Fact xchoose_subproof P exP : {x | find P (ex_minn (@complete P exP)) = Some x}.Implicit Type T : countType.Local Notation dc := decode.Implicit Types P Q : pred T.Definition xchoose P exP := sval (@xchoose_subproof T P exP).

Lemma chooseP P x0 : P x0 -> P (choose P x0).