I am learning proof by induction in my math class and I am having trouble with this problem dealing with congruences.
Let $s$ be a positive integer. Then $X \equiv \{a,b,c\} \pmod{2^sk}$ implies $X \equiv \{a,b,c\} \pmod{2^{s+1}k}$. By induction we have $X = \{a,b,c\}$.
My thought is that since the statement clearly states that the former implies latter, we don't need any further calculation to imply the induction, but how am I to state in words that this statement is obvious?