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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <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"> (  <a href="toler_1.html#NK1" title="TOLER_1:NK.1">Total</a> <font color="Maroon" title="c1">X</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">X</font> implies <font color="Maroon" title="c1">X</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:2"/><span class="lab"><font color="Green" title="E2">A1</font></span>: 
 <a href="toler_1.html#NK1" title="TOLER_1:NK.1">Total</a> <font color="Maroon" title="c1">X</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">X</font>
 ; <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"> <font color="Maroon" title="c1">X</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> </span><br/>

<span class="kw">assume </span><a NAME="E2:2"/>
 not <font color="Maroon" title="c1">X</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> 
 ; <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"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E4:2"/><span class="lab"><font color="Green" title="E3">A2</font></span>: 
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> )
 <span class="kw">and </span><br/><a NAME="E5:2"/><span class="lab"><font color="Green" title="E4">A3</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D10" onmouseover="rs('zfmisc_1/D10')" onmouseout="rh()">ZFMISC_1:def 10</a></span>;<br/>
<a NAME="E6:2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="toler_1.html#NK1" title="TOLER_1:NK.1">Total</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:2"><span class="lab"><font color="Green" title="E3">A2</font></span></a>, <a class="ref" href="toler_1.html#T2" onmouseover="rs('toler_1/T2')" onmouseout="rh()">TOLER_1:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:2"><span class="lab"><font color="Green" title="E2">A1</font></span></a>, <a class="txt" href="#E5:2"><span class="lab"><font color="Green" title="E4">A3</font></span></a>, <a class="ref" href="relat_1.html#D10" onmouseover="rs('relat_1/D10')" onmouseout="rh()">RELAT_1:def 10</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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