question and trial

$ \begin{array}{l} prove{\rm that} \\ {\rm gcd(a,b)} \le {\rm a - b , a} \succ {\rm b} \\ {\rm solution:} \\ {\rm note}\;{\rm that}\;{\rm gcd(a,b) = gcd(a, - b)} \\ \Rightarrow {\rm d\backslash a , d\backslash - b} \Rightarrow {\rm d\backslash a + - b} \\ {\rm this}\,\;{\rm means}\;{\rm that}\;{\rm d} \le {\rm a - b } \Rightarrow {\rm gcd(a,b)} \le {\rm a - b }{\rm .} \\ \\ \end{array}$