::< ref > Proof: Apply the rank-nullity theorem to the inequality:

Sketch of Proof: Apply the structure theorem for finitely generated modules over a principal ideal domain to V, viewing it as an F-module.

: Proof: Apply Statement 2 to M / N.

#* Proof: If q divides 2 < sup > p </ sup > − 1 then 2 < sup > p </ sup > ≡ 1 ( mod q ).

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

Proof: Notice that the nim-sum (⊕) obeys the usual associative and commutative laws of addition (+), and also satisfies an additional property, x ⊕ x = 0 ( technically speaking, the nonnegative integers under ⊕ form an Abelian group of exponent 2 ).

Proof: Since p is a prime number the only possible values of gcd ( p < sup > k </ sup >, m ) are 1, p, p < sup > 2 </ sup >, ..., p < sup > k </ sup >, and the only way for gcd ( p < sup > k </ sup >, m ) to not equal 1 is for m to be a multiple of p. The multiples of p that are less than or equal to p < sup > k </ sup > are p, 2p, 3p, ..., p < sup > k − 1 </ sup > p = p < sup > k </ sup >, and there are p < sup > k − 1 </ sup > of them.

Proof of Lemma 2:

#" 80 Proof Bottle of Tear Stopper " ( Darryl Staedtler ) – 2: 12

* Proof Thro ' the Night ( December 25, 1942 – January 2, 1943 )

Proof: It is straightforward to prove that ∇ satisfies the Leibniz identity and is C < sup >∞</ sup >( S < sup > 2 </ sup >) linear in the first variable.

Proof: Using the same sum for R ( p, n ) as in Lemma 2, we see that since p < sup > 2 </ sup > > 2n, in fact only the first term is nonzero ; this term is exactly the right-hand side of the above equation.

; Loveline, which Adam hosted ; as well as contributing the song " This Photograph Is Proof ( I Know You Know )" to the soundtrack for Spider-Man 2.

The sixth century Digest of Justinian ( 22. 3. 2 ) provides, as a general rule of evidence: Ei incumbit probatio qui dicit, non qui negat " Proof lies on him who asserts, not on him who denies ".

** Application Note Implementing Proofing, SoftProofing and Proof Approval in JDF 1. 2

D12, in turn, responded with the song " Instigator ", dissing Natas, while Proof made 2 diss tracks aimed specifically at Esham, " Every Sucker Has A Moment " and " Uh Huh ", though the latter was not released.

* 2 Proof of Facts 2nd 365 et seq ( child abuse )

* In episode # 2. 15 of CSI: Crime Scene Investigation entitled " Burden of Proof " a murder victim's body is dumped at the Body Farm among other bodies.

#" 80 Proof Bottle of Tear Stopper " ( Staedtler ) – 2: 15

Proof of ( 1 ) and ( 2 ): One has from Fermat's little theorem,

DeShaun Dupree Holton ( October 2, 1973 – April 11, 2006 ), better known by his stage name Proof, was an American rapper and actor from Detroit, Michigan.

Woodford Reserve's alcohol concentration is 45. 2 % alcohol by volume ( 90. 4 US Proof ).

Proof: If we have a description in, we can convert it into a description in our optimal language by first describing as a computer program ( part 1 ), and then using the original description as input to that program ( part 2 ).

*" Makube Rock " in Black Jack online Flash animation episode 9-2001 / 2 ( retelling of Print Proof )

The single, " Grip Like a Vice ", was released on 2 July 2007, and the new album, called Proof of Youth, was released on 10 September in the UK and a day later in the US.

* Proof Coin: 1. the sample coins provided by the mint 2. Effect attained on high quality die stuck coins by high pressure and multiple strikes producing mirror finish background with satin finish relief areas.

Tentative Proof: If the underlying Hilbert space is finite-dimensional, the spectral theorem says that N is of the form

Most of the games played at tournaments are available from Wff ' N Proof Learning Games.

WFF ' N Proof is a board and cube game that was created by Professor Layman Allen in 1961 to teach the basics of symbolic logic.

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

* A Proof of the Queueing Formula L = λ W, Sigman, K., Columbia University

Proof: Take parameter r =

* M. Huemer: A Proof of Free Will

* Imagination and Proof: Selected Essays of A. M. Hocart ( 1987 ) editor Rodney Needham

* Lovell, M., 2008, A Simple Proof of the FWL ( Frisch, Waugh, Lovell ) Theorem, Journal of Economic Education.

A. Rogers ", 100 Amazing Facts About the Negro, With Complete Proof: A Shortcut to the World History of the Negro ( St. Petersburg, Florida: Helga M. Rogers, Publisher, 1995 ).

* Proof ( TV series ), an Irish TV drama / thriller

* Proof, 1980 B / W student film by Black-and-white, expanded to Fandango

* Tobias Nipkow, Lawrence C. Paulson, Markus Wenzel: Isabelle / HOL-A Proof Assistant for Higher-Order Logic

* Revealing the Universe: Prediction and Proof in Astronomy / edited by James Cornell and Alan P. Lightman.

* Proof of Concept: How to create a live CD / DVD from your HDD Installation

# redirect Proof that 22 / 7 exceeds π

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.

She co-starred with former Rent alum Tracie Thoms in the Quentin Tarantino throwback movie Death Proof in 2007, part of the Tarantino / Robert Rodriguez double feature Grind House.

# redirect Proof that 22 / 7 exceeds π

# redirect Proof that 22 / 7 exceeds π

Frigidaire Imperial " Frost Proof " model FPI-16BC-63, top refrigerator / bottom freezer with brushed chrome door finish made by Frigidaire | General Motors Canada in 1963

* Online Notes / Proof by Paul Dawkins, Lamar University.

The basic software has such features as support for multi-branch operations, integrated interface for emailing and faxing ( using VsiFax ), customer calling queue ( troubletickets ), and several add-ons are available for an employee punch-clock, RF warehousing, Digital Imaging, Proof of Delivery / Signature Capture, and many others.

* http :// www. uscourts. gov / uscourts / RulesAndPolicies / rules / BK_Forms_Current / B_010. pdf Proof of claim form published by the US Department of Justice for use by creditors in bankruptcy cases

* Proof of the Man ( Ningen no Shomei ) ( Fuji TV / 2004 )

*" Rock " in Black Jack / Finger-1974 ( sealed-rewritten as " Print Proof " 1978 )

# REDIRECT Proof that 22 / 7 exceeds π

1 ) Bullet Proof Vest: Dragon Skin: http :// www. 2100science. com / Videos / Bullet_Proof_Vest_Dragon_Skin. aspx