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 Th7:
  G1 == G2 & G1 is connected implies G2 is connected
proof
  assume that
A1: G1 == G2 and
A2: G1 is connected;
  now
    let u,v be Vertex of G2;
    reconsider u9=u,v9=v as Vertex of G1 by A1,GLIB_000:def 34;
    consider W9 being Walk of G1 such that
A3: W9 is_Walk_from u9,v9 by A2;
    reconsider W = W9 as Walk of G2 by A1,GLIB_001:179;
    take W;
    thus W is_Walk_from u,v by A3,GLIB_001:19;
  end;
  hence thesis;
end;
