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At: pigeon-hole

  n,m:, f:(nm). Inj(n; m; f)  nm

By: Auto THEN Inst Thm: finite-partition [n;m;f] THEN ExRepD


Generated subgoal:

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

9 steps

About:
listintnatural_numberless_thanapplyfunction
equalimpliesandallexists
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