We show that, given a projective regular function f: X --> Con a smooth qua
si-projective variety, the corresponding cohomology groups of the twisted d
e Rham complex (Omega(x)(.), d ---> df boolean AND) and of the complex (Ome
ga(x)(.), df boolean AND) have the same dimension. We generalize the result
to de Rham complexes with coefficients in a mixed Hedge Module.