Assuming that you do mean intuitionistic logic: Intuitively (!), $X$ does not ituitionistically imply $Y$.
What $X$ says is "If you give me an $A$, then I'm going to give you a $B$ or a $C$ in return, but I will not tell you which before I get to see your $A$."
On the other hand in intuitionistic logic, the meaning of $Y$ is: "I'm going to promise you either that if you give me an $A$ I will give you a $B$, or that if you give me an $A$ I will give you a $C$ -- and you can ask me which of these it will be before I even see your $A$."
Having somebody who promises me $X$ is not going to help me satisfy contract $Y$.
Arguments in this style use the Brouwer-Heyting-Kolmogorov interpretation of what an intuitionistic proof ought to be. It is connected to the Curry-Howard isomorphism.