reserve x,y,z,w for ExtReal,
  r for Real;
reserve f,g for ExtReal;
reserve t for ExtReal;

theorem :: extension of REAL_1:34
  x <> +infty & x <> -infty & x <> 0 implies x*(1/x) = 1 & (1/x)*x = 1
proof
  assume that
A1: x <> +infty & x <> -infty and
A2: x <> 0;
  x in REAL by A1,XXREAL_0:14;
  then reconsider a = x as Real;
  x * (1 / x) = a * (1/a) .= 1 by A2,XCMPLX_1:106;
  hence thesis;
end;
