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 Th21:
  L~<*p,q*> = LSeg(p,q)
proof
  set f = <*p*>;
A1: len f = 1 by FINSEQ_1:39;
  thus L~<*p,q*> = L~(f^<*q*>) by FINSEQ_1:def 9
    .= L~f \/ LSeg(f/.len f,q) by Th19
    .= L~f \/ LSeg(p,q) by A1,FINSEQ_4:16
    .= {} \/ LSeg(p,q) by A1,TOPREAL1:22
    .= LSeg(p,q);
end;
