Question: Are Dafne and Dido and Aeneas both compositions made for the opera?

Context paragraphs:
Didon (Piccinni): Didon ("Dido") is a tragédie lyrique in three acts by the composer Niccolò Piccinni with a French-language libretto by Jean-François Marmontel.  The opera is based on the story of Dido and Aeneas from Virgil's "Aeneid" as well as Metastasio's libretto "Didone abbandonata" (which Piccinni himself had set in 1770).  "Didon" was first performed at Fontainebleau on 16 October 1783 in the presence of the French sovereigns, Louis XVI and Marie Antoinette.  After being remounted at court twice, the opera had its Paris public premiere on 1 December 1783.  It proved to be the composer's greatest success and was billed almost every year till 1826, enjoying a total of 250 performances al the Paris Opera.  "Didon" had some influence on Berlioz's opera on the same theme, "Les troyens".

Noémi Rime: Noémi Rime is a French soprano.  She regularly appears in opera productions by William Christie's Les Arts Florissants ensemble.  Her roles have included Cleone in "Médée", Dido in "Dido and Aeneas", and Fatime in "Les Indes galantes".  She currently teaches on the faculty of the Conservatoire à rayonnement régional de Poitiers.

Dafne (Opitz-Schütz): Die Dafne (1627) to a libretto by Martin Opitz (which survives), and music by Heinrich Schütz (which is lost), has traditionally been regarded as the first German opera, though it has also been proposed more recently that it was in fact a spoken drama with inserted song and ballet numbers.

Dido, Queen of Carthage (opera): Dido, Queen of Carthage was an opera in three acts by Stephen Storace.  Its English libretto by Prince Hoare was adapted from Metastasio's 1724 libretto, "Didone abbandonata" ("Dido Abandoned"), which had been set by many composers.  Storace's opera premiered on 23 May 1792 at The King's Theatre in London combined with a performance of his masque, "Neptune's Prophecy".  The story is based on that of Dido and Aeneas in the fourth book of Virgil's "Aeneid".  The opera was not a success and was never revived after its original run of performances.  The score has been lost.

Dido, Queen of Carthage (play): Dido, Queen of Carthage is a short play written by the English playwright Christopher Marlowe, with possible contributions by Thomas Nashe.  The story of the play focuses on the classical figure of Dido, the Queen of Carthage.  It tells an intense dramatic tale of Dido and her fanatical love for Aeneas (induced by Cupid), Aeneas' betrayal of her and her eventual suicide on his departure for Italy.  The playwrights depended upon Books 1, 2, and 4 of Virgil's "Aeneid" as their main source.

Didone abbandonata (Sarro): Didone abbandonata ("Dido Abandoned") is an opera in three acts composed by Domenico Sarro to a libretto by Pietro Metastasio, which was based on the story of Dido and Aeneas from the fourth book of Virgil's "Aeneid".  The opera premiered on 1 February 1724 at the Teatro San Bartolomeo in Naples.

Dido and Aeneas: Dido and Aeneas (Z. 626) is an opera in a prologue and three acts, written by the English Baroque composer Henry Purcell with a libretto by Nahum Tate.  The dates of the composition and first performance of the opera are uncertain.  It was composed no later than July 1688, and had been performed at Josias Priest's girls' school in London by the end of 1689.  Some scholars argue for a date of composition as early as 1683.  The story is based on Book IV of Virgil's "Aeneid".  It recounts the love of Dido, Queen of Carthage, for the Trojan hero Aeneas, and her despair when he abandons her.  A monumental work in Baroque opera, "Dido and Aeneas" is remembered as one of Purcell's foremost theatrical works.  It was also Purcell's only true opera, as well as his only all-sung dramatic work.  One of the earliest known English operas, it owes much to John Blow's "Venus and Adonis", both in structure and in overall effect.  The influence of Cavalli's opera "Didone" is also apparent.

Didone abbandonata (Albinoni): Didone abbandonata ("Dido Abandoned") was an opera in three acts composed by Tomaso Albinoni.  Albinoni's music (now lost) was set to Pietro Metastasio's libretto, "Didone abbandonata", which was in turn based on the story of Dido and Aeneas from the fourth book of Virgil's "Aeneid".  The opera premiered on 26 December 1724 at the Teatro San Cassiano in Venice and was the first time that an opera based on a Metastasio libretto was performed in Venice.

Dido's Lament: Dido's Lament is the aria "When I am laid in earth" from the opera "Dido and Aeneas" by Henry Purcell (libretto by Nahum Tate).

Didone (opera): The plot is based on Virgil's "Aeneid" (Book 4 in particular), though Busenello, in his second libretto for Cavalli, replaces Dido's tragic suicide of Virgil with a happy ending in which Dido marries Iarbas, King of the Getuli, who saves Dido from herself after Aeneas abandons her.  The action is divided into a prologue and 3 acts.

Supporting paragraphs: Dafne (Opitz-Schütz) Dido and Aeneas
Answer: yes