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Big O Notation is an informal name of the "O(x)" notation used to describe asymptotic behaviour of functions. It is a special case of Landau notation, where the O is the Greek letter capital omicron. Please consider using the [landau-notation] tag instead if your question is related to small omicron, omega, or theta in Landau notation.
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Order notation subtractions in Fibonacci Heap
Can order notation on its own imply:
$O(D(n)) + O(t(H)) - t(H) = O(D(n))$
My guess is that you cannot since the constant in the O(t(H)) would still exist after the subtraction if the constant is > 0 …