The Proof process is that of testing a firearm for integrity using a severely overcharged cartridge, or Proof load which is fired through the gun in an armoured testing chamber.

Proof: By symmetry, it suffices to prove that there is some constant c such that for all bitstrings s

Generally this is in a very small detail, such as the number of leaves on the ear of corn on the recent US Wisconsin state quarter: File: 2004 WI Proof. png.

From the criterion it also follows that Carmichael numbers are cyclic .< ref > Proof sketch: If is square-free but not cyclic, for two prime factors and of.

* Demonstratio evangelica ( Proof of the Gospel ) is closely connected to the Praeparatio and comprised originally twenty books of which ten have been completely preserved as well as a fragment of the fifteenth.

He famously put the point into dramatic relief with his 1939 essay " Proof of an External World ", in which he gave a common sense argument against scepticism by raising his right hand and saying " Here is one hand ," and then raising his left and saying " And here is another ," then concluding that there are at least two external objects in the world, and therefore that he knows ( by this argument ) that an external world exists.

Proof of second property: since a * b and b * b < sup >− 1 </ sup > are defined, so is a * b * b < sup >− 1 </ sup >=

#* Proof: Then so Thus However, is prime, so or In the former case, hence ( which is a contradiction, as neither 1 nor 0 is prime ) or In the latter case, or If however, which is not prime.

#* Proof: suppose that p is composite, hence can be written with a and Then is prime, but and contradicting statement 1.

#* Proof:, so is a square root of 2 modulo.

* In Hal Clement's short story Proof ( 1942 ), neutronium is the only form of solid matter known to Solarians, the inhabitants of the Sun's interior.

Proof: If there is no possible move, then the lemma is vacuously true ( and the first player loses the normal play game by definition ).

Proof: Let d be the position of the leftmost ( most significant ) nonzero bit in the binary representation of s, and choose k such that the dth bit of x < sub > k </ sub > is also nonzero.

( Proof: either 1 is positive or − 1 is positive.

Proof by contradiction is also known as indirect proof, apagogical argument, proof by assuming the opposite, and reductio ad impossibilem.

* Proof that R is uncountable

Proof: Suppose G = ⟨ H | R ⟩ is a finitely presented, residually finite group.

* Proof of Fermat's Last Theorem is discovered by Andrew Wiles.

Proof: We only give the proof in the simplified case ; the general case is similar.

Proof of Principle or PoP relates to later clinical development, Phase III, typically invoilving larger numbers of patients treated at doses and durations representative of marketed use, and in randomised comparison to placebo and / or existing active drugs.

Proof of this is shown by the diplomatic correspondence from the rulers of Assyria, Mitanni, Babylon, and Hatti which is preserved in the archive of Amarna Letters ; these letters document frequent requests by these rulers for gold and numerous other gifts from the pharaoh.

Discharging these proof obligations is performed using the SPADE Simplifier ( an automated theorem prover ) and the SPADE Proof Checker ( a manual theorem prover, used for those VCs too thorny for the Simplifier to automatically discharge ).

Songs such as " Shatter Proof " and the early short films of Parker and Stone were considered to be a part of the new DVD, but these additions were ultimately rejected.

Echo had originally planned to release " Proof " as a single to promote the second album, but after agreeing on artwork and a track listing ( and commissioning a video featuring Christopher Eccleston, directed by Krishna Stott ), the label shelved these ideas and subsequently issued the single as a download only ( though a few copies were issued in Europe on the PIAS imprint ).

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* Sanjeev Saxena, " A Simple Proof of Bernoulli's Inequality ", viXra: 1205. 0068, May 2012

: Proof: Let A be infinite RE.

* Gödel's Proof ( 2002 revised edition ) by Ernest Nagel and James R. Newman, edited by Hofstadter ( ISBN 0-8147-5816-9 ).

‡ Proof.

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Proof: Suppose that and are two identity elements of.

Proof: Suppose that and are two inverses of an element of.

Proof.

Proof.

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A more successful effort was the Standard Proof for Pythagoras ' Theorem, that replaced the more than 100 incompatible existing proofs.

Proof for the existence of a common Germanic goddess once known as * Fraujon does not exist, but scholars have commented that this may simply be due to lack of evidence.