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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</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">X</font>, <font color="Olive" title="b2">Y</font>, <font color="Olive" title="b3">Z</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span> holds  <font color="Olive" title="b1">X</font> <a href="mathmorp.html#K3" title="MATHMORP:func.3">(-)</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">Y</font> <a href="mathmorp.html#K4" title="MATHMORP:func.4">(+)</a> <font color="Olive" title="b3">Z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">X</font> <a href="mathmorp.html#K3" title="MATHMORP:func.3">(-)</a> <font color="Olive" title="b3">Z</font></span>)</span> <a href="mathmorp.html#K3" title="MATHMORP:func.3">(-)</a> <font color="Olive" title="b2">Y</font></span><br/><b>let </b><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</font>, <font color="Maroon" title="c4">Z</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">X</font> <a href="mathmorp.html#K3" title="MATHMORP:func.3">(-)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="mathmorp.html#K4" title="MATHMORP:func.4">(+)</a> <font color="Maroon" title="c4">Z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="mathmorp.html#K3" title="MATHMORP:func.3">(-)</a> <font color="Maroon" title="c4">Z</font></span>)</span> <a href="mathmorp.html#K3" title="MATHMORP:func.3">(-)</a> <font color="Maroon" title="c3">Y</font></span><br/>







<font color="Maroon" title="c2">X</font> <a href="mathmorp.html#K3" title="MATHMORP:func.3">(-)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="mathmorp.html#K4" title="MATHMORP:func.4">(+)</a> <font color="Maroon" title="c4">Z</font></span>)</span> = 
<font color="Maroon" title="c2">X</font> <a href="mathmorp.html#K3" title="MATHMORP:func.3">(-)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Z</font> <a href="mathmorp.html#K4" title="MATHMORP:func.4">(+)</a> <font color="Maroon" title="c3">Y</font></span>)</span>
<b>by </b><i><a class="ref" href="mathmorp.html#T12" target="_self" title="MATHMORP:th.12">Th12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="mathmorp.html#K3" title="MATHMORP:func.3">(-)</a> <font color="Maroon" title="c4">Z</font></span>)</span> <a href="mathmorp.html#K3" title="MATHMORP:func.3">(-)</a> <font color="Maroon" title="c3">Y</font>
<b>by </b><i><a class="ref" href="mathmorp.html#T23" target="_self" title="MATHMORP:th.23">Th23</a></i>
;<br/>
<b>hence </b><a NAME="E2:30"/>
<font color="Maroon" title="c2">X</font> <a href="mathmorp.html#K3" title="MATHMORP:func.3">(-)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="mathmorp.html#K4" title="MATHMORP:func.4">(+)</a> <font color="Maroon" title="c4">Z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="mathmorp.html#K3" title="MATHMORP:func.3">(-)</a> <font color="Maroon" title="c4">Z</font></span>)</span> <a href="mathmorp.html#K3" title="MATHMORP:func.3">(-)</a> <font color="Maroon" title="c3">Y</font>
 ; <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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