There three sources of inflation; money creation, money velocity, and essential resource shortage.
The first two are obvious, although some would argue that credit money is an expression of money velocity. Meaning, if a bank can lend out 10x the deposit amount, then it has actually made that same parcel of money 10x faster through parallelization. From this abstraction, money velocity obviously affects prices.
The third occurs when there is an essential resource shortage.
About the relationship between inflation and monetary velocity:
When 1 $ is “printed”, assuming a velocity of 2, the GDP can increase by 2 $ without any effect on prices (leaving out of the discussion the effect of international trade balance for simplicity).
If the GDP growth is less than that (say 1 $), then we have either money going in slower motion (velocity has decreased to 1) OR prices going down (divided by 2 = deflation).
If the GDP growth is stronger (say 4$), then it may be attributable to inflation (prices multiplied by 2) or to higher monetary velocity or to both effects combined.
In short, there is NO direct relationship between monetary velocity and inflation (dP) but a rather complex one between 4 variables:
V= PT/M
dV = TdP/M + PdT/M –PTdM/M2
I take it that you consider a resource shortage as a negative determinant of dT (T: amount of transactions in real terms, not monetary terms).
Maybe I mis-understood what you said, so I'll write what I think is 'right' and continue from there.
1BTC is printed and velocity is 2, then total money supply is 2BTC. Therefore if Real GDP(inflation adjusted) is 2BTC then inflation is zero. This means 2BTC worth of goods & services are produced.
If Real GDP growth is less than this, then the amount of Goods & Services will be less than 2BTC, which means inflation has occurred.
If Real GDP growth is above this, then the Real Output is above 2BTC, meaning that deflation will occur.
It appears you are using the Money Exchange Equation:
MV = PQ M is the total dollars in the nation’s money supply
V is the number of times per year each dollar is spent
P is the average price of all the goods and services sold during the year
Q is the quantity of assets, goods and services sold during the year
So P = MV/Q, my calculus skills aren't as advanced as yours so I'll make observations on this relationship.
In short your right. My point about credit money, is that all things being equal, if credit money is derived from real money then this could be seen as increase in the velocity of real money. Therefore if M and Q remain constant, and V increases by definition P must increase.
Personally I think the Money Exchange Equation starts to fall apart during times of extreme resource shortage. This is because money will start to move towards the suppliers of such resource. Therefore you would expect to see prices fall according to the Money Exchange Equation as the supply of money falls, caused by the suppliers cash stockpile. Sometimes this is offset by a contraction in Real Output, but velocity usually falls as economic interactions fall due the lack of the essential resource. The suppliers don't care about the fact that there is only so much money circulating, therefore they will charge any price they like regardless of the Money Exchange Equation. The Money Exchange Equation functions in 'ideal' markets. When markets are no longer 'ideal' it falls apart.