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

theorem
  for G3 being removeLoops of G1, G4 being removeLoops of G2
  holds G4 is G3-Disomorphic implies
    G1.allSpanningTrees(),G2.allSpanningTrees() are_Disomorphic
proof
  let G3 be removeLoops of G1, G4 be removeLoops of G2;
  G1.allSpanningTrees() = G3.allSpanningTrees() &
    G2.allSpanningTrees() = G4.allSpanningTrees() by Th176;
  hence thesis by Th181;
end;
