reserve A,B for Ordinal,
        o for object,
        x,y,z for Surreal,
        n for Nat,
        r,r1,r2 for Real;

theorem Th72:
  for s be Surreal st r<>0 & x is (s,y,r)_term & x== z holds
    z is (s,y,r)_term
proof
  let s be Surreal;
  assume
A1: r<>0 & x is (s,y,r)_term & x==z;
  then
A2: not x + - s == 0_No &
  omega-y (x +- s) == y & omega-r (x + - s) = r;
  A3: x + - s == z+-s by A1,SURREALR:43;
  not z + - s ==0_No by A2,A3,SURREALO:4;
  hence thesis by A1,A3,Th70;
end;
