fact: Definition max_common_initial {X:hSet} (S T : TOSubset X) : hsubtype X := λ x, ∃ (B : hsubtype X), B x ∧ common_initial B S T.
imports: UniMath.MoreFoundations.DecidablePropositions UniMath.MoreFoundations.Propositions UniMath.MoreFoundations.Subtypes UniMath.MoreFoundations.Sets UniMath.MoreFoundations.AxiomOfChoice UniMath.Combinatorics.OrderedSets