End InternalTheory.
End Choice.
Export Choice.Exports.
Section ChoiceTheory.
Implicit Type T : choiceType.
Local Notation dc := decode.
Section OneType.
Variable T : choiceType.
Implicit Types P Q : pred T.
Definition xchoose P exP := sval (@xchoose_subproof T P exP).

Lemma sigW P : (exists x, P x) -> {x | P x}.