reserve x, y, z, s for ExtReal;
reserve i, j for Integer;
reserve n, m for Nat;

theorem Th8:
  y <> +infty & y <> -infty & y <> 0 implies x / y * y = x
  proof
    assume that
A1: y <> +infty & y <> -infty and
A2: y <> 0;
    thus x / y * y = x * (1 / y) * y by XXREAL_3:81
    .= x * ((1 / y) * y) by XXREAL_3:66
    .= x * 1 by A1,A2,XXREAL_3:87
    .= x by XXREAL_3:81;
  end;
