reserve X for AffinPlane;
reserve o,a,a1,a2,a3,a4,b,b1,b2,b3,b4,c,c1,c2,d,d1,d2, d3,d4,d5,e1,e2,x,y,z
  for Element of X;
reserve Y,Z,M,N,A,K,C for Subset of X;

theorem
  X is satisfying_indirect_Scherungssatz implies X is satisfying_Scherungssatz
proof
  assume
A1: X is satisfying_indirect_Scherungssatz;
  then X is satisfying_major_indirect_Scherungssatz;
  then
A2: X is satisfying_major_Scherungssatz by Th4;
  X is satisfying_minor_indirect_Scherungssatz by A1,Th1;
  then X is satisfying_minor_Scherungssatz by Th3;
  hence thesis by A2,Th2;
end;
