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For "natural enough" systems of ordinal notation we show that tl times iterated local reflection schema over a suflicientiy strong arithmetic T proves the same KIF-sentences as CO" times iterated consistency. A corollary is that the two hierarchies catch up module relative interpretability exactly at E-numbers. We also derive the following more general '"mixed" formulas estimating the consistency strength of iterated local reflection: for all ordinals CI 2 1 and all p, (T")fl En: TU*.~l+~),doi:10.1016/0168-0072(95)00007-4 fatcat:utzrvcl5pfcl7mcq3jw5sotqtu