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transformations. If I take
You say (A) and (C) are compatible and lead to the Lorentz
one of those transformations, namely
x = (x' + vt')/sqrt(1-v^2/c^2)
and substitute x' = -vt', I get x=0, which is your statement (B).
You have chosen a version of Lorentz transformations that agrees with
(B) but does not agree with (A). Substitute x=vt and you will not
obtain x'=0.