[see also: assertion, conclusion, formulation
The following three statements are equivalent:......
Now, (3) is merely an abbreviation for the statement that......
Here is a more explicit statement of what the theorem asserts.
The convergence of the sum on the left is of course a weaker statement than the convergence of (2).
It is important that the orders of F and G are comparable, a statement made more precise by the following lemma.
However, (ii) is nothing but the statement that...... [= only the statement that]