Proof of the non-intervention theorem

Question

I cannot prove the non-intervention theorem. This theorem states that if you sort the rows, and then the columns of the matrix, the rows will be sorted.

I read a sketch of the evidence that says:

• sort strings
• Rearrange rows to sort the first column
• rearrange the rows for each of which it discards the first element, sort the second column, and so on.
• The invariant is that the rows remain sorted at every step. (whatever that means - I quote the steps)

I can’t ignore it. Can someone give me a more detailed proof or a link to some article?

Answer 1

. A, B, r A n A, r, : B n , r ( n A). , r. r A, . .

:

, :

, ( , A, B ):

, , 2 . , , B, 1 - :

, A , 3 . , B , 3 . - , 2 .

, A , 3 . , B , 3 . - , 3 .

. , , , , (, , 7). 7 , > 7 B. 4 :

:

, . , , :

[4 7 8  9]
[1 5 10 12]
[2 3 6  11]

, :

[1 3 8  9]
[2 5 10 12]
[4 7 6  11]

3 . 3 10, .