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<span class="kw">consider </span><font color="Maroon" title="c2">u</font>, <font color="Maroon" title="c3">w</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E2:157_1_1"/><span class="lab"><font color="Green" title="E53">W0</font></span>: 
<font color="Maroon" title="c2">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">f</font>
 <span class="kw">and </span><br/><a NAME="E3:157_1_1"/><span class="lab"><font color="Green" title="E54">W1</font></span>: 
<font color="Maroon" title="c3">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">f</font>
 <span class="kw">and </span><br/><a NAME="E4:157_1_1"/><span class="lab"><font color="Green" title="E55">W2</font></span>: 
<font color="Maroon" title="c2">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">w</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D10" title="ZFMISC_1:def.10">ZFMISC_1:def 10</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">u1</font>, <font color="Maroon" title="c5">u2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E6:157_1_1"/><span class="lab"><font color="Green" title="E56">W3</font></span>: 
<font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">u2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:157_1_1"><span class="lab"><font color="Green" title="E53">W0</font></span></a>, <a class="ref" href="relat_1.html#D1" title="RELAT_1:def.1">RELAT_1:def 1</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">w1</font>, <font color="Maroon" title="c7">w2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E8:157_1_1"/><span class="lab"><font color="Green" title="E57">W4</font></span>: 
<font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">w1</font>,<font color="Maroon" title="c7">w2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:157_1_1"><span class="lab"><font color="Green" title="E54">W1</font></span></a>, <a class="ref" href="relat_1.html#D1" title="RELAT_1:def.1">RELAT_1:def 1</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">u1</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="zfmisc_1.html#D10" title="ZFMISC_1:def.10">ZFMISC_1:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c4">u1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> &amp;  not <font color="Maroon" title="c4">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c6">w1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">u1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> &amp; <font color="Maroon" title="c6">w1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> &amp;  not <font color="Maroon" title="c4">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">w1</font> )</span><br/>

<span class="kw">thus </span><a NAME="E9:157_1_1"/>
( <font color="Maroon" title="c4">u1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> &amp; <font color="Maroon" title="c6">w1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:157_1_1"><span class="lab"><font color="Green" title="E56">W3</font></span></a>, <a class="txt" href="#E8:157_1_1"><span class="lab"><font color="Green" title="E57">W4</font></span></a>, <a class="txt" href="#E2:157_1_1"><span class="lab"><font color="Green" title="E53">W0</font></span></a>, <a class="txt" href="#E3:157_1_1"><span class="lab"><font color="Green" title="E54">W1</font></span></a>, <a class="ref" href="relat_1.html#D4" title="RELAT_1:def.4">RELAT_1:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c4">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">w1</font></span><br/>

<span class="kw">thus </span><a NAME="E10:157_1_1"/>
<font color="Maroon" title="c4">u1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">w1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:157_1_1"><span class="lab"><font color="Green" title="E53">W0</font></span></a>, <a class="txt" href="#E3:157_1_1"><span class="lab"><font color="Green" title="E54">W1</font></span></a>, <a class="txt" href="#E4:157_1_1"><span class="lab"><font color="Green" title="E55">W2</font></span></a>, <a class="txt" href="#E6:157_1_1"><span class="lab"><font color="Green" title="E56">W3</font></span></a>, <a class="txt" href="#E8:157_1_1"><span class="lab"><font color="Green" title="E57">W4</font></span></a>, <a class="ref" href="funct_1.html#D1" target="_self" title="FUNCT_1:def.1">Def1</a></span>; <a class="txt" 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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