fact: Definition poweR x r := match x with | x'%:E => (x' `^ r)%:E | +oo => if r == 0%R then 1%E else +oo | -oo => if r == 0%R then 1%E else 0%E end.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum matrix) mathcomp(interval rat) mathcomp(boolp classical_sets functions) mathcomp(mathcomp_extra) reals ereal signed topology normedtype landau sequences derive realfun itv convex