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, just as all the buildings have not fallen and flowed back to their original mud, so the values which wanted them and saw that they were built have not all disappeared.

However, his subject matter and basic themes have remained surprisingly consistent, and these, together with certain key poetic images, may be traced through all his work, including the new jazz experiments.

However, only Illinois, Oregon, Louisiana and Rhode Island have a situation in which the sundry units of government vary widely in relation to fiscal uniformity.

However, the aircraft which we have today are tied to large, `` soft '' airfields.

However, first I thoughtfully study my sketch for improvement of color and design along the lines I have described.

However, whether you arrange to have a European or American model, if you rent a car with the proper seating capacity in relation to the number of people in your party, your transportation expense will average very close to $10.00 per day per passenger.

However, it is not known to either the union or the public precisely how much of a cost increase is caused by a given change in the basic wage rate, although the companies are presumed to have reliable estimates of this magnitude.

However, the Attorney General of California, at the request of the Secretary of Labor, sought to have the jurisdiction over the issue removed to the Federal District Court, on grounds that it was predominantly a Federal issue since the validity of the Secretary's Regulation was being challenged.

However, as we have seen, in later childhood the child begins to substitute the standards of the peer group for those of parents and teachers.

However, by cultivating a wine dealer and accepting his advice, one will soon enough ascertain whether he has any knowledge of wines ( as opposed to what he may have been told by salesmen and promoters ) and, better yet, whether he has a taste for wine.

However, in the same three-month period, toll-road bonds, as a group, have bucked this trend.

However much we may have to criticize liberal theology's constructive formulations, the theology we ourselves must strive to formulate can only go beyond liberalism, not behind it.

However well chosen and cleverly arranged, such memorabilia unfortunately amounted to more of an interruption than an auxiliary to the evening's main business, which ( considering the talent at hand ) should probably have been the gathering of fresh samples of the Chicago style.

However, some productions have recorded success: Carnival fi Dachra produced by Mohamed Oukassi and Athmane Aliouet in 1994, or as " Salut Cousin!

However, traditional cakes made at home have a vast directory of revenue, according to the habits and customs of each family.

However, recent classifications have abandoned Mon – Khmer as a taxon, either reducing it in scope or making it synonymous with the larger family ( Diffloth 2005, Sidwell 2009 ).

However, Ancient Egyptian is highly divergent from Proto-Afroasiatic ( Trombetti 1905: 1 – 2 ), and considerable time must have elapsed in between them.

However, certain critical interlocutory court orders, such as the denial of a request for an interim injunction, or an order holding a person in contempt of court, can be appealed immediately although the case may otherwise not have been fully disposed of.

However, wall depictions of this instrument have not been discovered, casting some doubt over the extent to which this instrument was used.

Experiments have been conducted to attempt the synthesis of ununennium ( Uue ), which is likely to be the next member of the group, but they have all met with failure .< ref name =" link "> However, ununennium may not be an alkali metal due to relativistic effects, which are predicted to have a large influence on the chemical properties of superheavy elements.

However, advancements in robotic technology have allowed the design of functional and realistic humanoid robots.

However, several telescope manufacturers have recently developed telescope systems that are calibrated with the use of built-in GPS, decreasing the time it takes to set up a telescope at the start of an observing session.