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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p2"><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></span>)</span> <a href="funcop_1.html#K1" title="FUNCOP_1:func.1">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/>





<a NAME="E1:24"/><i><font color="Green" title="E13">A1</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p3"><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></span>)</span> <a href="funcop_1.html#K1" title="FUNCOP_1:func.1">~</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p2"><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></span>)</span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#D1" target="_self" title="FUNCOP_1:def.1">Def1</a></i>;<br/>
<a NAME="E2:24"/><b>then </b><i><font color="Green" title="E14">A2</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p3"><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></span>)</span> <a href="funcop_1.html#K1" title="FUNCOP_1:func.1">~</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" target="_self" title="FUNCOP_1:th.19">Th19</a></i>;<br/>
<a NAME="E3:24"/><b>then </b><i><font color="Green" title="E15">A3</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p3"><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></span>)</span> <a href="funcop_1.html#K1" title="FUNCOP_1:func.1">~</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" target="_self" title="FUNCOP_1:th.19">Th19</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">z</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p3"><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></span>)</span> <a href="funcop_1.html#K1" title="FUNCOP_1:func.1">~</a> </span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p3"><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></span>)</span> <a href="funcop_1.html#K1" title="FUNCOP_1:func.1">~</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">z</font> )</span><br/><b>assume </b><a NAME="E1:24_1"/><i><font color="Green" title="E16">A4</font></i>: 
<font color="Maroon" title="c4">z</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p3"><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></span>)</span> <a href="funcop_1.html#K1" title="FUNCOP_1:func.1">~</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p3"><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></span>)</span> <a href="funcop_1.html#K1" title="FUNCOP_1:func.1">~</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">z</font></span><br/><a NAME="E2:24_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p2"><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></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">z</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">x</font>,<font color="Maroon" title="c3">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="txt" href="#E2:24"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="funcop_1.html#T13" target="_self" title="FUNCOP_1:th.13">Th13</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p3"><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></span>)</span> <a href="funcop_1.html#K1" title="FUNCOP_1:func.1">~</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">z</font> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="#E1:24"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="#E1:24_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="ref" href="funcop_1.html#D1" target="_self" title="FUNCOP_1:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">z</font>
<b>by </b><i><a class="txt" href="#E2:24"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E1:24_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="ref" href="funcop_1.html#T13" target="_self" title="FUNCOP_1:th.13">Th13</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:24"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p2"><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></span>)</span> <a href="funcop_1.html#K1" title="FUNCOP_1:func.1">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="txt" href="#E3:24"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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