reserve G,G1,G2 for _Graph;
reserve W,W1,W2 for Walk of G;
reserve e,x,y,z for set;
reserve v for Vertex of G;
reserve n,m for Element of NAT;

theorem Th168:
  for G1 being _Graph, G2 being Subgraph of G1, W being Walk of
G1 st W.vertices() c= the_Vertices_of G2 & W.edges() c= the_Edges_of G2 holds W
  is Walk of G2
proof
  let G1 be _Graph, G2 be Subgraph of G1, W be Walk of G1;
  assume that
A1: W.vertices() c= the_Vertices_of G2 and
A2: W.edges() c= the_Edges_of G2;
  now
    per cases;
    suppose
      W is non trivial;
      hence thesis by A2,Th167;
    end;
    suppose
A3:   W is trivial;
      W.first() in W.vertices() by Th86;
      hence thesis by A1,A3,Th166;
    end;
  end;
  hence thesis;
end;
