We study the behavior of generalized lc pairs with b-log abundant nef part, a meticulously designed structure on algebraic varieties. We show that this structure is preserved under the canonical bundle formula and sub-adjunction formulas, and is also compatible with the non-vanishing conjecture and the abundance conjecture in the classical minimal model program. * A canonical bundle formula for a projective surjective morphism f is given as the composition of a Fujino-Gongyo type canonical bundle formula [FG12] and a Kodaira type canonical bundle formula [Kod63] via the Stein factorization of f . We refer the reader to Subsection 2.4 formal definitions.
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