De Rham derivative satisfies Leibniz rule
Then satisfies the Leibniz rule:
In other words, is a derivation from the algebra to the module .
To verify equality of the two sides, we need to verify that for any vector field , the two sides evaluate to the same thing for . The left side, evaluated on , yields:
The right side, evaluated on , yields:
The equality of these two sides follows from the Leibniz rule for derivations.