This proved to be a very popular alternative milieu, so much so that much of the supplemental material is now included in the core rule book.

The higher-dimensional chain rule can be proved using a technique similar to the second proof given above.

The Moroccans proved unable to rule the kingdom effectively, however, and it split into many small kingdoms.

Depending on the particular formalism adopted for the calculus, it may be seen as a simple application of a " functional substitution " rule of inference, as in Gödel's paper, or it may be proved by considering the formal proof of, replacing in it all occurrences of Q by some other formula with the same free variables, and noting that all logical axioms in the formal proof remain logical axioms after the substitution, and all rules of inference still apply in the same way.

There were some opposition to his rule in Normandy, yet it proved remarkably easy to rule, especially compared to the County of Toulouse which had been brutally conquered.

The Albanians proved generally faithful to Ottoman rule following the end of the resistance led by Skanderbeg, and accepted Islam more easily than their neighbors.

it is chiefly the rule of substitution which would have to be proved " ( Gödel 1944: 124 )

Contrary to the modern notion of a dictator as an usurper, Roman Dictators were freely chosen, usually from the ranks of consuls, during turbulent periods when one-man rule proved more efficient.

The acquisition of Lorraine for the former Polish king, however, proved of lasting benefit to France, as it passed under direct French rule with Stanisław's death in 1766.

Willkie proved the exception to this rule.

Babylon proved to be relatively weak under the long rule of the Kassites, and spent long periods under Assyrian and Elamite domination and interference.

When the Netherlands revolted against Spanish rule, beginning in 1566, the territories in what is now Nord-Pas-de-Calais were those most loyal to the throne, and proved the base from which the Duke of Parma was able to bring the whole southern part of the Netherlands back under Spanish control.

His rule proved highly unpopular within his own country ( due to the reforms mentioned earlier ), and in the Soviet Union.

In 1522, the Taíno Cacique Enriquillo ( Little Henry ) successfully rebelled against Spanish rule, forcing them to agree to a treaty that granted the natives the human rights of Freedom and of Possession ; yet that forced concession proved inconsequential, because European diseases, slavery, and ritual infanticide and suicide ( meant to avoid adult and infantile enslavement ) quickly killed most of the Taíno people.

About 4 months later, Carleton's apprehensions regarding the ability of the Canadian noblesse ( nobility ) and clergy to rule over the people are proved right.

There is no special reason to think that Cavour now envisaged the unification of the rest of Italy under Piedmontese rule since these areas were of little interest economically and could be a financial burden, but events proved to have a life of their own.

During the eighth century, Pamplona and its hinterland oscillated between two powerful states, Moors and Franks, but they proved unable to permanently secure its rule over the Basque region.

After half a century of largely unrestricted parliamentary rule proved just as ruinous, King Gustav III seized back royal power in the coup d ' état of 1772, and later once again abolished the privy council under the Union and Security Act in 1789, which, in turn, was rendered void in 1809 when Gustav IV Adolf was deposed in a coup and the constitution of 1809 was put in its place.

It proved to be the last major rebellion against Bolshevik rule.

He became a magistrate, and soon proved himself as an efficient enforcer of French rule against a series of anti-colonial disturbances in 1939.

Once Vietnam did succumb to foreign rule, however, it proved unable to escape from it, and for 1, 100 years, Vietnam had been successively governed by a series of foreign powers: the Hans, Eastern Hans, Eastern Wus, Cao Wei, Jins, Liu Songs, Southern Qis, Liangs, Suis, Tangs, and Southern Hans ; leading to the losses of its writing system, language, and national identity.

In proof by mathematical induction, a single " base case " is proved, and an " induction rule " is proved, which establishes that if a certain case is true, then another case is true.

When the automobile was in its embryonic stage, such roads as existed were pretty much open roads with the tacit understanding that horses should not be unduly terrified being about the only rule governing where, when and how fast a car could go.

In October 2009, when visiting Yerevan, the World Bank ’ s managing director, Ngozi Okonjo-Iweala, warned that Armenia will not reach a higher level of development unless its leadership changes the " oligopolistic " structure of the national economy, bolsters the rule of law and shows " zero tolerance " towards corruption.

The current conflict over Nagorno-Karabakh ( NK ) began in 1988 when Armenian demonstrations against Azerbaijani rule broke out in both Nagorno-Karabakh and Armenia and the Nagorno-Karabakh Supreme Soviet voted to secede from Azerbaijan and join Armenia.

In Homer's Iliad, when Alcmene was about to give birth to Heracles, Zeus announced to all the gods that on that day a child, descended from Zeus himself, would be born who would rule all those around him.

Although, the young prince's troops could get the mastery in 1189 when the boyars of Halych rose against his rule, but shortly afterwards Prince Vladimir II Yaroslavich managed to escape from his captivity and he expelled the Hungarian troops from Halych.

* Full stops / Periods in abbreviations: Americans tend to write Mr., Mrs., St., Dr .; the British will most often write Mr, Mrs, St, Dr, following the rule that a full stop / period is used only when the last letter of the abbreviation is not the last letter of the complete word.

One exception to this rule was the Italian Cannone da 90 / 53 which was highly effective when mounted on trucks, a fit known as the " autocannoni da 90 / 53 ".

The Emperor planned to have Felix and Liberius rule jointly, but when Liberius returned Felix was forced to retire to Porto, near Rome, where, after making an unsuccessful attempt to establish himself again in Rome, he died on 22 November 365.

One problem with sports arbitrage is that bookmakers sometimes make mistakes and this can lead to an invocation of the ' palpable error ' rule, which most bookmakers invoke when they have made a mistake by offering or posting incorrect odds.

Per baseball official rule 6. 08 ( b ), a batter becomes a baserunner and is awarded first base when he or his equipment ( except for his bat ):

The rule works this way because a smart fielder can theoretically purposely bobble the ball and run with it at the same time towards the infield and only completely catch it when he is within a good throwing distance to home plate.

Under the new rule, when any runner is thrown out, and the other ( s ) are successful, the successful runners will not be credited with a stolen base.

Occasional exceptions to this rule are tolerated when the alternative is political chaos.

Swapping among three parties often helps satisfy tastes when trying to get around the rule that money is not allowed.

The result is decided when an opponent is deemed incapable to continue by a referee, is disqualified for breaking a rule, resigns by throwing in a towel, or is pronounced the winner or loser based on the judges ' scorecards at the end of the contest.

To balance the situation, the Crawford rule requires that when a player first reaches a score one point short of winning, neither player may use the doubling cube for the following game, called the Crawford game.

The coalition's main chance came in 62 BC, when the Greek cities rebelled against Roman rule.

Gildas, in his 6th century De Excidio et Conquestu Britanniae, may have been alluding to Boudica when he wrote " A treacherous lioness butchered the governors who had been left to give fuller voice and strength to the endeavours of Roman rule.

The convention in naval warfare of the time was that ships of the line did not attack frigates when there were ships of equal size to engage, but in firing first French Captain Claude-Jean Martin had negated the rule and Saumarez waited until the frigate was at close range before replying.

Five years later when asked for his view of the rule change, the current president, Stephen Jones, replied, " I've never been more proud of my dad than the night he ... lifted that policy.

The first Persian invasion was a response to Greek involvement in the Ionian Revolt, when Athens and Eretria had sent a force to support the cities of Ionia in their attempt to overthrow Persian rule.

This mandate was said to be taken when rulers became unworthy of their position and provided a shrewd justification for Zhou rule.

With an essential principle like " when the epoch changed, the ways changed ", it upholds the rule of law and is thus a theory of jurisprudence.

The CRTC contends that this low level of Canadian content, particularly when compared to the 35 % rule on local radio stations, was necessary because unlicenced U. S. receivers were already flooding into the country, so that enforcing a ban on these receivers would be nearly impossible ( see below ).