reserve F for Field;
reserve a,b,c,d,p,q,r for Element of MPS(F);
reserve e,f,g,h,i,j,k,l,m,n,o,w for Element of [:the carrier of F,the carrier
  of F,the carrier of F:];
reserve K,L,M,N,R,S for Element of F;
reserve FdSp for FanodesSp;
reserve a,b,c,d,p,q,r,s,o,x,y for Element of FdSp;

theorem
  a,b,c are_collinear & a,c,d are_collinear & a<>c implies b,c,d are_collinear
proof
  assume that
A1: a,b,c are_collinear and
A2: a,c,d are_collinear & a<>c;
A3: a,c,c are_collinear by Th12;
  a,c,b are_collinear by A1,Th10;
  hence thesis by A2,A3,Th13;
end;
