reserve a,b,s,t,u,lambda for Real,
  n for Nat;
reserve x,x1,x2,x3,y1,y2 for Element of REAL n;

theorem :: EUCLID:35
  a*x = 0*n implies a = 0 or x = 0*n
proof
  assume that
A1: a*x = 0*n and
A2: a <> 0;
  thus x = 1*x by Th3
    .= ((1/a)*a)*x by A2,XCMPLX_1:106
    .= (1/a)*(a*x) by RVSUM_1:49
    .= 0*n by A1,Th2;
end;
