Nuprl - Proof: pigeon-hole 1 1 1

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

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
9. j: m

||p(j)||1

By: AllHyps (InstHyp [j]) THEN SupposeNot

Generated subgoal:

1 10. x:||p(j)||. (p(j))[x] < n & f((p(j))[x]) = j
11. x,y:||p(j)||. x < y (p(j))[x] > (p(j))[y]
12. ||p(j)||1
||p(j)||1 6 steps

About:

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