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test implication

hello mathematica community,
knowing tha x,xP,y,yP are integer variables so
y + Log[2, x] == yP + Log[2, xP] ==> y + Floor[Log[2, x]] == yP + Floor
[Log[2, xP]]
 is true
how should I formulate this sentence in mathematica in order to have
as output the value true?
thank you.

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