Before "showing" this nonsense, Einstein wrestled with his conscience "over a lengthy period of time, to the point of despair":
John Stachel: "But this seems to be nonsense. How can it happen that the speed of light relative to an observer cannot be increased or decreased if that observer moves towards or away from a light beam? Einstein states that he wrestled with this problem
over a lengthy period of time, to the point of despair." http://www.aip.org/history/exhibits/einstein/essay-einstein-relativity.htm
"Seems to be nonsense" is a euphemism. "The speed of light within a vacuum is the same no matter the speed at which an observer travels" is obvious nonsense. Frequency and speed of light pulses vary proportionally for the moving observer https://youtube.
com/watch?v=bg7O4rtlwEE, in accordance with the formula
(frequency at observer) = (speed of light pulses relative to observer)/(distance between pulses)