Why we get inequality form an equation? In the paper linear forms in the logarithms of real algebraic numbers close to 1, it is written on page 5 that-
$\varLambda \leq \frac{1}{by^n}$ (see equation 7 on page 5) 
But we get it from an equation. As I understand , it should be   $\varLambda = \frac{1}{by^n}$. 
How   $\varLambda$ could be less than $\frac{1}{by^n}$?
If it is  $\varLambda \leq \frac{1}{by^n}$ then why not  $\varLambda \geq \frac{1}{by^n}$?

$$a=b$$ implies both $$a\le b$$ and $$a\ge b.$$
It's the author's choice to weaken the comparison for the requirements of the exposition.

Quiz:
Are these propositions true ? ($\land$ is and, $\lor$ is or)


*

*$a=b\implies a\le b\land a\ge b$ ?

*$a=b\implies a\le b\lor a\ge b$ ?

*$a=b\implies a< b\lor a=b\lor a> b$ ?

*$a=b\implies a< b\land a=b\land a> b$ ?

