reserve G, G1, G2 for _Graph, H for Subgraph of G;

theorem
  for G3 being removeLoops of G1, G4 being removeLoops of G2
  holds G3 == G4 iff G1.allForests() = G2.allForests()
proof
  let G3 be removeLoops of G1, G4 be removeLoops of G2;
  hereby
    assume A1: G3 == G4;
    thus G1.allForests() = G3.allForests() by Th87
      .= G4.allForests() by A1, Th88
      .= G2.allForests() by Th87;
  end;
  assume A2: G1.allForests() = G2.allForests();
  G3.allForests() = G1.allForests() by Th87
    .= G4.allForests() by A2, Th87;
  hence thesis by Th88;
end;
