reserve r,s,t,x9,y9,z9,p,q for Element of RAT+;
reserve x,y,z for Element of REAL+;

theorem
  x *' (y *' z) = x *' y *' z
proof
  thus x *' (y *' z) = GLUED(DEDEKIND_CUT x *' (DEDEKIND_CUT y *' DEDEKIND_CUT
  z)) by Lm12
    .= GLUED((DEDEKIND_CUT x *' DEDEKIND_CUT y) *' DEDEKIND_CUT z) by Lm39
    .= x *' y *' z by Lm12;
end;
