Inclusion-exclusion formula and its alias names

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I am reading Probability by A. N. Shiryaev.

  1. One of the problems refers to "inclusion-exclusion formulas", also known as Poincaré’s formulas, Poincaré’s theorems, Poincaré’s identities.
  2. One of my college textbooks refers to the formula as Jordan’s formula.

I can't find any material on the naming of the formula from Wikipedia or Wolfram. My question is, do these two aliases truly exist?