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<b>let </b><font color="Maroon">T</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">B0</font> be    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T</font>;<br/>





<b>assume </b><a NAME="E1:31"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">B0</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> &amp; ( for <font color="Olive">x</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font> holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> &amp; ( for <font color="Olive">U</font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">U</font> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="tarski.html#R1">c=</a> <font color="Olive">U</font> ) ) ) )
 ;<br/>

<b>consider </b><font color="Maroon">B</font> being    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E3:31"/><i><font color="Green">E31</font></i>: 
 <a href="card_1.html#K1">Card</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="waybel23.html#K2">weight</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="waybel23.html#T75">WAYBEL23:75</a></i>;<br/>
<b>set </b><font color="Maroon">M</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Olive">C</font></span>)</span> where <font color="Olive">C</font> is    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">T</font> : verum </span>}</span> ;<br/>
<a NAME="E4:31"/><i><font color="Green">E33</font></i>: 
 <a href="waybel23.html#K2">weight</a> <font color="Maroon">T</font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Olive">C</font></span>)</span> where <font color="Olive">C</font> is    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">T</font> : verum </span>}</span> 
 
<b>by </b><i><a class="ref" href="waybel23.html#D5">WAYBEL23:def 5</a></i>;<br/>
<a NAME="E5:31"/>
 <a href="card_1.html#K1">Card</a> <font color="Maroon">B0</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Olive">C</font></span>)</span> where <font color="Olive">C</font> is    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">T</font> : verum </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E6:31"/>
 <a href="waybel23.html#K2">weight</a> <font color="Maroon">T</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">B0</font>
 <b>by </b><i><a class="ref" href="topgen_2.html#T1" target="_self">Th1</a>, <a class="ref" href="setfam_1.html#T4">SETFAM_1:4</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<a NAME="E7:31"/>
<font color="Maroon">B0</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E8:31"/>
 <a href="card_1.html#K1">Card</a> <font color="Maroon">B0</font> <a href="tarski.html#R1">c=</a>  <a href="waybel23.html#K2">weight</a> <font color="Maroon">T</font>
 <b>by </b><i>, <a class="ref" href="card_1.html#T27">CARD_1:27</a></i>;<br/>


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