(10steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc

At: pigeon-hole 1
1. n:
2. m:
3. f: nm
4. Inj(n; m; f)
5. p: m( List)
6. sum(||p(j)|| | j < m) = n
7. j:m, x,y:||p(j)||. x < y (p(j))[x] > (p(j))[y]
8. j:m, x:||p(j)||. (p(j))[x] < n & f((p(j))[x]) = j
nm
By: Assert (sum(||p(j)|| | j < m)1m)
Generated subgoal:

1 sum(||p(j)|| | j < m)1m8 steps

About:
listintnatural_numbermultiplyless_thanapplyfunctionequalimpliesall

(10steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc