reserve GS for GraphStruct;
reserve G,G1,G2,G3 for _Graph;
reserve e,x,x1,x2,y,y1,y2,E,V,X,Y for set;
reserve n,n1,n2 for Nat;
reserve v,v1,v2 for Vertex of G;

theorem Th92:
  G1 == G2 & G1 is Subgraph of G3 implies G2 is Subgraph of G3
proof
  assume that
A1: G1 == G2 and
A2: G1 is Subgraph of G3;
A3: the_Edges_of G1 = the_Edges_of G2 by A1;
A4: the_Source_of G1 = the_Source_of G2 & the_Target_of G1 = the_Target_of
  G2 by A1;
  the_Vertices_of G1 = the_Vertices_of G2 by A1;
  hence the_Vertices_of G2 c= the_Vertices_of G3 & the_Edges_of G2 c=
  the_Edges_of G3 by A2,A3,Def32;
  let e be set;
  assume e in the_Edges_of G2;
  hence thesis by A2,A3,A4,Def32;
end;
