reserve G for IncProjStr;
reserve a,a1,a2,b,b1,b2,c,d,p,q,r for POINT of G;
reserve A,B,C,D,M,N,P,Q,R for LINE of G;

theorem Th11:
  a,b,c are_collinear implies a,c,b are_collinear & b,a,c
  are_collinear & b,c,a are_collinear & c,a,b are_collinear &
  c,b,a are_collinear
proof
  assume a,b,c are_collinear;
  then consider P such that
A1: {a,b,c} on P;
A2: {c,b,a} on P by A1,Th1;
A3: {b,c,a} on P & {c,a,b} on P by A1,Th1;
  {a,c,b} on P & {b,a,c} on P by A1,Th1;
  hence thesis by A3,A2;
end;
