Therefore, if a lower court has ruled in an improper manner, or against legal precedent, that judgment will stand if not appealed – even if it might have been overturned on appeal.

Therefore, it works as a neutron reflector and neutron moderator, effectively slowing the neutrons to the thermal energy range of below 0. 03 eV, where the total cross section is at least an order of magnitude lower – exact value strongly depends on the purity and size of the crystallites in the material.

Therefore, the distillate will not be pure – its composition will be identical to the composition of the vapors at the given temperature and pressure, and can be computed from Raoult's law.

Therefore it is advised to change terrain occasionally – such as trail, beach, or grass running.

Therefore, to properly understand the theory of evolution via natural selection, one must understand the genotype – phenotype distinction.

Therefore the EGP is now turning its attention to Eastern Europe – all these countries have Green parties, but in materially poor Eastern Europe the success of Green Parties is very patchy, except for Hungary, where the local Green party, Politics Can Be Different ( LMP ), has succeeded in getting into the parliament and many city councils.

Therefore, other members of the survivor ’ s family – in particular the spouse and children – are also offered treatment and counselling.

Therefore, the radius of an atom is more than 10, 000 times the radius of its nucleus ( 1 – 10 fm ), and less than 1 / 1000 of the wavelength of visible light ( 400 – 700 nm ).

Therefore it is also sometimes called the DJP algorithm, the Jarník algorithm, or the Prim – Jarník algorithm.

Therefore RDF swaps object for subject that would be used in the classical notation of an Entity – attribute – value model within Object oriented design ; object ( sky ), attribute ( color ) and value ( blue ).

Therefore the two other – very close – definitions: 1200 / 7227 inch and 350 / 83 mm are both unofficial.

Therefore Gaiseric freed Licinia Eudoxia ( thus fulfilling Daniel's prophesy ) and her daughter Placidia ( Olybrius ' wife ), but did not stop his raids on Italian's coasts, in order to press for the election of his candidate on the Western throne, but his project failed, because Ricimer, who had become the Magister militum of the West, chose Libius Severus as new Emperor ( 461 – 465 ).

Therefore, this approach to treatment of Tay – Sachs disease has also been ineffective so far.

Therefore, Luns decided to study law at Amsterdam University during the period 1932 – 1937.

Therefore, 36 – 48 m < sup > 2 </ sup > of solar-exposed thermal mass is required.

* United States of America – Our Lady of the Immaculate Conception unofficial due to the Establishment Clause of the First Amendment to the Constitution of the United States which states, " Congress ( Therefore the U. S. Government ) shall make no law respecting an establishment of religion ,..."

Therefore the only online exchange that meets the railway line is Pescara – Rome station Avezzano.

Therefore, the only rail interchange is characterized by the Adriatic railway line Bologna – Bari, Abruzzo is Martinsicuro rail-Broad-S.

Therefore large variety of euphemisms were used instead, including comparisons, human names and other anthropomorphic terms – e. g. snakes were likened to ropes or called brides, while wolf was named Juris or Ansis or referred to as man ( also brother or friend ) of the forest.

Therefore we see that any two spins can be lined with a ferromagnetic or an antiferromagnetic bond and the distribution of these is given exactly as in the case of Edwards – Anderson model.

Therefore, winning 4 – 1 on aggregate.

Therefore, there is nothing " magical " about the number 7, and Miller used the expression only rhetorically.

Therefore, in one of the biggest successes of the club's history, the triumph in the 1972 European Cup Winners ' Cup Final, Miller was not on the pitch.

For example, the prime number theorem states that the number of prime numbers less than or equal to N is asymptotically equal to N / ln N. Therefore the proportion of prime integers is roughly 1 / ln N, which tends to 0.

Therefore, just as Bayes ' theorem shows, the result of each trial comes down to the base probability of the fair coin:.

Therefore, to establish a mathematical statement as a theorem, the existence of a line of reasoning from axioms in the system ( and other, already established theorems ) to the given statement must be demonstrated.

Therefore, by the first isomorphism theorem, GL ( n, F )/ SL ( n, F ) is isomorphic to F < sup >×</ sup >.

Therefore, the theorem says that the sequence l ( n · P ) reads

Therefore when the field K is the complex numbers, we can assume that each p < sub > i </ sub > has degree 1 ( by the fundamental theorem of algebra ) the numerators will be constant.

Therefore particles, with the same start and end points, but travelling along two different routes will acquire a phase difference Δφ determined by the magnetic flux Φ < sub > B </ sub > through the area between the paths ( via Stokes ' theorem and ), and given by:

Therefore, if the theorem is true for polygons constructed from n triangles, the theorem is also true for polygons constructed from n + 1 triangles.

Therefore the general theorem is sometimes known as the Löwenheim – Skolem – Tarski theorem.

Therefore, knowing the radius of the sphere, and the distance from the plane of the small circle to C, the radius of the small circle can be determined using the Pythagorean theorem.

Therefore, the planar graphs have a forbidden minor characterization, which in this case is given by Wagner's theorem: the set H of minor-minimal nonplanar graphs contains exactly two graphs, the complete graph K < sub > 5 </ sub > and the complete bipartite graph K < sub > 3, 3 </ sub >, and the planar graphs are exactly the graphs that do not have a minor in the set

Now by applying the Riesz representation theorem we can identify H < sup >*</ sup > with H. Therefore the definition of rigged Hilbert space is in terms of a sandwich:

Therefore, the spectral theorem implies that there is a basis of modular forms that are eigenfunctions for these Hecke operators.

Therefore, the theorem connects the linear response relaxation of a system from a prepared non-equilibrium state to its statistical fluctuation properties in equilibrium.

Therefore, by the De Bruijn – Erdős theorem, P itself also has a w-colorable incomparability graph, and thus has the desired partition into chains.

Therefore, the complement of any comparability graph is perfect ; this is essentially just Dilworth's theorem itself, restated in graph-theoretic terms.

Therefore, by the Robertson – Seymour theorem, the linklessly embeddable graphs have a forbidden graph characterization as the graphs that do not contain any of a finite set of minors.

Therefore one may prove theorems about the more complicated cases by proving them in two simple cases and then using the Riesz – Thorin theorem to pass from the simple cases to the complicated cases.

Therefore we may invoke the Riesz – Thorin theorem to get, for any 1 < p < 2 that T, as an operator from to, is bounded with norm 1, where

Therefore the Riesz – Thorin theorem gives

Therefore, assuming the numerical existence property, if is a theorem of, so is, by the numerical existence property there exists some such that is a theorem.