fact: Definition f (x: point_set S1) : point_set ClosedUnitInterval := quotient_projection _ (exist _ (f1 (proj1_sig x)) (f1_helper _ (proj2_sig x))).
imports: Coq(Reals.Ratan Lia Lra Logic.IndefiniteDescription Program.Subset) ZornsLemma(Quotients) Topology(ProductTopology AdjunctionSpace SubspaceTopology RTopology RFuncContinuity Homeomorphisms)