Proof

Shōmei (証明) is the fourth chapter of Attack on Titan: No Regrets, written by Gun Snark and illustrated by Hikaru Suruga.

Overview
After completing their training, Levi, Furlan and Isabel begin their first mission. Furlan is visibly scared of leaving the Walls, but Isabel appears quite happy and excited for the mission to start. Soon after going out, Erwin orders the Long-range Scouting Formation to commence. However, when reaching a Forest of Giant Trees, a normal Titan and a Deviant Type Titan attack the soldiers. Levi, along with Furlan and Isabel, manage to kill the aberrant, leading Erwin to believe that he made the right decision in choosing them.

Summary
After their training is completed, Levi, Furlan, and Isabel get their first glimpse of the world outside the Walls. They take part in an expedition launched from the Shiganshina District to explore the world beyond the walls with the Survey Corps. Furlan appears to be scared and he cannot believe that what is happening. As soon as they go out, the three are amazed at the beauty and freedom seen outside the walls. Levi then claims that he will take care of the any Titans to calm Furlan down, but he appears to be unconfidant. Isabel then makes fun of him before another member of the Corps, Sairam, comes over to them, saying that killing Titans is not a child's game and that the three are just criminals that cannot be compared to the soldiers that have died in combat. Isabel answers him, saying that if she can kill a Titan, she will be better than all the soldiers that have died before her. The argument is haulted by Levi, and Flagon Turret, their squad leader, claims that it is necessary to keep the formation and forget the fight.

Not long after their departure a 15 meter class Titan is sighted. Part of the Survey Corps, lead by Keith Shadis, jumps into action, working in unison to try and take out the Titan. At the same time a 20 meter class Deviant Type Titan appears from the forest. Another group of soldiers try to fight it, but the Titan manages to evade the incoming attacks and even kills a member of the group. With the formation beginning to fail, it's up to Levi's squad to get rid of the new threat. Levi orders Furlan and Isabel to cut the Titan's knees to stop it while he climbs to the Deviant Type Titan's back. With the Titan crippled, Levi jumps above the Titan and finishes it off with a powerful slash to the nape while falling. Levi's kill amazes the rest of the squad, including Sairam and Flagon. The three friends congratulate themselves after disposing the Titan. Meanwhile, Erwin Smith marvels at their accomplishment, satisfied that he made the right decision.