theorem Th25:
  e in the carrier' of G & e orientedly_joins v1,v2 implies Weight
  (v1,v2,W)=W.e
proof
  set EG=the carrier' of G;
  assume
A1: e in EG & e orientedly_joins v1,v2;
  then consider e1 being set such that
A2: XEdge(v1,v2) = e1 and
A3: e1 in EG & e1 orientedly_joins v1,v2 by Def6;
  e=e1 by A1,A3,Th10;
  hence thesis by A2,A3,Def7;
end;
