OpenLLM-France/wikimedia huggingface dataset:
# Mostowski collapse lemma

In mathematical logic, the Mostowski collapse lemma, also known as the Shepherdson–Mostowski collapse, is a theorem of set theory introduced by Andrzej Mostowski (1949, theorem 3) and John Shepherdson (1953).

## Statement

Suppose that R is a binary relation on a class X such that
* R is set-like: R$^{−1}$[x] = {y : y R x} is a set for every x,
* R is well-founded: every nonempty subset S of X contains an R-minimal element (i.e. an element x ∈ S such that R$^{−1}$[x] ∩ S is empty),
* R is extensional: R$^{−1}$[x] ≠ R$^{−1}$[y] for every distinct elements x and y of X
The Mostowski collapse lemma states that for every such R there exists a unique transitive class (possibly proper) whose structure under the membership relation is isomorphic to (X, R), and the isomorphism is unique. The isomorphism maps each element x of X to the set of images of elements y of X such that y R x (Jech 2003:69).

## Generalizations

Every well-founded set-like relation can be embedded into a well-founded set-like extensional relation. This implies the following variant of the Mostowski collapse lemma: every well-founded set-like relation is isomorphic to set-membership on a (non-unique, and not necessarily transitive) class.
A mapping F such that F(x) = {F(y) : y R x} for all x in X can be defined for any well-founded set-like relation R on X by well-founded recursion. It provides a homomorphism of R onto a (non-unique, in general) transitive class. The homomorphism F is an isomorphism if and only if R is extensional.
The well-foundedness assumption of the Mostowski lemma can be alleviated or dropped in non-well-founded set theories. In Boffa's set theory, every set-like extensional relation is isomorphic to set-membership on a (non-unique) transitive class. In set theory with Aczel's anti-foundation axiom, every set-like relation is bisimilar to set-membership on a unique transitive class, hence every bisimulation-minimal set-like relation is isomorphic to a unique transitive class.

## Application

Every set model of ZF is set-like and extensional. If the model is well-founded, then by the Mostowski collapse lemma it is isomorphic to a transitive model of ZF and such a transitive model is unique.
Saying that the membership relation of some model of ZF is well-founded is stronger than saying that the axiom of regularity is true in the model. There exists a model M (assuming the consistency of ZF) whose domain has a subset A with no R-minimal element, but this set A is not a "set in the model" (A is not in the domain of the model, even though all of its members are). More precisely, for no such set A there exists x in M such that A = R$^{−1}$[x]. So M satisfies the axiom of regularity (it is "internally" well-founded) but it is not well-founded and the collapse lemma does not apply to it.
# Rick Gilstrap

Rick Gilstrap is a former American football player and coach. He served as the head football coach at Mars Hill University in Mars Hill, North Carolina from 1983 to 1984 and at Wofford College in Spartanburg, South Carolina from 1985 to 1987, compiling a career college football coaching record of 18–35-2. Gilstrap helped guide Wofford's transition from the National Association of Intercollegiate Athletics (NAIA) to the National Collegiate Athletic Association (NCAA). Gilstrap played college football at Clemson University between 1969 and 1971, starting 18 games at running back or quarterback. He has been married to Kiki Kirkland Gilstrap, Miss USA 1973 Miss Congeniality since 1977, and they are the parents of award-winning, professional soccer goalkeeper and coach, Hunter Gilstrap.

## Head coaching record

| Year | Team | Overall | Conference | Standing |
| Mars Hill Lions (SAC-8) (1983–1984) ||||||
| 1983 | Mars Hill | 4–6–1 | 3–3–1 | 5th |
| 1984 | Mars Hill | 6–5 | 4–3 | 5th |
| Mars Hill: | Mars Hill: | 10–11–1 | 7–6–1 | |
| Wofford Terriers (NAIA Division I independent) (1985–1987) ||||||
| 1985 | Wofford | 3–8 | | |
| 1986 | Wofford | 4–6–1 | | |
| 1987 | Wofford | 1–10 | | |
| Wofford: | Wofford: | 8–24–1 | | |
| Total: | Total: | 18–35–2 | | |
# Rip Off (video game)

Rip Off is a multidirectional shooter with black and white vector graphics written by Tim Skelly and released as an arcade video game by Cinematronics in 1980. It was the first shooter with cooperative gameplay and an early game to exhibit flocking behavior. A port for the Vectrex was published in 1982.
The objective of Rip Off is to prevent computer-controlled enemies from stealing eight canisters at the center of the screen. One or two players control tank-like vehicles while game-controlled "pirate" tanks rush onto the field and attempt to drag the canisters off the edge of the screen. Enemies can be defeated by shooting or colliding with them. The game speed and difficulty increase with each successive wave until all the canisters have been taken ("ripped off").

## Gameplay

One or two players attempt to protect fuel canisters from groups of invading pirate tanks that appear from the edges of the screen. There are six styles of pirate tanks in the game worth 10 to 60 points each. The value of each style is determined by its speed and strategy. Low point value tanks are very slow and generally head directly for the fuel. Higher point tanks are much faster and may work together to lure the player to destruction.
Higher-level pirate tanks are armed with short-range lasers, while player tanks (at all levels) are equipped with a cannon. Invading tanks are destroyed when they are hit by a cannon shot or by a collision with a player's tank. There is no penalty to the player for destroying enemy tanks this way except for the brief period of time he is out of the game. When playing a two-player game, it is not possible to shoot the other player, although you will both be destroyed if your tanks collide.
The game is organized into waves and bonus levels. Two or three enemy tanks attack in each wave. A wave ends when all the pirate tanks have either been destroyed by the players or have dragged a fuel canister off the screen. After a number of waves, the bonus level increases 10, 20 etc. and another round begins, starting with 10-point tanks. Each successive round is slightly faster and harder than the one before it. The bonus level gives additional points for each enemy tank destroyed. The game proceeds this way until all fuel canisters have been "ripped off" by the pirate tanks.

## Legacy

Rip Off was cloned as Bacterion!, published in 1984 as a type-in program for the Atari 8-bit computers.
# Rippershausen

Rippershausen is a municipality in the district Schmalkalden-Meiningen, in Thuringia, Germany.
# Rino Mondellini

Rino Mondellini (1908-1974) was an Italian art director known for his work in the French film industry.

## Selected filmography

* Come Down, Someone Wants You (1951)
* The Night Is My Kingdom (1951)
* Shadow and Light (1951)
* Forbidden Fruit (1952)
* Children of Love (1953)
* Mademoiselle from Paris (1955)
* Trapeze (1956)
* The Lebanese Mission (1956)
* The Adventures of Arsène Lupin (1957)
* Lift to the Scaffold (1958)
* Tabarin (1958)
* Serenade of Texas (1958)
* Ravishing (1960)
* Le Tracassin (1961)
* Fanny (1961)
* The Champagne Murders (1967)
* Two Weeks in September (1967)
* The Young Wolves (1968)
# Rino Salviati

Gastone Tisalvi, best known as Rino Salviati (12 June 1922 – 2 January 2016) was an Italian singer, guitarist and film actor.

## Life and career

Born in Montelibretti, Salviati started his career in 1940, performing in a series of shows for the armed forces. In 1945 he entered the stage company of Erminio Macario, as the musical attraction in the revue Venticello del sud. The same year he started recording several albums for La Voce del Padrone.
After performing with various orchestras, Salviati became well-known as a regular in a popular radio program about guitarists. Starting from the 1950s, he toured all over the world, often alongside Nilla Pizzi. He also appeared in a number of films.

## Selected filmography

* Milanese in Naples (1954)
# Rino Serri

Rino Serri (23 January 1933 – 6 April 2006) was an Italian Communist politician.

## Biography

In the mid-1950s, Serri was in charge of the Reggio Emilia Province in the Italian Communist Youth Federation. In 1957 he entered the Central Committee of the Italian Communist Youth Federation and from 3 October 1960 to 29 October 1962, he was the National Secretary.
From 1963 to 1969 in the PCI he was provincial secretary of Reggio Emilia. From 4 January 1965 to 1970 he was a municipal councilor in Reggio Emilia.
In the seventies he became regional secretary of the PCI in Veneto and in 1979 he entered the Chamber of Deputies. In 1987, he became a Senator and held office until 1992 and then again in 1994 .
He opposed the dissolution of the PCI and February 3, 1991, became one of the founding fathers of Rifondazione Comunista; in 1995 that group became pasrt of the Movement of Unitarian Communists (MCU). In 1998 he joined the Democrats of the Left with the MCU.
In 1996 he became undersecretary for Foreign Affairs of the Prodi I Cabinet. Here he dealt mainly with the countries of the Horn of Africa, In 2000 he was a mediator on behalf of the European Union to reconcile Ethiopia and Eritrea, which would happen with the Algiers Agreement. From 1984 to 1989, he also held the position of national president of the Associazione Ricreativa e Culturale Italiana (ARCI).
# Hassi Delaa

Hassi Delaa is a town and commune in Laghouat Province, Algeria. According to the 1998 census, it has a population of 6,930.
# Hasler Hundred

50°37′03″N 2°07′04″W﻿ / ﻿50.6176°N 2.1178°W﻿ / 50.6176; -2.1178 Hasler Hundred or Hasilor Hundred was a hundred in the county of Dorset, England, containing the following parishes:
* Arne
* Church Knowle
* East Holme
* Kimmeridge
* Steeple
* Tyneham
# Rivière à la Chasse

Rivière à la Chasse may refer to:
* Rivière à la Chasse (Baie-Comeau), a tributary of the Gulf of St. Lawrence in the town of Baie-Comeau, Quebec, Canada
* Rivière à la Chasse (lac Saint-Jean), a tributary of lac Saint-Jean in the Le Domaine-du-Roy Regional County Municipality, Quebec, Canada
# Rita Carvalho

Rita Carvalho is a Portuguese artist who posts online under the username Rita Oak (her last name means "oak" in Portuguese) and has gained notoriety for illustrating NFL player Jimmy Garoppolo.

## Education

Rita Carvalho studied art in high school and in 2021, graduated from the ESAD College of Arts and Design, an art school in Matosinhos, Portugal. Choosing to take a gap year after graduation, Carvalho experimented with different artistic mediums, including digital illustrations.

## Online posts

Brainstorming with her 49ers fan boyfriend, Carvalho decided to create an illustration of Jimmy Garoppolo who at the time was injured and enmeshed in trade rumors. She posted her illustration on Reddit on February 3, 2022, and later said it was the first time she posted her art online. The illustration depicted Garoppolo with hearts and a tag that said "Thank you for everything Jimmy." She said "my first drawing was sort of just a 'Thank You' note showing how grateful we were for everything he did for the team. I was kind of sad to see him go." The post garnered 1,300 upvotes and Carvalho was overwhelmed with the positive response. The following day, she posted another illustration of Garoppolo with the tag "Drawing Jimmy G everyday until he gets traded. Day 2" and continued to post a new one in the days following that, receiving growing praise and attention. She created the drawings using her iPad with a stylus and the graphics editing app Procreate.
Carvalho began to integrate pop culture references: day 7 was Garoppolo on the cover of GQ, day 12 was Valentine's Day themed and on day 18, Garoppolo was depicted as Jimmy "James" Bond. She also started an online shop where fans could purchase her drawings on hoodies, mugs and t-shirts.
Instead of being traded as most predicted, Garoppolo signed a one-year extension with the 49ers on August 29, 2022, which corresponded with day 208 of her series. On day 209, she posted a witty response to the extension rooted in the movie The Wolf of Wall Street with the movie quote "I'm not leaving! The show goes on!" She continued her series until Garoppolo signed with the Las Vegas Raiders in 2023 for a total of 404 daily drawings. The final drawing incorporated a Shawshank Redemption theme and showed Garoppolo kneeling as Andy Dufresne breaking out of prison, shirtless and arms wide open as he's embracing the rain and quotes of praise from his 49ers teammates, coaches and general manager.
Garoppolo has commented on her drawings, saying "I really appreciate it. It's really cool, just the uniqueness to it." 49ers teammate George Kittle also commented on the drawings, saying "she drew me as Cartman, and I thought that was pretty good." Kittle made the depiction of himself in Carvalho's drawing his avatar on Twitter.

## Personal life

She lives in Porto, Portugal and continues to publish her illustrations.
# Rita Chiarelli

Rita Chiarelli is a Canadian blues singer. She was called "the goddess of Canadian blues" by Shelagh Rogers at CBC Radio One.

## Biography

Born and raised in Hamilton, Ontario, Chiarelli began performing in Ronnie Hawkins' band in the early 1980s. She subsequently spent several years in Italy. When she returned to Canada, she quickly attracted the attention of film director Bruce McDonald, who included her "Have You Seen My Shoes?" on the soundtrack to his 1989 film Roadkill. Chiarelli and Colin Linden subsequently recorded a cover of Bob Dylan's "Highway 61 Revisited" for McDonald's 1991 film Highway 61, and Chiarelli released her debut album the following year on Stony Plain Records.
Her albums Just Getting Started and Breakfast at Midnight were both nominated for the Juno Award for Best Blues Album.

## Discography
### Solo

* Road Rockets (1992)
* Just Getting Started (1995)
* What a Night (1997)
* Breakfast at Midnight (2001)
* No One to Blame (2004)
* Cuore: The Italian Sessions (2006)
* Uptown Goes Downtown... Rita Chiarelli with the Thunder Bay Symphony Orchestra (2008)
* Sweet Paradise (2009)
* Music From The Big House Soundtrack (2011)

### Compilation inclusions

* Saturday Night Blues: 20 Years (CBC, 2006)
# Hatata (disambiguation)

Hatata (/hɑːˈtɑːtə/; Ge'ez: ሐተታ ḥätäta "inquiry") is a Ge'ez term describing an investigation and refers to two 17th century ethical and rational philosophical treatises in Ethiopia.
Hatata may also refer to:
* Hatata, island located west of Ambon, Indonesia
* Magdy Hatata (born 1941), Egyptian military officer
* Sherif Hatata (1923–2017), Egyptian doctor, author and communist activist
# Hay knife

A hay knife is an agricultural hand tool: a long-bladed knife which may have large rounded serrations on the edge, or a smooth edge used for sawing off sections at the end of a stack or compact pile of hay or silage. In the south of England hay knives may have smooth edges.
Hay knives are needed as loose hay or silage becomes compacted within a stack: to remove it a hay knife is used to make a vertical cut so that sections can be removed easily as the intertwined stalks are cut. The offset handle allows the user to work down a face. Once one section has been removed the worker starts again at the top creating another section to be removed.
* This agriculture article is a stub. You can help Wikipedia by expanding it.
* v
* t
* e
* This article relating to knives is a stub. You can help Wikipedia by expanding it.
* v
* t
* e
# Rivers State Civil Service Commission

The Rivers State Civil Service Commission is a statutorily constituted executive body authorized to oversee the development and administration of the state's civil service system. It also has power to make appointments, exercise disciplinary control and remove persons holding or acting in offices within the civil service. The Commission is headed by a Chairman, who is appointed by the Governor with the consent of the State House of Assembly.

## Composition

Part II, section 197 (1), of the Constitution of 1999 (Third Schedule) specifies: "A State Civil Service Commission shall comprise the following members -"
* A Chairman
* Not less than two and not more than four other persons, who shall, in the opinion of the Governor, be persons of unquestionable integrity and sound political judgment.
# Rob Paris (producer)

Rob Paris is an American film producer and former talent agent. He began his entertainment career at CAA as a literary agent, then moving to Ed Snider's production company, and finally establishing his own firm, ParisFilm.

## Filmography

* The Maiden Heist (2009)
* Dirty Girl (2010)
* Gambit (2012)
* Everly (2014)
* The Blackcoat's Daughter (2015)
* I Am the Pretty Thing That Lives in the House (2016)
* The Last Laugh (2019)
* Please Baby Please (2022)
# Rob Womack

Robin "Rob" Womack (born 29 May 1971) is a Paralympian track and field athlete from England competing mainly in category F55 throwing events. In 2012 he qualified as a member of the Great Britain team for the 2012 Summer Paralympics in London and took the bronze medal in the shot put.

## Life history

Womack was born in Dewsbury, England in 1971. Womack, a paraplegic after having prolapsed disc in 2003, became involved in athletics during rehabilitation at the spinal unit at Stoke Mandeville. In 2006 Womack qualified for his first major tournament, representing Great Britain the IPC Athletics World Championships, held in Assen in the Netherlands. Despite this he was not selected for the 2008 Summer Paralympics in Beijing, much to Womack's disappointment.
Womack continued to compete throughout 2009, throwing a season's best of 10.66 in the shot put and 26.14 in the discus. His results in 2010 were an improvement on the previous season, and posted a distance of 10.87 in the National Championships in Nottingham. In 2011, Womack was part of the Great Britain team that travelled to Christchurch in New Zealand to compete in the 2011 IPC Athletics World Championships in the shot put. This was the first time Womack had represented Britain in three years, and he responded with a personal best of 10.93, leaving him in 7th place in the F54/55/56 category.
On the 7 July 2012, at a Stoke Mandeville meet, Womack recorded a distance in the shot of 11.01, his personal best and the first time he had thrown competitively over 11 metres. The result was good enough to see Womack selected for the Great Britain team for the 2012 Summer Paralympics in the shot put. In the final he threw a personal best of 11.34m to take the bronze medal.
Womack is married to Debbie, and has three children.
# Road Atlanta Can-Am

The Road Atlanta Can-Am races were Can-Am series sports car races held at Road Atlanta in Braselton, Georgia, from 1970 until 1984.

## Winners

| Date | Driver | Team | Car | Distance/Duration | Race Title | Report |
| 1970 | Tony Dean | A. G. Dean Ltd. | Porsche 908/3 | 300 km (190 mi) | | report |
| 1971 | Peter Revson | McLaren Cars Ltd. | McLaren M8F-Chevrolet | 300 km (190 mi) | | report |
| 1972 | George Follmer | Penske Racing | Porsche 917/10 | 300 km (190 mi) | | report |
| 1973 | George Follmer | Rinzler Motoracing / Royal Crown | Porsche 917/10 | 2 hours | Carling Can-Am | report |
| 1974 | Jackie Oliver | Phoenix Racing Organizations, Inc. | Shadow DN4-Chevrolet | 1 hour | WQXI Can-Am | report |
| 1975-1976 Series not contested |||||||
| 1977 | No race | No race | No race | No race | No race | No race |
| 1978 | Alan Jones | Carl A. Haas Racing Team, Ltd. | Lola T333CS-Chevrolet | 1 hour | Citicorp Can-Am Challenge | report |
| 1979 | Keke Rosberg | Newman-Freeman Racing | Spyder NF-11-Chevrolet | 1 hour | Citicorp Can-Am Challenge | report |
| 1980 | Geoff Brabham | Racing Team V.D.S. | Lola T530-Chevrolet | 125 miles (201 km) | SCCA Citicorp Can-Am | report |
| 1981 | No race | No race | No race | No race | No race | No race |
| 1982 | Al Unser Jr. | Galles Racing | Frissbee-Galles GR2-Chevrolet | 150 miles (240 km) | The G.E. Silicons Grand Prix | report |
| 1983 | No race | No race | No race | No race | No race | No race |
| 1984 | Jim Crawford | RK Racing | March 847-Chevrolet | 1 hour | CRC Chemicals Can-Am Challenge | report |
# Robert Choulet

Robert Choulet (born 28 February 1935) is a French aerodynamics engineer influential in race car dynamics.

## Career

A disciple of aerodynamics pioneer Charles Deutsch, Choulet worked for Deutsch's Société d'Études et de Réalisations Automobiles (SERA-CD ) from 1963 to 1967. During this period, he worked on the aerodynamics of the CD cars.
He then joined Matra in 1968. One of his first projects was the Matra M640 Le Mans 24 Hours car. Following that, he returned to SERA-CD and was involved in designing the famous Porsche 917 especially the LH version, and the Can-Am cars that followed. He later was influential in designing the Alfa Romeo 33TT12.
From 1976 to 1980, Choulet worked with the Ligier Formula One team, being involved in the design of the JS5, JS7, JS9, JS11 and JS11/15 models.
SERA and Choulet also worked with the Alfa Romeo sports car team in 1977 and on Alfa's Formula One car in 1979.
Choulet created the Aérodyne company in 1983 working on such different cars as Formula Ford Rondeau and Audi Quattro for rally racing. He then worked for many years for Peugeot. He was also influential in the Group C Peugeot 905 programme (notably the Ev1bis and Ev 2 "Supercopter" with radical aerodynamic solutions) as well as for Jordan Formula One team and the rally cars Peugeot 206 and Citroën Xsara WRC.
In the 2000s, he became involved with Panasonic Toyota Racing and has been a consultant for Toyota Motorsport GmbH (TMG) in Cologne since 2011.

## Education

* Lycée du Parc
* Ecole centrale Paris in 1959
* IFP School - Ecole Nationale Supérieure du Pétrole et des Moteurs (Major : Engines) in 1960.

## Distinctions

* Joseph Béthenod Prize
* Society of Automotive Engineers : Massion Award (1987)

## Others

* Membership : SIA (Society of Automotive Engineers)
* Auto Hebdo n° 229, 21 August 1980
# Robert Christie

Robert or Bob Christie may refer to:
* Robert Christie (actor) (1913–1996), Canadian actor and director
* Robert Christie (footballer) (1865–1918), Scottish football (soccer) player
* Robert Christie (Ontario politician), member of the Ontario provincial parliament, 1867–1874
* Robert Christie (Lower Canada politician) (1787–1856), historian and political figure from the Gaspé region of Quebec
* Robert Christie Jr. (1824–1875), New York politician
* Robert Christie (cricketer) (1942–2012), English cricketer
* Bob Christie (announcer), Scottish TV and radio announcer
* Bob Christie (film director), Canadian documentary film director
* Bob Christie (politician) (1925–2020), former Australian politician
* Bob Christie (racing driver) (1924–2009), American racecar driver
# Rob de Wit

Rob de Wit may refer to:
* Robert de Wit (born 1962), Dutch Olympic decathlete and bobsledder
* Rob de Wit (footballer) (born 1963), Dutch footballer
# Robert Beasley (burgess)

Robert Beasley was a member of the Virginia House of Burgesses, the elected lower house of the colonial Virginia General Assembly, from Isle of Wight County, in 1655 and 1656.
Upon the petition of Beasley and the other burgesses from Isle of Wight County (Major John Bond and Nicholas Smith), a Commission was established which resulted in Ragged Island and Terascoe Neck being transferred from Nansemond County (then Upper Norfolk County) to Isle of Wight County in 1656.
A descendant of Robert Beasley, Dr. Robert Sanford Beazley (1821–1910), was a member of the Virginia State Convention of 1867–1868, which adopted the Underwood Constitution following the American Civil War. Dr. Beazley also served as a Virginia state senator from Albemarle County and Greene County for four years in 1874–1877.
# Robert Beasley

Robert Noble Beasley was an English cricketer active from 1907 to 1911 who played for Northamptonshire. He was born in Dallington, Northampton on 17 December 1882 and died in Northampton on 21 January 1966. Beasley appeared in ten first-class matches as a righthanded batsman. He scored 109 runs with a highest score of 28.