Typecheckers help avoid bugs in code by catching errors early. Their implementation can, however, be incorrect, leading to inconsistencies in their operation. This research explores how we can use Agda and correct-by-construction programming to create a typechecker guaranteed to be correct in its implementation. For this purpose, I based a toy language on the simply typed lambda calculus extended with records and subtyping. The resulting typechecker is proven to be sound and complete with respect to the typing and subtyping rules of the toy language. This paper compares the correct-by-construction method to existing typecheckers. The new approach offers a greater degree of trust in its implementation but comes at the cost of being more demanding to develop and maintain.