The ownership and purchase of firearms requires a specific reason: if one wants to have a gun for hunting or target shooting, a person must obtain a proof of their membership in a shooting sports organization.

The latter requires a proof of rain, whereas the former merely requires a proof that rain would not be contradictory.

This crime requires an extra level of satisfactory proof, as prosecutors must show not only that perjury occurred, but also that the defendant positively induced said perjury.

In most legal proceedings, one party has a burden of proof, which requires it to present prima facie evidence for all of the essential facts in its case.

One of the Millennium Prize Problems announced by the Clay Mathematics Institute requires a claimant to produce such a proof.

The more severe penalties available in criminal law also means that it requires a higher burden of proof to be discharged than the related tort.

Under a no-fault divorce system, divorce requires no allegation or proof of fault of either party.

The fallacy of petitio principii, or " begging the question ", is committed " when a proposition which requires proof is assumed without proof ", or more generally denotes when an assumption is used, " in some form of the very proposition to be proved, as a premise from which to deduce it ".

In the United Kingdom and countries such as Malaysia and Singapore, informed consent in medical procedures requires proof as to the standard of care to be expected as a recognised standard of acceptable professional practice ( the Bolam Test ), that is, what risks would a medical professional usually disclose in the circumstances ( see Loss of right in English law ).

For many natural P-complete graph problems, where the graph is expressed in a natural representation such as an adjacency matrix, solving the same problem on a succinct circuit representation is EXPTIME-complete, because the input is exponentially smaller ; but this requires nontrivial proof, since succinct circuits can only describe a subclass of graphs.

According to Quebec law, Montreuil could not change her record of sex because this requires proof of a completed sex reassignment surgery, which she has not had.

Gödel's original statement and proof of the incompleteness theorem requires the assumption that the theory is not just consistent but ω-consistent.

J. Barkley Rosser ( 1936 ) strengthened the incompleteness theorem by finding a variation of the proof ( Rosser's trick ) that only requires the theory to be consistent, rather than ω-consistent.

Another proposed scheme is DHAES, whose proof requires an assumption that is weaker than the DDH assumption.

The section requires proof that the announcement is both provably false, and has actual or likely market impact.

In this standard, a greater degree of believability must be met than the common standard of proof in civil actions, " Preponderance of the Evidence ", which requires that the facts as a threshold be more likely than not to prove the issue for which they are asserted.

This falls out of the fact that is an equivalence relation and also requires a proof that ( 1 ) and ( 2 ) are independent of the choice of class representatives.

A Consistency proof requires ( i ) an axiomatic system ( ii ) a demonstration that it is not the case that both the formula p and its negation ~ p can derived in the system.

Theophrastus introduced his Physics with the proof that all natural existence, being corporeal and composite, requires principles, and first and foremost, motion, as the basis of all change.

It is submitted to the state by an auto insurance company to serve as proof that a driver has the minimum liability insurance that the states requires. SR-22s are typically filed with the respective State's DMV, and in some States must be carried by the licensed driver, or in the registered vehicle ( particularly if the licensee has been cited for coverage lapses, DUI or other administrative infractions ).

Whether you experienced the passion of desire I have, of course, no way of knowing, nor indeed have I wished with even the most fleeting fragment of a wish to know, for the fact that one constitutes by one's mere existence so to speak the proof of some sort of passion makes any speculation upon this part of one's parents' experience more immodest, more scandalizing, more deeply unwelcome than an obscenity from a stranger.

As proof of devotion to his family, Caligula arranged the most distinguished soldiers available to carry the urns of his mother and two brothers in two biers at noon in Rome, when the streets were at their busiest, to the Mausoleum of Augustus.

Among his major accomplishments were the 1940 proof, of the Riemann hypothesis for zeta-functions of curves over finite fields, and his subsequent laying of proper foundations for algebraic geometry to support that result ( from 1942 to 1946, most intensively ).

And a single programmer could do most or all of the computer programming needed to generate the proof of concept to launch a new " killer " application.

That he did represent the genius of the average is the most convincing proof of his strength.

Sometimes Excalibur and the Sword in the Stone ( the proof of Arthur's lineage ) are said to be the same weapon, but in most versions they are considered separate.

The most famous contribution of this manuscript was a novel proof that there is no quintic formula-that is, fifth and higher degree equations that are not solvable by radicals.

This theorem by Henkin is the most directly obtained version of the completeness theorem in its simplest proof.

A proof from Euclid | Euclid's Euclid's Elements | Elements, widely considered the most influential textbook of all time.

Irenaeus pointed to Scripture as a proof of orthodox Christianity against heresies, classifying as Scripture not only the Old Testament but most of the books now known as the New Testament, while excluding many works, a large number by Gnostics, that flourished in the 2nd century and claimed scriptural authority.

While it is one of the most commonly used concepts in logic it must not be mistaken for a logical law ; rather, it is one of the accepted mechanisms for the construction of deductive proofs that includes the " rule of definition " and the " rule of substitution " Modus ponens allows one to eliminate a conditional statement from a logical proof or argument ( the antecedents ) and thereby not carry these antecedents forward in an ever-lengthening string of symbols ; for this reason modus ponens is sometimes called the rule of detachment.

Paul Joseph Cohen ( April 2, 1934 — March 23, 2007 ) was an American mathematician best known for his proof of the independence of the continuum hypothesis and the axiom of choice from Zermelo – Fraenkel set theory, the most widely accepted axiomatization of set theory.

The second part of the 1st Critique is Kant ’ s examination of the rationalist claims to absolute knowledge, taking on the most famous of these, the ontological proof of God ’ s existence, and showing that he can, through pure, non-experiential logic, both prove the affirmative and the negative of a proposition about a “ noumenal object ” ( i. e. an object like “ God ” which can never be an object of direct experience for a contingent being ).

However, analysis of thousands of high-quality games ( most of them computer-generated ) appears to lead to a reliable conclusion ( pending actual proof if true ) that, on the standard 8-by-8 board, perfect play on both sides results in a draw.

The transcendence of π allowed the proof of the impossibility of several ancient geometric constructions involving compass and straightedge, including the most famous one, squaring the circle.

This term sometimes connotes a statement with a simple proof, while the term theorem is usually reserved for the most important results or those with long or difficult proofs.

Wherefore the King, by most cogent proof, shows him that the blame rests not with him, but with the knight's own evil fortune ; after which, he bestows upon him a noble gift.

Tequila is most often made at a 38 – 40 % alcohol content ( 76 – 80 proof ), but can be produced between 31 – 55 % alcohol content ( 70 – 110 proof ).

As a further proof, Dumézil cites the story of Tullus Hostilius ( the most belligerent of the Roman kings ), who was killed by Juppiter with a lightning bolt ( indicating that he did not enjoy the god's favour ).

His findings led him to oppose contemporary Darwinists, most notably Francis Galton and Karl Pearson, who held the occurrence of normal distributed trait variation in populations as proof of gradual genetic variation on which selection could act.

Given an object X, a functor G ( taking for simplicity the first functor to be the identity ) and an isomorphism proof of unnaturality is most easily shown by giving an automorphism that does not commute with this isomorphism ( so ).

The most decisive proof of the absurdity of the indiscriminate use of any strong manure was obtained at Bingen, a town on the Rhine, where the produce and development of vines were highly increased by manuring them with animal matters such as shavings of horn.

Many different types of glue held these sections together most commonly Irish glue and bone glue until hilton glue or cement glue was introduced because of its water proof qualities.