reserve n for Nat;
reserve i for Integer;
reserve r,s,t for Real;
reserve An,Bn,Cn,Dn for Point of TOP-REAL n;
reserve L1,L2 for Element of line_of_REAL n;
reserve A,B,C for Point of TOP-REAL 2;

theorem Th10:
  |(An-Bn,An-Cn)| = |(Bn-An,Cn-An)|
  proof
A1: |(An - Bn, An-Cn)| = |(-(An - Bn),-(An - Cn))| by EUCLID_2:23;
    -(An-Bn)=Bn-An & -(Cn-An)=An-Cn by RVSUM_1:35;
    hence thesis by A1;
  end;
