The compactness in C 1 ( [ 0, 1 ] ) of the set of all fixed points of then implies that is finite, i.e., S = { u 1, …, u N } for some positive integer N. Denote by B ( u, r ) the open ball in C 1 ( [ 0, 1 ] ) centered at u and having radius r.
This then implies that the rate is not independent of hydrodynamics in the impeller region.
But she then implies that it would be unfair to oppose Judge Alito based on that record.
The play then implies that worst fears have been realized and their child is born with terrible deformities and cognitive disabilities.
Mr. Holder's decision, then, implies that justice wasn't done five years ago probably because high-level officials in the George W. Bush administration put their thumbs on the scale of justice.
This then implies that below some level the electromagnetic (EM) energy can be regarded as "safe" and above it as "hazardous" and that exposure to it should be controlled.
Then implies that (2.50).
Equality (4.20) then implies that (4.17) holds.
If we take then implies that.
Lemma 3 then implies that condition (11) holds, as desired.
Then implies that, where is any solution of (2.3).
