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 Th37:
  v is cut-vertex implies G is non _trivial
proof
  assume
A1: v is cut-vertex;
  now
    assume G is _trivial;
    then reconsider G9=G as _trivial _Graph;
    set G2 = the removeVertex of G9,v;
    G9.numComponents() = 1 & G2.numComponents() = 1 by Lm18;
    then 1 in 1 by A1;
    hence contradiction;
  end;
  hence thesis;
end;
