reserve P for Subset of TOP-REAL 2,
  f,f1,f2,g for FinSequence of TOP-REAL 2,
  p,p1,p2,q,q1,q2 for Point of TOP-REAL 2,
  r1,r2,r19,r29 for Real,
  i,j,k,n for Nat;

theorem
  p <> q & (p`1 = q`1 or p`2 = q`2) implies LSeg(p,q) is being_S-P_arc
proof
  assume that
A1: p <> q and
A2: p`1 = q`1 or p`2 = q`2;
  take f = <*p,q*>;
  thus f is being_S-Seq by A1,A2,Th43;
  thus thesis by Th21;
end;
