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

At: pigeon-hole 1 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
sum(||p(j)|| | j < m)1m

By: BackThru Thm* k,b:, f:(k). (x:k. f(x)b) sum(f(x) | x < k)bk

Generated subgoal:

19. j: m
||p(j)||1
7 steps

About:
listintnatural_numbermultiplyless_thanapplyfunctionequalimpliesall

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