reserve MS for OrtAfPl;
reserve MP for OrtAfSp;

theorem Th4:
  for x,y,z being Element of MP st LIN x,y,z holds LIN x,z,y & LIN
  y,x,z & LIN y,z,x & LIN z,x,y & LIN z,y,x
proof
  let x,y,z be Element of MP such that
A1: LIN x,y,z;
  reconsider x9=x,y9=y,z9=z as Element of the AffinStruct of MP;
A2: LIN x9,y9,z9 by A1,ANALMETR:40;
  then
A3: LIN y9,z9,x9 & LIN z9,x9,y9 by AFF_1:6;
A4: LIN z9,y9,x9 by A2,AFF_1:6;
  LIN x9,z9,y9 & LIN y9,x9,z9 by A2,AFF_1:6;
  hence thesis by A3,A4,ANALMETR:40;
end;
