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

theorem
  y<=0 & z<=0 implies x*(y+z) = x*y +x*z
proof
  assume
A1: y<=0 & z<=0;
  thus x*(y+z) = --(x*(y+z)) .= -(x*-(y+z)) by Th92
    .= -(x*(-y+-z)) by Th9
    .= -(x*(-y)+x*(-z)) by A1,Th96
    .= -(-x*y+x*(-z)) by Th92
    .= -(-x*y+-x*z) by Th92
    .= --(x*y +x*z) by Th9
    .= x*y +x*z;
end;
