Which word refers to gradually but firmly establishing a belief or value in someone?

The term that best captures the process of gradually and firmly establishing a belief or value in someone is "instill." This word conveys the idea of introducing concepts, beliefs, or values slowly over time, allowing them to take root and become an integral part of a person's mindset or behavior. Instilling often involves consistent reinforcement, teaching, or modeling of the desired belief, thereby promoting internalization.

In contrast, the other words do not convey a similar meaning. "Erase" implies the opposite action of eliminating or removing an idea or belief. "Discourage" focuses on actively dissuading someone from pursuing a particular action or belief. Lastly, "dispel" refers to the act of driving away or causing something feared or believed in to disappear, which does not align with introducing or embedding beliefs or values.