The fat-over-lean rule means that the painting is build in layers, and with each new layer the artist adds more oil/medium to his/her paints. While the first layers have no medium at all (but a little bit of Gamsol to dilute/thin out the paint), the following layers receive more medium.
It's best not to go wild with the use of painting mediums and keep it simple: add just enough to make the paint flow, as the mediums weaken the paint film.
The most stable medium is linseed oil. There are many other alternatives that affect the drying time of the paint, such as poppy oil, walnut oil,etc.
The process is described in my most popular video here:https://www.youtube.com/watch?v=Dgyu9Tvzr20
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