Whatever the fortunes of the rites in the meantime, in the last decade of the 5th century they prompted Pope Gelasius I's taunt to the senators who were intent on preserving them: " If you assert that this rite has salutary force, celebrate it yourselves in the ancestral fashion ; run nude yourselves that you may properly carry out the mockery.

A kind of converse of this theorem was proved by Anne C. Davis: If every order preserving function f: L → L on a lattice L has a fixed point, then L is a complete lattice.

If the track rod is placed ahead of the axle, it should instead be longer in comparison, thus preserving this same " toe out ".

If built properly they can create a region of null time in the burial chamber, preserving the body of the Pharaoh forever.

If time capsules have a museum-like goal of preserving the culture of a particular time and place for study, they fulfill this goal very poorly in that they, by definition, are kept sealed for a particular length of time.

If and are complete, and both and are continuous functors, then the comma category is also complete, and the projection functors and are limit preserving.

If F is an ordered field ( not just orderable, but a definite ordering is fixed as part of the structure ), the Artin – Schreier theorem states that F has an algebraic extension, called the real closure K of F, such that K is a real closed field whose ordering is an extension of the given ordering on F, and is unique up to a unique isomorphism of fields ( note that every ring homomorphism between real closed fields automatically is order preserving, because x ≤ y if and only if ∃ z y = x + z < sup > 2 </ sup >).

If all bidders in Vickrey auction reveal their valuations to each other, they can lower some or all of their valuations, while preserving who wins the auction.

If this be done, the nations of the world will no longer require any armaments, except for the purpose of preserving the security of their realms and of maintaining internal order within their territories.

If members of overpopulous species, such as deer, ought to be “ culled ” or “ harvested ,” in the name of preserving the integrity, stability, and beauty of the biotic community, and if staggeringly overpopulous Homo sapiens is also but “ a plain member and citizen ” of the biotic community, then why should culling and harvesting humans be any less obligatory?

If we are to regard as a glorious and a hallowed reward the civic crown, presented for preserving the life of a single citizen, and him, perhaps, of the very humblest rank, what, pray, ought to be thought of a whole army being saved, and indebted for its preservation to the valour of a single individual?

If A is a metric space and B its completion then any isometry from A to a complete metric space C can be extended to a unique isometry from B to C. The analogous statement for complete Boolean algebras is not true: a homomorphism from a Boolean algebra A to a complete Boolean algebra C cannot necessarily be extended to a ( supremum preserving ) homomorphism of complete Boolean algebras from the completion B of A to C. ( By Sikorski's extension theorem it can be extended to a homomorphism of Boolean algebras from B to C, but this will not in general be a homomorphism of complete Boolean algebras ; in other words, it need not preserve suprema.

If his circumspection in regard to Philip's sensibilities went so far that he even refused to grant a dispensation for the marriage of Amadee's daughter, Agnes, to the son of the dauphin of Vienne -- a truly peacemaking move according to thirteenth-century ideas, for Savoy and Dauphine were as usual fighting on opposite sides -- for fear that he might seem to be favoring the anti-French coalition, he would certainly never take the far more drastic step of ordering the return of Gascony to Edward, even though, as he admitted to the English ambassadors, he had been advised that the original cession was invalid.

If we are to believe the list of titles printed in Malraux's latest book, La Metamorphose Des Dieux, Vol. 1 ( ( 1957 ), he is still engaged in writing a large novel under his original title.

If the original word was capitalised, then the first letter of its abbreviation should retain the capital, for example Lev.

If Acorn had thought to include this small modification in the original Electron design it is likely the machine would have had a much greater impact as it would have nearly doubled the amount of motion possible in games and saved modes 0 – 3 ( including the only 16 colour mode ) from being nearly useless due to contended memory timings.

* Split ( only available as first decision of a hand ): If the first two cards have the same value, the player can split them into two hands, by moving a second bet equal to the first into an area outside the betting box of the original bet.

If all four players pass in the first round, the deal is not played ; in rubber bridge the deal is not scored and the hand is redealt by the original dealer, while in duplicate the score is recorded as zero for each pair and returned to the board.

If you admired a necklace worn by Bette Davis in The Private Lives of Elizabeth and Essex, you could buy a copy from Joseff of Hollywood, who made the original.

If later characters are stereotypes, it's because they are from the same original mould.

If the original penalty yardage would have resulted in a first down or moving the ball past the goal line, a first down is awarded.

To make a figure larger or smaller is equivalent to multiplying the Cartesian coordinates of every point by the same positive number m. If ( x, y ) are the coordinates of a point on the original figure, the corresponding point on the scaled figure has coordinates

If the earlier completion procedure is applied to a normed vector space, the result is a Banach space containing the original space as a dense subspace, and if it is applied to an inner product space, the result is a Hilbert space containing the original space as a dense subspace.

If Wisda's Landscaping breaks the contract, and Neal Townsend is forced to hire another service for $ 60 an hour, expectation ( direct ) damages paid to Neal Townsend would equal $ 100 ($ 10 an hour, the difference in price between the original contract and the new contract ).

To avoid debates about the possibility of in-vitro fertilization, artificial insemination, or cloning, the original Darwin Awards book applied the following " deserted island " test to potential winners: If the person were unable to reproduce when stranded on a deserted island with a fertile member of the opposite sex, he or she would be considered sterile.

If the polar reciprocal of the canonical form in the sphere is congruent to the original, then the figure is self-dual.

If an aftershock is larger than the main shock, the aftershock is redesignated as the main shock and the original main shock is redesignated as a foreshock.

If this triangulated graph is colorable using four colors or less, so is the original graph since the same coloring is valid if edges are removed.

If we study the Four Noble Truths with the help of these references and explanations, we get a fairly good and accurate account of the essential teachings of the Buddha according to the original texts.

If, supposing it turns out that the original Ship of Theseus, S1, was actually stolen property, and the rightful owner demands its return, should the police give him S2 or S3?

If a compression scheme is lossless — that is, you can always recover the entire original message by uncompressing — then a compressed message has the same quantity of information as the original, but communicated in fewer bits.

If any other person has put in the eye and eyebrow of a face, I can perceive whose work the original face is, and who has painted the eye and eyebrow.

If Joe answers Jim, saying " That may be true for you, but it is not true for me ," he has given an answer which is fallacious as well as being somewhat meaningless in the context of Jim's original statement.

It features the band members ' favorite original songs plus three new tracks, " If I Die Tomorrow ", " Sick Love Song " ( co-written by Sixx and James Michael ), and a cover of The Rolling Stones ' classic " Street Fighting Man ".

If a concessionaire runs the cafeteria, keep an eye out for quality and price.

If he foresaw any problem because of the quality of the hymen, it was recommended that simple procedures be undertaken at once to incise the hymen or, preferably, to dilate it.

If the sound of the word is emphasized during the encoding process, the cue that should be used should also put emphasis on the phonetic quality of the word.

If some specific deductive system of first-order logic is sound and complete, then is it " perfect " ( a formula is provable iff it is a semantic consequence of the axioms ), thus equivalent to any other deductive system with the same quality ( any proof in one system can be converted into the other ).

If readers and viewers have a priori views on the current state of affairs and are uncertain about the quality of the information about it being provided by media outlets, then the latter have an incentive to slant stories towards their customers ' prior beliefs, in order to build and keep a reputation for high-quality journalism.

If a customer offers a top quality, brand-name valuable at too low a price the pawnbroker may turn down the offer, because this suggests that the item may either be counterfeit or stolen.

If there are too many low-value, poor quality items, such as old toasters, scratched-up 20 year-old TVs, and worn-out sports gear piled into cardboard boxes, the store may begin to look more like a rummage sale or flea market.

If the original specification does not reflect the correct quality requirements, quality cannot be inspected or manufactured into the product.

If a quality assurance program is in force, customers and program compliance efforts can also directly influence the calibration approach.

If it is compromised, it affects the quality of life of someone with CF, and their ability to complete such tasks as everyday chores.

If one spoke in the lingua or sermo Latinus one merely spoke Latin, but if one spoke latine or latinius (" more Latinish ") one spoke good Latin, and formal Latin had latinitas, the quality of good Latin, about it.

If the quality of rule became questionable because of repeated natural disasters such as flood or famine, or for other reasons, then rebellion was justified.

If an HMO only contracts with providers meeting certain quality criteria and advertises this to its members, a court may be more likely to find that the HMO is responsible, just as hospitals can be liable for negligence in selecting physicians.

If images are not gamma encoded, they allocate too many bits or too much bandwidth to highlights that humans cannot differentiate, and too few bits / bandwidth to shadow values that humans are sensitive to and would require more bits / bandwidth to maintain the same visual quality.

If the publisher accepts unsolicited manuscripts, then the manuscript is placed in the slush pile, which publisher's readers sift through to identify manuscripts of sufficient quality or revenue potential to be referred to acquisitions editors for review.

If a high level quality control protocol is used, the accuracy can be further improved.

If the product is of high quality it is known as " gentle " cork, and, ideally, is used to make stoppers for wine and champagne bottles.

If a comparison visualizes an action, state, quality, object, or a person by means of a parallel which is drawn to a different entity, the two things which are being compared do not necessarily have to be identical.

If the Party chose, all its people could live in luxury, but they instead choose to lower the quality of living: It is important that the lower classes remain stupefied by poverty and the struggle for mere survival ; if they were to become too comfortable, they might learn to think for themselves and rebel against the Party.

If present, they simply add visual appeal and are no indication of the quality of the tea.

If an office worker with scoliosis can sit for longer periods, increased work output is likely to occur and could improve quality of life.

The foundation of the Royal Exchange is the background of Thomas Heywood's play: If You Know Not Me, You Know Nobody part 2, in which a Lord extols the quality of the building when asked if he has ever seen " a goodlier frame ":

If the edge-emitter does not work, whether due to bad contacts or poor material growth quality, the production time and the processing materials have been wasted.