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

At: finite-partition 2 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 [(n-1) / (p(j))] else p(j) fi|| | j < k) = n
By: Subst' (sum(||if c(n-1)=j [(n-1) / (p(j))] else p(j) fi|| | j < k) = sum(if c(n-1)=j ||[(n-1) / (p(j))]|| else ||p(j)|| fi | j < k)) 0
Generated subgoals:

1 sum(||if c(n-1)=j [(n-1) / (p(j))] else p(j) fi|| | j < k) = sum(if c(n-1)=j ||[(n-1) / (p(j))]|| else ||p(j)|| fi | j < k)1 step
 
2 sum(if c(n-1)=j ||[(n-1) / (p(j))]|| else ||p(j)|| fi | j < k) = n6 steps

About:
listconsifthenelseintnatural_number
subtractless_thanapplyfunctionequalimpliesall

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