Generalized Vojta-R\'emond inequality

International Journal of Number Theory, 16(1), 107-120 (2020) Following and generalizing unpublished work of Ange, we prove a generalized version of R\'emond's generalized Vojta inequality. This generalization can be applied to arbitrary products of irreducible positive-dimensional projective varieties, defined over the field of algebraic numbers, instead of powers of one fixed such variety. The proof runs closely along the lines of R\'emond's proof.