reserve x, y, z, v for set,
  n, m, k for Nat;
reserve G, G1, G2, G3 for Graph;
reserve x, y for Element of (the carrier of G);

theorem
  for G being oriented Graph st G1 c= G holds G1 is oriented
proof
  let G be oriented Graph;
  assume G1 c= G;
then A1: G1 is Subgraph of G;
   for x,y being set st x in the carrier' of G1 & y in the carrier' of G1 &
  (the Source of G1).x = (the Source of G1).y &
  (the Target of G1).x = (the Target of G1).y holds x = y
  proof
    let x, y be set;
    assume that
A2: x in the carrier' of G1 and
A3: y in the carrier' of G1 and
A4: (the Source of G1).x = (the Source of G1).y and
A5: (the Target of G1).x = (the Target of G1).y;
A6: (the carrier' of G1) c= (the carrier' of G) by A1,Def18;
A7: (the Source of G).x = (the Source of G1).y by A1,A2,A4,Def18
      .= (the Source of G).y by A1,A3,Def18;
 (the Target of G).x = (the Target of G1).y by A1,A2,A5,Def18
      .= (the Target of G).y by A1,A3,Def18;
    hence thesis by A2,A3,A6,A7,Def7;
  end;
  hence thesis;
end;
