Question

Élie for sure. The formula is derived in "Les systèmes differentiels extérieurs et leur applications géométriques" which was probably written before Henri was born. BTW, here is a very short proof that Chern showed me long ago. The exterior derivative is an anti-derivation of the exterior algebra and so is the interior product with a vector field while the Lie derivative is a derivation. (These are all trivial to check.) Also, the anti-commutator of a derivation and a derivation is an anti-derivation. Hence both sides of the "magic formula" are anti-derivations. It is obvious that two anti-derivations are equal if they agree on 0-forms and 1-forms, since the latter generate the exterior algebra. Finally it is trivial that both sides of the magic formula agree on forms of degree 0 and 1.