Sure. But don't confuse abstractions with analogies.
Here is a good proof about both the integers and rational numbers. Every integer and rational is a real number (abstraction). When you add any 2 real numbers, you get the same result regardless of their order (fact). So it must be true that, when you add any 2 integers, you get the same result regardless of their order (correct conclusion #1). It also must be true that, when you add any 2 rationals, you get the same result too (correct conclusion #2).
Here is a bad proof about the integers and rational numbers. Both the integers and rationals are very similar: you can add them, subtract them and so on (analogy). Between every 2 rational numbers there is another rational number (fact). So it must be true that between every 2 integers there is another integer (wrong conclusion).
Sure. But don't confuse abstractions with analogies.
Here is a good proof about both the integers and rational numbers. Every integer and rational is a real number (abstraction). When you add any 2 real numbers, you get the same result regardless of their order (fact). So it must be true that, when you add any 2 integers, you get the same result regardless of their order (correct conclusion #1). It also must be true that, when you add any 2 rationals, you get the same result too (correct conclusion #2).
Here is a bad proof about the integers and rational numbers. Both the integers and rationals are very similar: you can add them, subtract them and so on (analogy). Between every 2 rational numbers there is another rational number (fact). So it must be true that between every 2 integers there is another integer (wrong conclusion).