Nuprl - Proof: finite-partition 2 1 2 1 1 2

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

At: finite-partition 2 1 2 1 1 2

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
9. 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

By: MoveToConcl -1 THEN SplitOnConclITE

Generated subgoals:

None

About:

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