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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">M</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font> holds   <a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Olive" title="b1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <span class="p1">(<span class="default"><a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Olive" title="b1">M</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">M</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Maroon" title="c2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <span class="p1">(<span class="default"><a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Maroon" title="c2">M</font></span>)</span></span>)</span></span><br/>



<b>set </b><font color="Maroon" title="c3">N</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Maroon" title="c2">M</font></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">N</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Maroon" title="c2">M</font></span>)</span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font> <b>by </b><i><a class="ref" href="rusub_1.html#D1" title="RUSUB_1:def.1">RUSUB_1:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">N</font> = <font color="Maroon" title="c4">N</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font> ;<br/>
<a NAME="E3:32"/>
<font color="Maroon" title="c5">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Maroon" title="c5">N</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="rusub_5.html#T25" target="_self" title="RUSUB_5:th.25">Th25</a></i>;<br/>
<a NAME="E4:32"/><b>then </b><i><font color="Green" title="E20">A1</font></i>: 
<font color="Maroon" title="c5">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <span class="p3">(<span class="default"><a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Maroon" title="c2">M</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="rusub_5.html#T27" target="_self" title="RUSUB_5:th.27">Th27</a></i>;<br/>
<b>set </b><font color="Maroon" title="c6">L</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Maroon" title="c2">M</font></span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">L</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Maroon" title="c2">M</font></span>)</span></span>)</span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font> <b>by </b><i><a class="ref" href="rusub_1.html#D1" title="RUSUB_1:def.1">RUSUB_1:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">L</font> = <font color="Maroon" title="c7">L</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font> ;<br/>
<a NAME="E7:32"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Maroon" title="c8">L</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Maroon" title="c2">M</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rusub_5.html#T25" target="_self" title="RUSUB_5:th.25">Th25</a>, <a class="ref" href="rusub_5.html#T26" target="_self" title="RUSUB_5:th.26">Th26</a></i>;<br/>
<a NAME="E8:32"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <span class="p3">(<span class="default"><a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Maroon" title="c2">M</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Maroon" title="c2">M</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rusub_5.html#T27" target="_self" title="RUSUB_5:th.27">Th27</a></i>;<br/>
<a NAME="E9:32"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <span class="p3">(<span class="default"><a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Maroon" title="c2">M</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Maroon" title="c2">M</font></span>)</span>
 
<b>by </b><i><a class="txt" href="rusub_5.html#E4:32"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>
<b>hence </b><a NAME="E10:32"/>
 <a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Maroon" title="c2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <span class="p1">(<span class="default"><a href="rusub_5.html#K2" title="RUSUB_5:func.2">Ort_Comp</a> <span class="p2">(<span class="default"><a href="rusub_5.html#K3" title="RUSUB_5:func.3">Ort_Comp</a> <font color="Maroon" title="c2">M</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="rusub_1.html#T24" title="RUSUB_1:th.24">RUSUB_1:24</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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