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 Th32:
  for x1,x2 be Element of REAL n st x1 // x2 holds ex a st a <> 0 & x1 = a*x2
proof
  let x1,x2 being Element of REAL n;
  assume
A1: x1 // x2;
  then consider a such that
A2: x1 = a*x2;
  x1 <> 0*n by A1;
  then a <> 0 by A2,EUCLID_4:3;
  hence thesis by A2;
end;
