Corrected iteration

For λ inaccessible, we may consider (< λ) -support iteration of some definable in fact specific (< λ) -complete λ⁺-c.c. forcing notions. But do we have “preservation by restricting to a sub-sequence of the iterated forcing"? To regain it we “correct" the iteration. We prove this for a characteristic case for iterations which holds by “nice” for λ= ℵ. This is done generally in a work H. Horowitz and the author Shelah. This work is use in a work of the author in (Trans Am Math Soc 373(8):5351–5369, arXiv:0904.0817, 2020) where we use so called strongly (< λ⁺) -directed m. We could here restrict ourselves to reasonable m (see 2.13(3)).