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 choose_id P x0 y0 : P x0 -> P y0 -> choose P x0 = choose P y0.