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

At: finite-partition

n,k:, c:(nk). 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)

By: InductionOnNat

Generated subgoals:

1 k:, c:(0k). p:(k( List)). sum(||p(j)|| | j < k) = 0 & (j:k, x,y:||p(j)||. x < y (p(j))[x] > (p(j))[y]) & (j:k, x:||p(j)||. (p(j))[x] < 0 & c((p(j))[x]) = j)2 steps
 
21. n:
2. 0 < n
3. k:, c:((n-1)k). p:(k( List)). sum(||p(j)|| | j < k) = n-1 & (j:k, x,y:||p(j)||. x < y (p(j))[x] > (p(j))[y]) & (j:k, x:||p(j)||. (p(j))[x] < n-1 & c((p(j))[x]) = j)
k:, c:(nk). 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)
23 steps

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listintnatural_numberless_thanapplyfunction
equalimpliesandallexists

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