not sure what you are trying to proof here , sounds confusing to me

In short a Muslim is some one who believe in one God ( all powerful all knowing - with no partners - and no sharing in divinity/salvation etc) and a believe that Muhammad is its messanger ; obviously certain rituals will apply to you as mentioned below ( but if some one does not perform them he/she will still be a Muslim) ; so legal term any one is a Muslim who believe in one God and that Muhammad is its mess-anger ( nothing more to it); it does not matter how pious it is or not

Below is Prophet Hadith on it ( hope it will help you)

"Islam is that you should testify that there is no deity worthy of worship except Allah and that Muhammad is His Messenger (ﷺ), that you should perform salah (ritual prayer), pay the zakah, fast during Ramadan, and perform Hajj (pilgrimage) to the House (the Ka`bah at Makkah), if you can find a way to it (or find the means for making the journey to it)." He said: "You have spoken the truth."

reference: https://sunnah.com/nawawi40:2

In Quran

(6:19) Say [O Muhammad], “Which testimony (shahada) is the greatest of all?” Say: “God is witness between me and you that He has revealed this Quran to me that I may warn you with it, as well as whomever it reaches. Do you really testify that there are other gods beside God?” Say: “I refuse to testify”. Say: “He Alone is the One and Only God, and I am innocent of what you ascribe (to Him).”

Same in bible ( Jesus is a Prophet Like Muhammad;

if Christians want to elevate him to divinity nothing Muslims can do about it)

(Deuteronomy 4:35) To you it was shown that you might know that the Lord, He is God; there is no other besides Him.

(Deuteronomy 32:39) ‘See now that I, I am He, And there is no god besides Me;

(Psalm 86:10) For You are great and do wondrous deeds; You alone are God.

(Isaiah 44:6) “Thus says the Lord, the King of Israel and his Redeemer, the Lord of hosts:

Even Quran is asking people of Book to come to common term ( Christians, Jews) on the concept of monotheism ..

Say: O People of the Book! Come to a statement common between us and you: That we serve none but God; that we associate none with Him; that we erect not, from among ourselves, lords other than God. And if they turn away, then say: Bear witness that we are submitters (to one God; cf. 3:19).

… O People of the Book, why do you reject God’s messages while you yourselves bear witness (to God’s oneness; cf. 3:18)?…