Canonical setI_monoid := Law (@setIA T) (@setTI T) (@setIT T).Canonical setI_comoid := ComLaw (@setIC T).Canonical setI_muloid := MulLaw (@set0I T) (@setI0 T).Canonical setU_monoid := Law (@setUA T) (@set0U T) (@setU0 T).Canonical setU_comoid := ComLaw (@setUC T).Canonical setU_muloid := MulLaw (@setTU T) (@setUT T).Canonical setI_addoid := AddLaw (@setUIl T) (@setUIr T).Canonical setU_addoid := AddLaw (@setIUl T) (@setIUr T).Definition imset := imset_def.Definition imset2 := imset2_def.

Lemma imsetE : imset = imset_def.