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Thank you so much Stefan !

Hi, please how to change the format of the title: I want it to be in lowercase letters like the second image.
any help is really appreciated!
https://i.ibb.co/XV5ftdR/image22.png
https://i.ibb.co/b556Fd7/image11.png
\documentclass[12pt,a4paper]{report ...

Thank you verry much, i really appreciate your help !

I really appreciate your help!
one more question please !
how to change the framework of the theorem to have something similar to that: i mean a red line surrounding the theorem :

Hello everyone . please help me to

change the name of the "proof" environment of the amsthm package which displays "Démonstration" to the name "preuve" written in bold!
enlarge the width of the part that contains the title in the image below!
https://i.ibb.co/F7TRDvP/imagee.png
here is the ...