How does 设A是..., 若A的..., 则称A是... work for mathematical definitions? From a Baidu page about 拉丁矩 (Latin rectangles, a topic in combinatorial mathematics, and one of my research topics), we have the following sentence (listed as 定义1; I trim back some of the mathematics notation):


  设A是一个m×s矩阵，若A的任一行是集{1,...,n}的一个s-排列，任一列是集{1,...,n}的一个m-排列，则称A是一个m×s拉丁矩。  


I translate this to something like:


  If A is an m×s matrix, such that every row is an s-permutation of {1,...,n} and every column is an m-permutation of {1,...,n}, then A is a Latin rectangle.


I'm confused about the grammar here, and in particular, the use of (what seems to be) the following:


  设A是[a mathematical object], 若A的[conditions], 则称A是[a special type of that mathematical object].


I'm seeking a better overall idea of how this structure works, e.g., how frequently this is used, other examples, and what 设, 若, 则 and 称 are doing in the sentence.

Question: How does 设A是..., 若A的..., 则称A是... work for mathematical definitions?
「設」is short for 假設 (Suppose that...)

「若」means if

「則稱」, literally then (it is) called, should just be taken as then.



設A是一個m×s矩陣，若A的任一行是集{1,...,n}的一個s-排列，任一列是集{1,...,n}的一個m-排列，則稱A是一個m×s拉丁矩。
「Suppose that」A is an m by s matrix.「If」every row of A is an s-permutation of {1, ..., n} and every column is an m-permutation of {1, ..., n},「then」A is an m by s Latin rectangle.