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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">Y</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>









<b>assume </b><a NAME="E1:40"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Y</font></span>)</span> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">B</font>
 ;<br/>

<a NAME="E2:40"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">y1</font> <a href="euclid.html#K17">+</a> <font color="Olive">y2</font></span>)</span> where <font color="Olive">y1</font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>, <font color="Olive">y2</font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span> : ( <font color="Olive">y1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Y</font> &amp; <font color="Olive">y2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> ) </span>}</span> 
 
;<br/>
<b>then consider </b><font color="Maroon">y1</font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>, <font color="Maroon">y2</font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span><b> such that </b><br/><a NAME="E4:40"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> <a href="euclid.html#K17">+</a> <font color="Maroon">y2</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">y2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> )
 ;<br/>
<a NAME="E5:40"/>
( <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E6:40"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">y3</font> <a href="euclid.html#K17">+</a> <font color="Olive">y4</font></span>)</span> where <font color="Olive">y3</font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>, <font color="Olive">y4</font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span> : ( <font color="Olive">y3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Olive">y4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> ) </span>}</span>  &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">y3</font> <a href="euclid.html#K17">+</a> <font color="Olive">y4</font></span>)</span> where <font color="Olive">y3</font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>, <font color="Olive">y4</font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span> : ( <font color="Olive">y3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Olive">y4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> ) </span>}</span>  )
 
<b>by </b><i/>;<br/>
<a NAME="E7:40"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">B</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">B</font> )
 
;<br/>
<b>hence </b><a NAME="E8:40"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">B</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="mathmorp.html#K4" target="_self">(+)</a> <font color="Maroon">B</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


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