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<span class="kw">set </span><font color="Maroon" title="c1">R</font> =  <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">P</font> =  the   <a href="realalg1.html#NM2" title="REALALG1:NM.2">Ordering</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>;<br/>
<a NAME="E1:106_1_1"/><span class="lab"><font color="Green" title="E52">A</font></span>: 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="realalg1.html#K1" title="REALALG1:func.1">-</a>  the   <a href="realalg1.html#NM2" title="REALALG1:NM.2">Ordering</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="realalg1.html#T14" onmouseover="rs('realalg1/T14')" onmouseout="rh()">REALALG1:14</a>, <a class="ref" href="realalg1.html#T25" onmouseover="rs('realalg1/T25')" onmouseout="rh()">REALALG1:25</a></span>;<br/>
<a NAME="E2:106_1_1"/>
 not  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a></span>)</span></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span>
 
;<br/>
<a NAME="E3:106_1_1"/><span class="kw">then </span>
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="realalg1.html#K1" title="REALALG1:func.1">-</a>  the   <a href="realalg1.html#NM2" title="REALALG1:NM.2">Ordering</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a></span>)</span></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106_1_1"><span class="lab"><font color="Green" title="E52">A</font></span></a>, <a class="ref" href="xboole_0.html#D5" onmouseover="rs('xboole_0/D5')" onmouseout="rh()">XBOOLE_0:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:106_1_1"/>
 not  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a></span>)</span> is  <a href="o_ring_1.html#V1" title="O_RING_1:attr.1">being_a_square</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="realalg2.html#T83" onmouseover="rs('realalg2/T83')" onmouseout="rh()">REALALG2:83</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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