Prove simple theorems in Haskell in automated way
Look at Agda [1][2]
I think that it's exactly what you are looking for.
I recommend using its emacs mode for autocompletion and hole/interactive programming. [2]/quick-guide.html
A very good introduction is plfa [3], also [2]/tutorial-list.html
[1] https://en.wikipedia.org/wiki/Agda_(programming_language)
[2] https://agda.readthedocs.io/en/v2.6.0.1/getting-started/what-is-agda.html
[3] https://plfa.github.io/