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 Th38:
  p`1 = q`1 or p`2 = q`2 implies <*p,q*> is special
proof
  assume
A1: p`1 = q`1 or p`2 = q`2;
  set f = <*p,q*>;
  let i be Nat such that
A2: 1 <= i and
A3: i+1 <= len f;
  len f = 1+1 by FINSEQ_1:44;
  then i <= 1 by A3,XREAL_1:6;
  then
A4: i = 1 by A2,XXREAL_0:1;
  then f/.i = p by FINSEQ_4:17;
  hence thesis by A1,A4,FINSEQ_4:17;
end;
