reserve i,j,k,n,m for Nat;

theorem Th4:
  for p,q being Point of TOP-REAL n, r being Real st r < 1 & p = (
  1-r)*q+r*p holds p = q
proof
  let p,q be Point of TOP-REAL n, r be Real such that
A1: r < 1 and
A2: p = (1-r)*q+r*p;
  set s = 1 -r;
  r + 0 < 1 by A1;
  then
A3: 0 < 1 - r by XREAL_1:20;
  p = (1-s)*p+s*q by A2;
  hence thesis by A3,Th3;
end;
