#* Proof: Then so Thus However, is prime, so or In the former case, hence ( which is a contradiction, as neither 1 nor 0 is prime ) or In the latter case, or If however, which is not prime.

Then however Maniakes fell out with his Lombard allies, while his Norman mercenaries, unhappy with their pay, abandoned the Byzantine general and raised a revolt on the Italian mainland, resulting in the temporary loss of Bari.

Then Austrian Transport Minister Hubert Gorbach called the experiment " a milestone in European transport policy-despite all predictions to the contrary "; however, the experiment was discontinued.

Then, by various accounts, she was either cast into the sea, or given to Nauplius to be either drowned or sold overseas, however she ended up in Mysia as the wife of King Teuthras.

Then, however, he declares that there is nothing wrong with his illegitimate children and denounces marriage as " out of date.

Then however in discussion with the novelist Marguerite Duras a fusion of fiction and documentary was developed which acknowedged the impossibility of speaking about Hiroshima ; one could only speak about the impossibility of speaking about Hiroshima.

Then, however, the deportations slowed to a standstill.

Then no man, however wise, will be able to avert the consequences that must ensue.

Then they throw their snare, and the fish, attracted and maddened by the color, comes straight at it, thinking from the pretty sight to gain a dainty mouthful ; when, however, it opens its jaws, it is caught by the hook, and enjoys a bitter repast, a captive.

Then, however, he discovers a collar decorating the coat which is inscribed with the words " If found, please return to Emma Hamilton, Marine Parade, Portsmouth ".

Then, in 1936, its 2. 3 million " voters " constituted a huge sample ; however, they were generally more affluent Americans who tended to have Republican sympathies.

Then however, the population from upstream southern Amazonia was discovered to be very distinct and must have been isolated for so long as to form a new species:

Then, however, Tsar Nicholas read Shevchenko's poem, " The Dream ".

Then, the corsair's defense decided to accelerate the trial and the judge decided, on December 9, to return all ships, papers and documents to Bouchard ; however the money and the booty were not given back.

Then, however, one of Steiner's NCOs rescues a young girl who fell into a mill race.

Then, however, he pockets still more " loans " from the merchants, promising to comply with their request.

Then she and Digory, Polly, Peter, Edmund, Eustace and Jill stay and live in Aslan's homeland for eternity, however Susan lives on in the real world.

Their biggest hit of the year, however, was a collaboration with Dionne Warwick, " Then Came You " ( led by Smith and Warwick ), which hit # 1 on the Billboard Hot 100, becoming each act's first chart-topping ' Pop ' hit.

Then, however, he declares that there is nothing wrong with his illegitimate children and denounces marriage as " out of date.

Then at Teple ot turns eastwards, however changes its way to east-southeast direction north of Harasmythka.

Then, however, investment bank Lazard, on the behalf of Banque de France and powered by J. P. Morgan & Co., bought immense amounts of francs, causing the franc to rise again, to 15 franc per dollar.

The song was never officially released by the duo until its 1999 album Now & Then ( it was, however, re-recorded and released without Buckner or Garcia's permission or knowledge by a group called the Starlight Children's Chorus on the album E. T., I Love You & Other Extra Terrestrial Songs for Children.

Then, Henry I married his daughter Matilda to Geoffrey V, however, the Anglo-Normans had to accept Matilda's inheritance to the throne of England.

Then, in early 1988 in " The Neutral Zone ", the last episode of the first season of Star Trek: The Next Generation, Picard explains to a banker from the 20th century that economics are quite different and the pursuit of money is no longer a part of human existence, however earlier in that season in " Encounter at Farpoint ", Beverly Crusher purchased a bolt of fabric, while asking for it to be billed to her account on the USS Enterprise.

Then, the question of a suitable extension of these concepts to fuzzy set theory arises.

Then the Alexandroff extension of X is a certain compact space X * together with an open embedding c: X → X * such that the complement of X in X * consists of a single point, typically denoted ∞.

Then as now, it was linked to downtown Savannah by White Bluff Road, the 19th-century extension of Bull Street.

Theorem: Let R be a Dedekind domain with fraction field K. Let L be a finite degree field extension of K and denote by S the integral closure of R in L. Then S is itself a Dedekind domain.

1 ) Let L be a finite extension of k of degree s. Then ( Spec L ) = Spec ( k ) and

Then sheaf cohomology enables us to consider a similar extension problem while " continuously varying " the Abelian group.

Then Q (√ d ) is a finite extension of Q, called a quadratic extension.

Indeed, let K be an imaginary quadratic field with class field H. Let E be an elliptic curve with complex multiplication by the integers of K, defined over H. Then the maximal abelian extension of K is generated by the x-coordinates of the points of finite order on some Weierstrass model for E over H.

Then L / K is a Kummer extension.

Then the question is this: is there a Galois extension field L / K such that the Galois group of the extension is isomorphic to G?

Let L be an extension of a field K. Then:

Then he studied an extension course of Information Science and Computer Technology .< ref name =" Biography ">

Then, in February 1968, a extension towards London was officially announced.

Then in the eighth chapter, life extension and mind uploading is discussed and elaborated upon.

Then A is a Frobenius extension of B with E: A → B defined by

* Let R ⊂ S be an integral extension of commutative rings, and P a prime ideal of R. Then there is a prime ideal Q in S such that Q ∩ R = P. Moreover, Q can be chosen to contain any prime Q < sub > 1 </ sub > of S such that Q < sub > 1 </ sub > ∩ R ⊂ P.

Then, in 1966, Chinatown ’ s survival was again threatened when the City released a draft Downtown Master Plan which proposed a major freeway, known as the “ east-west downtown penetrator ” to run as an extension of Bow Trail through downtown between second and third avenues ; directly through the heart of Chinatown.

Then B is an integral extension of A, and we let f be the inclusion map from A to B.

Then is a conservative extension of, which means that the theory has the same set of theorems in the original language ( i. e., without constants ) as the theory.

Then is a conservative extension of, i. e. the theories and prove the same theorems not involving the functional symbol ).

Then the morphism corresponds to an integral extension of rings B ⊂ A.