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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"> ( <font color="Maroon" title="c1">X</font> is  <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>  implies  not <font color="Maroon" title="c1">X</font> is  <a href="xtuple_0.html#V1" title="XTUPLE_0:attr.1">pair</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:1_1_1"/><span class="lab"><font color="Green" title="E1">A1</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</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">  not <font color="Maroon" title="c1">X</font> is  <a href="xtuple_0.html#V1" title="XTUPLE_0:attr.1">pair</a> </span><br/>

<span class="kw">assume </span><a NAME="E2:1_1_1"/>
<font color="Maroon" title="c1">X</font> is  <a href="xtuple_0.html#V1" title="XTUPLE_0:attr.1">pair</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">x1</font>, <font color="Maroon" title="c3">x2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E4:1_1_1"/><span class="lab"><font color="Green" title="E2">A2</font></span>: 
<font color="Maroon" title="c1">X</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="c2">x1</font>,<font color="Maroon" title="c3">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xtuple_0.html#D1" onmouseover="rs('xtuple_0/D1')" onmouseout="rh()">XTUPLE_0:def 1</a></span>;<br/>
<a NAME="E5:1_1_1"/>
<font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">x1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:1_1_1"><span class="lab"><font color="Green" title="E2">A2</font></span></a>, <a class="ref" href="tarski.html#D5" onmouseover="rs('tarski/D5')" onmouseout="rh()">TARSKI:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:1_1_1"><span class="lab"><font color="Green" title="E2">A2</font></span></a>, <a class="txt" href="#E1:1_1_1"><span class="lab"><font color="Green" title="E1">A1</font></span></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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