fact: Definition lt_ereal x1 x2 := match x1, x2 with | -oo, r%:E | r%:E, +oo => r \is Num.real | r1%:E, r2%:E => r1 < r2 | -oo, -oo | +oo, +oo => false | +oo, _ | _ , -oo => false | -oo, _ => true end.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra) signed