<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E34">Th51</font></span>: <a NAME="T51"><span class="comment"><font color="firebrick">:: TOPREALC:51</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">T</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">T</font>,<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">n</font></span>)</span><br/>  for <font color="Olive" title="b4">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">T</font>,<a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> holds  <font color="Olive" title="b3">f</font> <a href="valued_2.html#K64" title="VALUED_2:func.64">&lt;#&gt;</a> <font color="Olive" title="b4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font> <a href="valued_2.html#K85" title="VALUED_2:func.85">&lt;##&gt;</a> <span class="p1">(<span class="default"><a href="toprealc.html#K14" title="TOPREALC:func.14">incl</a> (<font color="Olive" title="b4">g</font>,<font color="Olive" title="b1">n</font>)</span>)</span></div></div>
