hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Subset
In mathematics, a set A is a subset of a set B if and only if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment). A is a subset of B may also be expressed as B includes (or contains) A or A is included (or contained) in B. A k-subset is a subset with k elements.

When quantified,  is represented as

One can prove the statement  by applying a proof technique known as the element argument:

Let sets A and B be given. To prove that 
suppose that a is a particular but arbitrarily chosen element of A
show that a is an element of B.

The validity of this technique can be seen as a consequence of universal generalization: the technique shows  for an arbitrarily chosen element c. Universal generalisation then implies  which is equivalent to  as stated above.

Index set
In mathematics, an index set is a set whose members label (or index) members of another set. For instance, if the elements of a set A may be indexed or labeled by means of the elements of a set J, then J is an index set. The indexing consists of a surjective function from J onto A, and the indexed collection is typically called an indexed family, often written as {Aj}j∈J.
Archipelago
An archipelago (/ˌɑːrkəˈpɛləɡoʊ/ ⓘ AR-kə-PEL-ə-goh), sometimes called an island group or island chain, is a chain, cluster, or collection of islands. An archipelago may be in an ocean, a sea, or a smaller body of water. Examples of archipelagos include the Aegean Islands (the origin of the term), the Canadian Arctic Archipelago, the Stockholm Archipelago, the Malay Archipelago (which includes the Indonesian and Philippine Archipelagos), the Lucayan (Bahamian) Archipelago, the Japanese archipelago, and the Hawaiian Archipelago.

Edgeøya
Edgeøya (Norwegian: [ˈɛdʒˌœ͡ʏɑ]), anglicised as Edge Island, is a Norwegian island located in southeast of the Svalbard archipelago; with an area of 5,073 square kilometres (1,960 sq mi), it is the third-largest island in this archipelago.  An Arctic island, it forms part of the Søraust-Svalbard Nature Reserve, home to polar bears and reindeer. An ice field covers its eastern side. The island takes its name from Thomas Edge (died  1624), an English merchant and whaler. It is seldom visited today and development of tourist facilities is forbidden by law because of its nature reserve status.
Alternator
An alternator (or synchronous generator) is an electrical generator that converts mechanical energy to electrical energy in the form of alternating current. For reasons of cost and simplicity, most alternators use a rotating magnetic field with a stationary armature. Occasionally, a linear alternator or a rotating armature with a stationary magnetic field is used. In principle, any AC electrical generator can be called an alternator, but usually, the term refers to small rotating machines driven by automotive and other internal combustion engines.

An alternator that uses a permanent magnet for its magnetic field is called a magneto. Alternators in power stations driven by steam turbines are called turbo-alternators.  Large 50 or 60 Hz three-phase alternators in power plants generate most of the world's electric power, which is distributed by electric power grids.

Engine control unit
An engine control unit (ECU), also called an engine control module (ECM), is a device that controls various subsystems of an internal combustion engine. Systems commonly controlled by an ECU include the fuel injection and ignition systems.

The earliest ECUs (used by aircraft engines in the late 1930s) were mechanical-hydraulic units; however, most 21st-century ECUs operate using digital electronics.
Augsburg University
Augsburg University is a private university in Minneapolis, Minnesota, United States. It is affiliated with the Evangelical Lutheran Church in America. It was founded in 1869 as a Norwegian-American Lutheran seminary known as Augsburg Seminarium. Today, the university enrolls approximately 2,400 undergraduate and 700 graduate students.

Hamline University
Hamline University (/ˈhæmlɪn/ HAM-lin) is a private university in Saint Paul, Minnesota, United States. Founded in 1854, Hamline is the second oldest university in Minnesota, the first coeducational university in the state, and is one of five Associated Colleges of the Twin Cities. The university is named after Bishop Leonidas Lent Hamline of the United Methodist Church. As of 2017, Hamline had 2,117 undergraduate students and 1,668 graduate students.

In 2022, the university attracted widespread criticism after firing an adjunct professor for showing paintings of the Islamic prophet Muhammad in a class on the history of Islamic art.
Stone Gossard
Stone Carpenter Gossard (born July 20, 1966) is an American musician and songwriter who serves as the rhythm guitarist for the rock band Pearl Jam. Along with Jeff Ament, Mike McCready, and Eddie Vedder, he is one of the founding members of the band.

Gossard is also known for his work prior to Pearl Jam with the Seattle-based grunge bands Green River and Mother Love Bone. Gossard was also a member of the bands Temple of the Dog and Brad. In addition to his performing career, he has been active in the music industry as a producer and the owner of a record label and recording studio.  He released his first solo album Bayleaf in 2001; his second, Moonlander, followed in 2013.

Gossard was inducted into the Rock and Roll Hall of Fame as a member of Pearl Jam in 2017.

Skerik
Eric "Skerik" Walton (born November 19, 1964) is an American saxophonist from Seattle, Washington. Performing on the tenor and baritone saxophone, often with electronics and loops, he is a pioneer in a playing style that has been called saxophonics.

He is a founding member of Critters Buggin, Garage a Trois, Ponga, Tuatara, Lorbo and Skerik's Syncopated Taint Septet. He is also an original member of both Les Claypool's Fancy Band and Frog Brigade. Skerik also worked with grunge band Mad Season.
Larsen & Toubro
Larsen & Toubro Limited (L&T) is an Indian multinational conglomerate headquartered in Mumbai. It operates in sectors including industrial technology, heavy industry, engineering, construction, manufacturing, power, information technology, defence, and financial services.

L&T was founded in 1938 in Bombay by Danish engineers Henning Holck-Larsen and Søren Kristian Toubro. As of  31 March 2022, the L&T Group consisted of 93 subsidiaries, 5 associate companies, 27 joint ventures, and 35 joint operations. As of 1 October 2023, S N Subrahmanyan serves as the chairman and managing director of L&T, having succeeded A M Naik.

Vapi high-speed railway station
Vapi high-speed railway station is an under-construction high-speed railway station on the Mumbai–Ahmedabad high-speed rail corridor. This station is located near Chanod Colony, Dungra, Vapi, Gujarat, India. It is the fifth station of the Mumbai–Ahmedabad high-speed rail corridor, after Boisar station and before Bilimora station. The station will have the second depot of the high-speed rail corridor, just north of it near Karvad.
Don Giovanni
Don Giovanni (Italian pronunciation: [ˈdɔn dʒoˈvanni]; K. 527; full title: Il dissoluto punito, ossia il Don Giovanni, literally 'The Rake Punished, or Don Giovanni') is an opera in two acts with music by Wolfgang Amadeus Mozart to an Italian libretto by Lorenzo Da Ponte. Its subject is a centuries-old Spanish legend about a libertine, Don Juan, as told by playwright Tirso de Molina in his 1630 play El burlador de Sevilla y convidado de piedra. It is a dramma giocoso blending comedy, melodrama and supernatural elements (although the composer entered it into his catalogue simply as opera buffa). It was premiered by the Prague Italian opera at the National Theatre (of Bohemia), now called the Estates Theatre, on 29 October 1787. Don Giovanni is regarded as one of the greatest operas of all time and has proved a fruitful subject for commentary in its own right; critic Fiona Maddocks has described it as one of Mozart's "trio of masterpieces with librettos by Da Ponte".

Zar und Zimmermann
Zar und Zimmermann (Tsar and Carpenter) is a comic opera in three acts, music by Albert Lortzing, libretto by the composer after Georg Christian Römer's Der Bürgermeister von Saardam, oder Die zwei Peter, itself based on the French play Le Bourgmestre de Saardam, ou Les deux Pierre by Mélésville, Jean-Toussaint Merle, and Eugène Centiran de Boirie. Ultimately, it goes back to the historical Grand Embassy of Peter the Great. Gaetano Donizetti had set the same story in his 1827 opera Il borgomastro di Saardam.
Whanganui Rugby Football Union
The Whanganui Rugby Football Union (WRFU) is the governing body for rugby union in the Whanganui region of New Zealand. The Whanganui Rugby Football Union was formed in 1888.

The Whanganui team play from Cooks Gardens, Whanganui, and have enjoyed much success on the playing field throughout their history. Although not a First division team they are one of the leading provinces in terms of the number of lower divisional titles won.

Hawke's Bay (National Provincial Championship)
Hawke's Bay (often known as the Hawke's Bay Magpies) are a New Zealand professional rugby union team based in Napier, New Zealand. The union was originally established in 1884, with the National Provincial Championship established in 1976. They now play in the reformed National Provincial Championship competition. They play their home games at McLean Park in Napier in the Hawke's Bay region. The team is affiliated with the Hurricanes Super Rugby franchise. Their home playing colours are black and white.
Richmond, California
Richmond is a city in western Contra Costa County, California, United States. The city was incorporated on August 3, 1905, and has a city council. Located in the San Francisco Bay Area's East Bay region, Richmond borders San Pablo, Albany, El Cerrito and Pinole in addition to the unincorporated communities of North Richmond, Hasford Heights, Kensington, El Sobrante, Bayview-Montalvin Manor, Tara Hills, and East Richmond Heights, and for a short distance San Francisco on Red Rock Island in the San Francisco Bay.

Richmond is one of two cities, the other being San Rafael, that sits on the shores of both San Francisco Bay and San Pablo Bay. Its population was 116,448 as of the 2020 United States census making it the second largest city in the United States named Richmond after Richmond, Virginia.

No Limit Records
No Limit Records is an American record company founded by Master P. The label's albums were distributed by Priority Records, Universal and Koch Records. The label included artists such as Snoop Dogg, Mercedes, Silkk the Shocker, Mystikal, Mia X, Mac, C-Murder, Magic, Romeo Miller, Fiend, Kane & Abel, and Soulja Slim. Anthony Boswell, head of Bout It Bout It Management, served as the vice president of operations as well as head of management for the label.

In the late nineties, No Limit Records enjoyed mainstream success with releases such as Master P's Ghetto D, T.R.U.'s Tru 2 da Game, and Snoop Dogg's Da Game Is to Be Sold, Not to Be Told.

No Limit was known for quickly producing lengthy albums consisting of up to twenty tracks, numerous cameo appearances by the label's other artists, cheap packaging of its CDs in cardboard cases, and garish Pen & Pixel-designed album covers.
Bill Nichols (politician)
William Flynt Nichols (October 16, 1918 – December 13, 1988) was an American politician. A member of the Democratic Party, he served in the United States House of Representatives for Alabama's 4th congressional district from 1967 to 1973 and Alabama's 3rd congressional district from 1973 until his death in 1988.

William L. Dickinson
William Louis Dickinson (June 5, 1925 – March 31, 2008) was an American politician. A member of the Republican Party, Dickinson served in the United States House of Representatives for Alabama's 2nd congressional district from 1965 to 1993.
Maxilla
In vertebrates, the maxilla (pl.: maxillae /mækˈsɪliː/) is the upper fixed (not fixed in Neopterygii) bone of the jaw formed from the fusion of two maxillary bones. In humans, the upper jaw includes the hard palate in the front of the mouth. The two maxillary bones are fused at the intermaxillary suture, forming the anterior nasal spine. This is similar to the mandible (lower jaw), which is also a fusion of two mandibular bones at the mandibular symphysis. The mandible is the movable part of the jaw.

Batrachotomus
Batrachotomus /ˌbætrəˈkɒtoʊməs/ is a genus of prehistoric archosaur. Fossils of this animal have been found in southern Germany and dated from the Ladinian stage of the Middle Triassic period, around 242 to 237 million years ago. Batrachotomus was described by palaeontologist David J. Gower 22 years after its discovery.

The locality where Batrachotomus lived was a swampy region and the name comes from the Greek batrachos/βάτραχος (frog) and tome/τομή (cutting, slicing), which refers to its preying on the large amphibian Mastodonsaurus. In contrast with sprawling reptiles, like crocodiles, this large carnivore was very agile with locomotor superiority due to its erect stance. A remarkable feature seen on its back was a row of paired, flattened bony plates. Batrachotomus was possibly an early relative of Postosuchus, which lived during the dawn of the dinosaurs.
Giles County, Virginia
Giles County is a county located in the U.S. state of Virginia on the West Virginia state line. As of the 2020 census, the population was 16,787. Its county seat is Pearisburg.

Giles County is included in the Blacksburg–Christiansburg metropolitan area.

Giles County is the location of Mountain Lake, one of only two natural fresh water lakes in Virginia. The lake drains into Little Stony Creek, which passes over a waterfall known as The Cascades before reaching the New River.

Augusta County, Virginia
Augusta County is a county in the Shenandoah Valley on the western edge of the Commonwealth of Virginia in the United States. The second-largest county of Virginia by total area, it completely surrounds the independent cities of Staunton and Waynesboro. Its county seat is Staunton, but most of the administrative services have offices in neighboring Verona.

The county was created in 1738 from part of Orange County and was named after Princess Augusta of Saxe-Gotha. It was originally a huge area, but many of its parts were carved out to form other counties and several states until the current borders were finalized in 1790.

As of the 2020 census, the county's population was 77,487. Along with Staunton and Waynesboro, it forms the Staunton–Waynesboro, VA Metropolitan Statistical Area.
Young Vic
The Young Vic Theatre is a performing-arts venue located on The Cut, near the South Bank, in the London Borough of Lambeth, United Kingdom.

The Young Vic was established by Frank Dunlop in 1970. Nadia Fall has been artistic director since 2025, succeeding Kwame Kwei-Armah, and David Lan before him.

Vanessa Kirby
Vanessa Nuala Kirby (born 18 April 1987 or 1988) is an English actress. She rose to international prominence with her portrayal of Princess Margaret in the Netflix drama series The Crown (2016–2017), for which she won the BAFTA for Best Supporting Actress. For her performance in the film Pieces of a Woman (2020), she won the Volpi Cup for Best Actress and received a nomination for the Academy Award for Best Actress.

Kirby made her professional acting debut on stage, with acclaimed performances in the plays All My Sons (2010), A Midsummer Night's Dream (2010), Women Beware Women (2011), Three Sisters (2012), and as Stella Kowalski in A Streetcar Named Desire (2014). She also appeared in the action films Hobbs & Shaw (2019), The Fantastic Four: First Steps (2025), and two Mission: Impossible films (2018–2023). Kirby portrayed Empress Joséphine in the historical drama Napoleon (2023).
Shi'ar
The Shi'ar (/ʃiːˈɑːr/ SHEE-ar) are a fictional species of aliens appearing in American comic books published by Marvel Comics. The Shi'ar empire (or Imperium) is a vast collection of alien species, cultures, and worlds situated close to the Skrull and Kree Empires. The Shi'ar are one of the three main extraterrestrial empires depicted in the Marvel Universe, alongside the Kree and Skrulls.

Ronan the Accuser
Ronan the Accuser is a character appearing in American comic books published by Marvel Comics. Created by writer Stan Lee and artist Jack Kirby, he first appeared in Fantastic Four #65 (August 1967). In his comic book appearances, Ronan is depicted as the Supreme Accuser of the Kree Empire, the militaristic government of the alien Kree, and commonly serves as an adversary of superhero teams such as the Fantastic Four, the Avengers, and the Guardians of the Galaxy. Initially portrayed as a supervillain, the character would later be presented as a more noble and honorable figure. Ronan has even been married to the Inhuman Crystal, a princess of the Inhuman Royal Family.

The character has been substantially adapted from the comics in various media incarnations, including animated television series and video games. Lee Pace portrayed Ronan in the Marvel Cinematic Universe (MCU) films Guardians of the Galaxy (2014) and Captain Marvel (2019).
Waka Tsukiyama
Waka Tsukiyama (月山 和香, Tsukiyama Waka; born January 26, 1992) is an American-born Japanese professional wrestler. She works for World Wonder Ring Stardom, where she a former New Blood Tag Team Champion.

Stardom in Showcase vol.2
Stardom in Showcase vol.2 (ショーケースのスターダムvol.1, Shōkēsu no sutādamu vol. 2) was a professional wrestling event promoted by World Wonder Ring Stardom. It was the second Stardom in Showcase and took place on September 25, 2022, in Tokyo at the Belle Salle Takadanobaba with a limited attendance due in part to the ongoing COVID-19 pandemic at the time.

Six matches were contested at the event, including one on the pre-show. The main event saw the Grim Reaper Army (Nanae Takahashi, Yuna Manase and Yuu) defeat the Rossy Ogawa Bodyguard Army (Syuri and Queen's Quest (Lady C and Utami Hayashishita)) in a Captain's Fall match.
Warrington Wolves
The Warrington Wolves are a professional rugby league club based in Warrington, England. They play home games at the Halliwell Jones Stadium and compete in the Super League, the top tier of British rugby league. 
Warrington are the only British-based club to have played every season in the top flight. They have won the League Championship three times and the Challenge Cup nine times.

The club's traditional home colours are white, primrose and blue. Warrington have local rivalries with Widnes Vikings, St Helens, Wigan Warriors, Salford Red Devils and Leigh Leopards.

2021 Challenge Cup final
The 2021 Challenge Cup Final was the 120th final of the Rugby Football League's Challenge Cup knock-out competition. It took place on 17 July 2021 at Wembley Stadium between the Castleford Tigers and St Helens.
First Merkel cabinet
The First Merkel cabinet (German: Kabinett Merkel I) was the Government of the Federal Republic of Germany from 22 November 2005 to 27 October 2009 throughout the 16th legislative session of the Bundestag. Led by Christian Democrat Angela Merkel, the first female Chancellor in German history, the cabinet was supported by a grand coalition between the Christian Democratic Union (CDU), Christian Social Union of Bavaria (CSU) and the Social Democratic Party (SPD).

It was installed following the 2005 federal election and succeeded the second Schröder cabinet. It ceased to function after the formation of second Merkel cabinet, which was installed after the 2009 federal elections and sworn in on 28 October 2009.

Federal Ministry for Economic Affairs and Energy
The Federal Ministry for Economic Affairs and Energy (German: Bundesministerium für Wirtschaft und Energie, [ˈbʊndəsminɪsˌteːʁiʊm fyːɐ̯ ˈvɪʁt.ʃaft ʔʊnt eneʁˈɡiː]; abbreviated BMWE, formerly BMWi) is a cabinet-level ministry  of the Federal Republic of Germany. It was previously known as the "Ministry of Economy". It was recreated in 2005 as "Ministry of Economics and Technology" after it had previously been merged with other ministries to form the Federal Ministry for Economics and Labour between 2002 and 2005. The ministry is advised by the Council of Advisors on Digital Economy.
New Farakka Junction railway station
New Farakka Junction is a railway station on the Howrah–New Jalpaiguri line and is located in Murshidabad district in the Indian state of West Bengal. New Farakka Junction railway station lies south of the Farakka Barrage.

Malda Town railway station
Malda Town Railway Station is a railway station on the Howrah–New Jalpaiguri line under Malda railway division of Eastern Railway zone. It serves the city of Malda in the Indian state of West Bengal. One of the first two Amrit Bharat Express trains originating from this station towards SMVT Bengaluru station was flagged off on 30 December 2023. It is 89th number railway station out of top 100 railway station of India in terms of revenue.
Music sequencer
A music sequencer (or audio sequencer or simply sequencer) is a device or application software that can record, edit, or play back music, by handling note and performance information in several forms, typically CV/Gate, MIDI, or Open Sound Control, and possibly audio and automation data for digital audio workstations (DAWs) and plug-ins.

Korg M1
The Korg M1 is a synthesizer and music workstation manufactured by the Japanese company Korg from 1988 to 1995. It is one of the bestselling synthesizers in history, selling an estimated 250,000 units, and was widely used in popular music and stock music in the late 1980s and early 1990s. The piano and organ presets were used in 1990s house music, such as the Madonna single "Vogue" and the Robin S single "Show Me Love".
1999–2000 All-Ireland Senior Club Hurling Championship
The 1999–2000 All-Ireland Senior Club Hurling Championship was the 30th staging of the All-Ireland Senior Club Hurling Championship, the Gaelic Athletic Association's premier inter-county club hurling tournament. The championship began on 17 October 1999 and ended on 17 March 2000.

St. Joseph's Doora-Barefield were the defending champions.

On 17 March 2000, Athenry won the championship following a 0–16 to 0–12 defeat of St. Joseph's Doora-Barefield in the All-Ireland final. This was their third All-Ireland title, their first in three championship seasons.

Athenry's Eugene Cloonan was the championship's top scorer with 3–24.

1991–92 All-Ireland Senior Club Hurling Championship
The 1991–92 All-Ireland Senior Club Hurling Championship was the 22nd staging of the All-Ireland Senior Club Hurling Championship, the Gaelic Athletic Association's premier inter-county club hurling tournament. The championship ran from 18 August 1991 to 29 March 1992.

Glenmore were the defending champions, however, they failed to qualify after being beaten by St Martin's in the 1991 Kilkenny SHC semi-finals. Cashel King Cormacs, Lismore and Moorefield made their championship debuts, while Birr returned after a long absence.

The All-Ireland final was played at Semple Stadium in Thurles on 29 March 1992, between Kiltormer of Galway and Birr of Offaly, in what was a first championship meeting between the teams. Kiltormer won the match by 0–15 to 1–08 to claim a first title.

Tommy Grogan, from the Cashel King Cormacs club, was the championship's top scorer with 1–35.