Many proofs and derivations need a certain steps to complete. Actions to get from one state to another are often commented in words of one or another language.

But there are so many commonly used sayings such as "We apply distributive law", "We use E expansion at the vicinity of a point x", "We use
T theorem", "We simplify this and that", ... and so on.

The idea is to define commands as operators which take in previous step(s) as an argument and give as a result the next step, this way replacing these wordy descriptions and making mathematical texts more detailed, yet succinct.