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<div><span class="kw">theorem </span><a NAME="T12"><span class="comment"><font color="firebrick">:: HILB10_4:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X1</font>, <font color="Olive" title="b2">X2</font> being   <a href="valued_0.html#V4" title="VALUED_0:attr.4">natural-valued</a>  <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a>  st  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Olive" title="b1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Olive" title="b2">X2</font> &amp; (  for <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Olive" title="b1">X1</font> holds <br/><font color="Olive" title="b1">X1</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b3">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">X2</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b3">n</font> ) holds <br/> <a href="hilb10_4.html#K1" title="HILB10_4:func.1">Product</a> <font color="Olive" title="b1">X1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="hilb10_4.html#K1" title="HILB10_4:func.1">Product</a> <font color="Olive" title="b2">X2</font></div></div>
