reserve G,G1,G2 for _Graph;
reserve e,x,y for set;
reserve v,v1,v2 for Vertex of G;
reserve W for Walk of G;

theorem
  for G1 being _Graph, G2 being Subgraph of G1, v1 being Vertex of G1,
  v2 being Vertex of G2 st v1 = v2 holds G2.reachableDFrom(v2) c= G1
  .reachableDFrom(v1)
proof
  let G1 be _Graph, G2 be Subgraph of G1, v1 be Vertex of G1, v2 be Vertex of
  G2;
  assume
A1: v1 = v2;
    let v be object;
    assume v in G2.reachableDFrom(v2);
    then consider W being DWalk of G2 such that
A2: W is_Walk_from v2,v by Def6;
    reconsider W as DWalk of G1 by GLIB_001:175;
    W is_Walk_from v1,v by A1,A2,GLIB_001:19;
    hence v in G1.reachableDFrom(v1) by Def6;
end;
