n-1
7. j:k, x,y:||p(j)||. x < y (p(j))[x] > (p(j))[y]
8. j:k, x:||p(j)||. (p(j))[x] < n-1 & c((p(j))[x]) = j
sum(if c(n-1)=j 1 else 0 fi | j < k) = 1

By: Inst Thm* n:, f:(n), m:n. (x:n. x = m f(x) = 0) sum(f(x) | x < n) = f(m) [k;j. if c(n-1)=j 1 else 0 fi;c(n-1)]

Generated subgoals:

19. x: k
10. x = c(n-1)
if c(n-1)=x 1 else 0 fi = 0
1 step
 
29. sum(if c(n-1)=x 1 else 0 fi | x < k) = if c(n-1)=c(n-1) 1 else 0 fi
sum(if c(n-1)=j 1 else 0 fi | j < k) = 1
1 step

About:
listifthenelseintnatural_numbersubtract
less_thanapplyfunctionequalimpliesall

(26steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc