If a nonnegative integer random variable has expectation below one, some sample has value zero. Keeping the exact identity in view prevents the geometric or probabilistic intuition from drifting.
Start locally
Extremal combinatorics asks how large a structure can be while avoiding a forbidden configuration. The probabilistic method proves existence by showing \(\mathbf P(X=0)>0\) or \(\mathbf E[X]<1\).
The typography mirrors the proof: first declare \(\mathsf D\), then state \(\mathsf C\). The symbol \(\Longrightarrow\) below is a logical dependency, not extra mathematical structure.
Compute before generalising
Here is a concrete symbolic test. Reading it from left to right reveals which transformation is reversible and which is only an implication.
The global view
The invariant statement is the one that does not depend on a convenient choice of coordinates, representatives, basis, or enumeration.
Edge conditions
An expectation below one proves that some outcome has zero bad objects only when the bad-object count is a nonnegative integer.
I would use the boxed line as a reference later, while returning to the full display whenever a hypothesis becomes uncertain. That division keeps compression from becoming ambiguity.