However, that particular case is a theorem of Zermelo – Fraenkel set theory without the axiom of choice ( ZF ); it is easily proved by mathematical induction.

However, in practice they proved to be too large to manoeuvre well in the close waters of estuaries and rivers, the only places in which a ' naval ' battle could occur.

However, shortly after this positive result, Kurt Gödel published On Formally Undecidable Propositions of Principia Mathematica and Related Systems ( 1931 ), showing that in any sufficiently strong axiomatic system there are true statements which cannot be proved in the system.

However, this design proved to be very difficult to remove from the console and was replaced by a second design.

However, chlorpromazine proved to reduce the effects of psychosis in a more effective and specific manner than lobotomy, even though it was known to be capable of causing severe sedation.

" However, his looks proved to be an asset in his personal and political relationships, as his law partner William Herndon wrote, " He was not a pretty man by any means, nor was he an ugly one ; he was a homely man, careless of his looks, plain-looking and plain-acting.

However, it was ultimately unable to achieve a significant market share and proved commercially unviable for Be Inc.

However, subscription-funded digital terrestrial television ( DTT ) proved less of a competitive threat.

However the rope available at the time proved too susceptible to wear and the system was abandoned in favour of steam locomotives after eight years.

However, the PDP-6 proved to be a " hard sell " with customers, as it offered few advantages over similar machines from the better established vendors like IBM or Honeywell, in spite of its low cost around $ 300, 000.

However, the plantations, both under their previous private ownership and under government administration, proved consistently unprofitable due to the introduction of new oils and lubricants in the international marketplace, and the establishment of vast coconut plantations in the East Indies and the Philippines.

However, Thomas Crow argues that this path " proved to be less a way forward than a cul-de-sac for history painting.

However, when Baden was transferred west to fight the French in 1692 his successors, first Caprara, then from 1696, Frederick Augustus, the Elector of Saxony, proved incapable of delivering the final blow.

However, the facilities proved to be able to barely handle the flood of immigrants that arrived in the years just before World War I.

However, General Niazi proved to be a failure and ineffective ruler.

" However the Times also reflected widespread skepticism as to whether the forward pass could be effectively integrated into the game: " There has been no team that has proved that the forward pass is anything but a doubtful, dangerous play to be used only in the last extremity.

However, according to the late Tomoyuki Tanaka, it proved to be difficult to obtain permission to use King Kong.

However the Eastern Question and the resulting Crimean War proved to be the downfall of his government.

However, the rise of quiz shows proved to be short-lived.

However, a campaign to reconquer Peru and Chile during the Chincha Islands War ( 1864 – 1866 ) proved disastrous and Spain suffered defeat before the determined South American powers.

However, Paul Henreid proved to be the best player.

However, his discoveries were not appreciated by his contemporaries and came into general use only with discoveries of British surgeon Joseph Lister, who in 1865 proved the principles of antisepsis in the treatment of wounds ; However, medical conservatism on new breakthroughs in pre-existing science prevented them from being generally well received during the 19th century.

However, the lamps proved a false dawn because they became unsafe very quickly and provided a weak light.

However, his captaincy proved to be an unhappy one ; he lost form and the team did not do well.

However, the system is designed, ingeniously and hopefully, so that no one man could initiate a thermonuclear war.

However, if there is no additional complex of singular lines, the order of the image regulus of a pencil is precisely Af.

However, there was no real question of the justice of creating a strong Poland, both industrially and agriculturally, and one unplagued by large minorities of Germans or Russians.

However, the leveling operation can be maintained and controlled remotely with no mechanical or optical contact with the platform.

However, this inaugural feast did its sponsors no good whatever.

However, one can argue that no such control is necessary as long as one pretends that the anti-trust laws are effective and rational.

However, no diagram of her brain patterns, no early I.Q. tests recorded certain essential facts about Helva that Central must eventually learn.

However, since no equipment existed to show the images in motion, such a series of images cannot be called animation in a true sense of the word .< ref >

However, no direct connection can be demonstrated, and the similarity of the abaci may be coincidental, both ultimately arising from counting with five fingers per hand.

However, the hydrogen-1 atom has no neutrons and a positive hydrogen ion has no electrons.

However, there is no evidence to support this practice and it may in fact delay healing.

However, no comprehensive environmental protection program has emerged, and decisions on environmental policy have been made on an ad hoc basis.

However, no new edition was released before Guardians of Order went out of business in 2006.

However, there is no one-to-one correspondence between words in ASL and English, and the inflectional modulation of ASL signs — a dominant part of the grammar — is lost.

However, there is no evidence that his son and ultimate successor, Constantius II, who was an Arian Christian, was exiled.

However, no incidents of violence against spring breakers were reported.

However, no Hermunduri appear in Ptolemy, though after the time of Ptolemy the Hermunduri joined with the Marcomanni in the wars of 166 – 180 against the empire.

However this leaves no prize for herself.

However, according to Josephus, in Antiquities, Book 7, Chapter 1, Joab had forgiven Abner for the death of his brother, Asahel, the reason being that Abner had slain Asahel honorably in combat after he had first warned Asahel and had no other choice but to kill him out of self defense.

However, there are no known year-names or other archaeological evidence verifying any of these later kings of Akkad or Uruk, apart from a single artifact referencing king Dudu of Akkad.

However, Wolfram points out that at the time " Clovis got no farther than the Seine ; only after several more years did the Franks succeed in occupying the rest of the Gallo-Roman buffer state north of the Loire.

However, he became gravely ill during the 1918 flu pandemic and, since Spain was neutral and thus under no wartime censorship restrictions, his illness and subsequent recovery were covered worldwide, giving the false impression ( in the absence of real news from anywhere else ) that Spain was the most-affected area.

However, much to his professional detriment, Lavoisier discovered no new substances, devised no really novel apparatus, and worked out no improved methods of preparation.