scala - Implementing trait PartialOrdered[T] -

as exercise, supposed implement trait partialordered[t].

trait partialordered[t] {   def below(that: t): boolean   def < (that: t): boolean = (this below that) && !(that below this)      /* followed other relations <=, >, >=, ==, .. */ } 

a class k extends trait should have below implemented such that

a.below(b: k) = { true   if <= b,                    false  in other case 

however, compiling gives following error:

value below not member of type parameter t def < (that: t): boolean = (this below that) && !(that below this)                                                         ^ 

so missing? in advance

edit: example class rectangle (in coordinate system), 2 opposing corners given, rectangle below if included

case class rectangle (x1: int, y1: int, x2: int, y2: int)    extends partialordered[rectangle] {    def below(r: rectangle): boolean = {     val (rx, ry) = r.topleft     val (tx, ty) = this.topleft     tx >= rx && ty <= ry &&     tx + this.width <= rx + r.width &&     ty - this.height >= ry - r.height   }    def width: int = {...}   def height: int = {...}   def topleft:(int, int) = {...} } 

you have tell scala t subtype of partialordered[t]:

trait partialordered[t <: partialordered[t]] { this: t =>   def below(that: t): boolean   def < (that: t): boolean = (this below that) && !(that below this)      /* followed other relations <=, >, >=, ==, .. */ } 

see also: scala self-type: value not member error