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In propositional logic, I have now the following formulas.

$X\equiv A \implies (B \vee C)$,

$Y\equiv (A \implies B) \vee (A \implies C)$.

I have already proven that Y implies X. But does X imply Y? Who can help me with a derivation, of a intuitionistic counterexample?

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    Which kind of counterexamples do you recognize?2012-07-10
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    I suddenly wonder: Are you aware that "intuitionistic" is a technical term in logic? That is, are you looking for an answer to whether $X$ implies $Y$ in the particular restricted system of logic called "intuitionistic logic", or do you just want an **intuitive** explanation of what happens in ordinary (classical, aka non-intuitionistic) propositional calculus. The answers to those to questions are not the same!2012-07-10

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