[spirochete]

In deriving the M.M. equation we make two assumptions: that concentration of substrate is high and that we're working early on so that the reverse reaction (enzyme plus product reverting back to the Enzyme-substrate complex) is not significant.

Now as I'm reading they say we also assume a steady state, IE the concentration of the enzyme-substrate complex is constant and thus the rate of the one reaction that forms the complex must be equal to the sum of the rates of the reactions which remove it from solution.

Is this third statement really an additional assumption, or just something that arises naturally from the first two assumptions?

[Yggdrasil]

It's an additional assumption.  I don't see how it would arise from the first two assumptions listed.