Original sentence: Some people (including Einstein at times) believe that the second postulate is redundant because it follows from the first postulate applied to Maxwell's equations; other people (again including Einstein at times) prefer to start by postulating Lorentz invariance or constant lightspeed
Edited sentence: " Of course, this is not to be construed as a "dropping" of the original postulates for the Lorentz transformation, since those are a subset of the augmented postulates."The new feature of [the 1905 relativity theory] was the realization of the fact that the bearing of the Lorentz transformation transcended its connection with Maxwell's equations and was concerned with the nature of space and time in general.A further new result was that the "Lorentz invariance" is a general condition for any physical theory.Also, regarding Maxwell's equations, Einstein already knew in 1905 that they could not claim exact validity, just as Newtonian mechanics could not.As he wrote in a letter to Carl Seelig in 1955.For purposes of making heuristic arguments for mass-radiation transformability, Einstein augmented the two basic principles (relativity and lightspeed invariance) with additional postulates concerning the momentum and energy of electromagnetic waves implied by Maxwell's equations.He acknowledged in his 1907 survey paper on special relativity that it was problematic to rely on Maxwell's equations for the heuristic mass-energy argument, and this is why he consistently based the derivation of Lorentz invariance (which is the essential core of special relativity) on just the two basic principles of relativity and lightspeed invariance.See, for example, his 1905 paper "Does the Inertia of a Body depend on its Energy-Content.The above postulates refer to the axiomatic basis of the Lorentz transformation.This was for me of particular importance because I had already previously found that Maxwell's theory did not account for the micro-structure of radiation and could therefore have no general validity