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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K3" target="_self">Ort_Comp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K3" target="_self">Ort_Comp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="rusub_1.html#D1">RUSUB_1:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E3:32"/>
<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K2" target="_self">Ort_Comp</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K3" target="_self">Ort_Comp</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="rusub_5.html#T25" target="_self">Th25</a></i>;<br/>
<a NAME="E4:32"/><b>then </b><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K2" target="_self">Ort_Comp</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K2" target="_self">Ort_Comp</a> <span class="p3">(<span class="default"><a href="rusub_5.html#K3" target="_self">Ort_Comp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="rusub_5.html#T27" target="_self">Th27</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K2" target="_self">Ort_Comp</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K3" target="_self">Ort_Comp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K2" target="_self">Ort_Comp</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K3" target="_self">Ort_Comp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="rusub_1.html#D1">RUSUB_1:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E7:32"/>
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="rusub_5.html#T25" target="_self">Th25</a></i>;<br/>
<a NAME="E8:32"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K3" target="_self">Ort_Comp</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K3" target="_self">Ort_Comp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="rusub_5.html#T26" target="_self">Th26</a></i>;<br/>
<a NAME="E9:32"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K2" target="_self">Ort_Comp</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K2" target="_self">Ort_Comp</a> <span class="p3">(<span class="default"><a href="rusub_5.html#K3" target="_self">Ort_Comp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K3" target="_self">Ort_Comp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="rusub_5.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E10:32"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K2" target="_self">Ort_Comp</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K2" target="_self">Ort_Comp</a> <span class="p3">(<span class="default"><a href="rusub_5.html#K3" target="_self">Ort_Comp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K3" target="_self">Ort_Comp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="rusub_5.html#E4:32"><i><font color="Green">E20</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<b>hence </b><a NAME="E11:32"/>
 <a href="rusub_5.html#K3" target="_self">Ort_Comp</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rusub_5.html#K2" target="_self">Ort_Comp</a> <span class="p1">(<span class="default"><a href="rusub_5.html#K2" target="_self">Ort_Comp</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K3" target="_self">Ort_Comp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="rusub_1.html#T24">RUSUB_1:24</a></i>;<br/>


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