 reserve A, B, C, A1, B1, C1, A2, B2, C2, C3 for Point of TOP-REAL 2,
  lambda, mu, nu, alpha, beta, gamma for Real,
  X, Y, Z for Subset of TOP-REAL 2;

theorem
  Th12: A in LSeg(B, C) implies A in Line(B, C)
proof
  assume A in LSeg(B, C);
  then consider lambda such that
  A1: A = (1 - lambda) * B + lambda * C & 0 <= lambda & lambda <=1;
  thus thesis by A1;
end;
