The speed of light is constant at these three levels. The speed of light remains constant in the same medium. The speed of light in different media is different, but it doesn't mean that they need to be used as media, just to express that light passes between them. For example, traveling in a vacuum is the fastest and slower in air, water and glass, but the speed of light is constant in the same medium, which is determined by electromagnetic laws.
We now know that light is electromagnetic wave, so light must also follow Maxwell's equation, from which it is easy to deduce the speed of light (electromagnetic wave speed). ε is the dielectric constant and μ is the magnetic permeability, which are fixed in the same medium. It is not difficult to see that the speed of light is a constant in the same medium, which is only related to dielectric constant and permeability. The speed of light does not change with the movement of the light source.
It is easy to understand that the speed of light does not change with the movement of the light source, but this is not only the electromagnetic wave of light, but also our ordinary water wave. Axiom is something that cannot be proved correct or not. If you want to play, you have to accept it Mathematics has many theoretical systems. You can put forward some axioms yourself, and then derive some useful theorems from these axioms, but you must ensure that the system you build is self-consistent. To put it simply, you should be decisive. Don't be led by one theorem that the triangle is 180, and another theorem that the angles of the triangle add up to 240 degrees, then your theory is directly finished.