reserve a,a1,a2,a3,b,b1,b2,b3,r,s,t,u for Real;
reserve n for Nat;
reserve x0,x,x1,x2,x3,y0,y,y1,y2,y3 for Element of REAL n;

theorem Th10:
  x1 - x0 = t*x & x1 <> x0 implies t <> 0
proof
  assume that
A1: x1 - x0 = t*x and
A2: x1 <> x0;
  assume not t <> 0;
  then x1 - x0 = 0*n by A1,EUCLID_4:3;
  hence contradiction by A2,Th9;
end;
