reserve x,y,X for set,
  i,j,k,m,n for Nat,
  p for FinSequence of X,
  ii for Integer;
reserve G for Graph,
  pe,qe for FinSequence of the carrier' of G,
  p,q for oriented Chain of G,
  W for Function,
  U,V,e,ee for set,
  v1,v2,v3,v4 for Vertex of G;

theorem Th10:
  for G being oriented Graph,v1,v2 be Vertex of G,e1,e2 be set st
e1 in the carrier' of G & e2 in the carrier' of G & e1 orientedly_joins v1,v2 &
  e2 orientedly_joins v1,v2 holds e1=e2
proof
  let G be oriented Graph,v1,v2 be Vertex of G,e1,e2 be set;
  assume that
A1: e1 in the carrier' of G & e2 in the carrier' of G and
A2: e1 orientedly_joins v1,v2 and
A3: e2 orientedly_joins v1,v2;
A4: (the Source of G).e2 = v1 & (the Target of G).e2 = v2 by A3,GRAPH_4:def 1;
  (the Source of G).e1 = v1 & (the Target of G).e1 = v2 by A2,GRAPH_4:def 1;
  hence thesis by A1,A4,GRAPH_1:def 7;
end;
