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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="topgen_2.html#K1" target="_self">Chi</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> where B is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> : verum </span>}</span> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> =  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="topgen_2.html#K1" target="_self">Chi</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> where B is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> : verum </span>}</span>  as  <a href="card_1.html#V1">cardinal</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  <b>by </b><i><a class="txt" href="topgen_2.html#E5"><i><font color="Green">Lemma5</font></i></a></i>;<br/>
<a NAME="E2:7"/>
( ( for <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> holds  <a href="topgen_2.html#K1" target="_self">Chi</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Maroon">c<sub>3</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being <a href="card_1.html#V1">cardinal</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  st ( for <font color="Olive">b<sub>2</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> holds  <a href="topgen_2.html#K1" target="_self">Chi</a> <font color="Olive">b<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Olive">b<sub>1</sub></font> ) holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Olive">b<sub>1</sub></font> ) )
 
<b>by </b><i><a class="txt" href="topgen_2.html#E5"><i><font color="Green">Lemma5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:7"/>
 <a href="topgen_2.html#K2" target="_self">Chi</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="topgen_2.html#K1" target="_self">Chi</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> where B is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> : verum </span>}</span> 
 <b>by </b><i><a class="ref" href="topgen_2.html#D2" target="_self">Def2</a></i>;<br/>


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