fact: Definition Splitting_PreIdempotent (f : PreIdempotent X) := { S : Splitting f & forall x, ap f (S.2 x)^ @ (S.2 (retract_idem S.1 x))^ @ ap (retract_sect S.1) (retract_issect S.1 (retract_retr S.1 x)) @ S.2 x = (isidem f x) }.
imports: HoTT.Basics HoTT.Types HFiber Constant Truncations.Core Modalities.Modality PathAny