"deeply rooted into" is a correct phrase and can be used in written English.
It is often used to describe something that is very ingrained or firmly established. Example: The tradition of Christmas gift-giving is deeply rooted into our culture, and has been passed down for generations.
After the attack, more than any superstitious sense of guilt, I felt regret for my aestheticizing vainglory and my failure to appreciate what, even in its obnoxiousness, had grown deeply rooted into and inextricably intertwined with the life of the city — and, as I quickly understood, had even exemplified it.
It was felt that clinical guidelines and checklists were already deeply rooted into today's medicine.
PolyViNE decision making and embedding process is deeply rooted into the location constraints that come with each VN request.
Regrettably, it is deeply rooted into Japanese culture and society.
I soon found out that prison life was deeply rooted into my present existence; a decade of life in an environment where survival mechanisms and behaviors were hardwired into daily existence had changed me profoundly.
The role of these factors in the construction of the salience map could thus be deeply rooted into the probabilistic structure of the visual world.
He then determined to follow not Hardy's hero, but Hardy himself (to the south west of England and into fiction deeply rooted in an individual's relation to the past).
7) Credit unions are deeply rooted in their communities and invest back into them with passion.
Growing up Kenyan, I regularly ran into cultural traditions so deeply rooted in history and largely rural lifestyles that they didn't square with my very Canadian life.
"He's actually deeply rooted in modernism.
They're deeply rooted in our cultures".
