Kyoshiro to Towa no Sora revolves around the life of Kuu Shiratori, a seemingly normal high school girl who enjoys her school life in the giant city Academia, which is thought of as a symbol of recovery for humanity since already ten years have passed since the greatest disaster mankind had ever seen, occurred. Kuu has recently been having a recurring dream where a prince meets her and takes her away. One day, while all the students at her school are preparing for the upcoming school festival, the prince, whom she has met several times in her dreams, appears. The prince, Kyoshiro Ayanokoji, requests of her just as he had done in Kuu's dreams, "Let's go... together..." (Source: Wikipedia)

Episodes 5.5 and 13.

The story follows the adventures of rabbit-shaped Jewelpet Ruby, her long-best human friend Airi Kirara and the other Jewelpets on their mission to restore the Jewel Castle, which had fallen from the skies into the middle of the town because of humanity's lack of faith in magic. To restore people's belief in magic, Jewelpets transform into humans to study more about them. (Source: ANN, edited)

In 2015, the Chaldea Security Organization draws on experts of both the magical and mundane fields to observe the future of mankind for possible extinction events. Humanity's survival seems assured for the next century—until the verdict suddenly changes, and now eradication of the species awaits at the end of 2016. The cause is unknown, but appears to be linked with the Japanese town of Fuyuki and the events of 2004 during the Fifth Holy Grail War. In response, Chaldea harnesses an experimental means of time travel, the Rayshift technology. With it, Ritsuka Fujimaru, a young man newly recruited to the organization, and the mysterious girl Mash Kyrielight, can travel back to 2004 and discover how to save humanity. A grand order to fight fate has been declared—an order to change the past and restore the future. [Written by MAL Rewrite]