:: deftheorem defines is_Rout JORDAN20:def 4 :
for P being Subset of (TOP-REAL 2)
for p1, p2, p being Point of (TOP-REAL 2)
for e being Real holds
( p is_Rout P,p1,p2,e iff ( P is_an_arc_of p1,p2 & p in P & p `1 = e & ex p4 being Point of (TOP-REAL 2) st
( p4 `1 > e & LE p,p4,P,p1,p2 & ( for p5 being Point of (TOP-REAL 2) st LE p5,p4,P,p1,p2 & LE p,p5,P,p1,p2 holds
p5 `1 >= e ) ) ) );