Proof of Fermat and Huygens–Fresnel principle

Hey guys, I don't know if here is the right section for this question but anyway. So I was looking for the proof or derivation of the Fermat's principle and all I got was the Huygens–Fresnel principle. However, neither could I understand how the Huygens–Fresnel principle derives the Fermat's principle nor how one can derive or prove the Huygens–Fresnel principle.
Any help is welcome!
Thanks