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<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>, <font color="Maroon">Y</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="pre_topc.html#K3">|</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>,<font color="Maroon">Y</font></span><a href="borsuk_1.html#K5">:]</a></span>,<font color="Maroon">Y</font>;<br/>





<b>set </b><font color="Maroon">Z</font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>;<br/>
<b>assume </b><a NAME="E1:18"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="funct_3.html#K10">pr2</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y</font>
 ;<br/>

<a NAME="E2:18"/><b>then </b><i><font color="Green">E26</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_3.html#D6">FUNCT_3:def 6</a></i>;<br/>
<b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E3:18"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> )
 <b>and </b><br/><a NAME="E4:18"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font>
 ;<br/>

<b>consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">x2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:18"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon">y1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E8:18"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">y2</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y1</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<i><font color="Green">E47</font></i>: <font color="Maroon">x1</font> = 
<font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>
<br/>.= 
<font color="Maroon">y1</font>
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>
;<br/>
<font color="Maroon">x2</font> = 
<font color="Maroon">f</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">x1</font>,<font color="Maroon">x2</font>
<b>by </b><i>, , <a class="ref" href="funct_3.html#D6">FUNCT_3:def 6</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">y2</font>
<b>by </b><i>, , <a class="ref" href="funct_3.html#D6">FUNCT_3:def 6</a></i>
;<br/>
<b>hence </b><a NAME="E11:18"/>
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, , </i>;<br/>


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