Contradiction in GDP (Expenditure) formula?

in the start of definition of gdp.....u r nt counting income of
anil kapoor or garry kirsten.....but in the topic....expenditure
method of calculating gdp....u have used exports-imports.....is this
nt contradictory.....kindly plz....xplain?

Anil kapoor-Garry Kirsten example was for GNP. [GNP= domestic product+income from abroad]

For GDP (expenditure), we've to calculate
consumption (C), Government's expenditure (G), investment(I) and eXport (X).
But what if government imports 5000 special mobile devices to print biometric UID smartcards? That is also counted in Government's expenditure accounts (G).
So, we've to deduct all the iMports (M) to prevent them from being counted into nation's GDP.
That's why

GDP (Expenditure)= C+I+G+(X-M)

Now, GNP (national product)= Domestic product + Income from abroad.
But since foreigners will be sending remittances to their families back home. So if every nation adds(+) foreigner's income (who is residing in their country) into their GNP, then it'll lead to double counting. So we've to deduct(-) the remittances.  
Hence  
GNP= GDP + Income from abroad - income earned by foreigners.