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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font>, <font color="Maroon" title="c4">d</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> implies <span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c3">c</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E1:12"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c3">c</font>)</span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">f</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>)</span>)</span>;<br/>
<a NAME="E2:12"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
 <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>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>)</span>)</span> <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"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T62" title="FUNCT_4:th.62">FUNCT_4:62</a></span>;<br/>
<a NAME="E3:12"/>
<font color="Maroon" title="c2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E14">A3</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font> = 
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="funct_1.html#T13" title="FUNCT_1:th.13">FUNCT_1:13</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T63" title="FUNCT_4:th.63">FUNCT_4:63</a></span>
<br/>.= 
<font color="Maroon" title="c3">c</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="funct_4.html#T63" title="FUNCT_4:th.63">FUNCT_4:63</a></span>
;<br/>
<a NAME="E5:12"/>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E15">A4</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font> = 
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="funct_1.html#T13" title="FUNCT_1:th.13">FUNCT_1:13</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="funct_4.html#T63" title="FUNCT_4:th.63">FUNCT_4:63</a></span>
<br/>.= 
<font color="Maroon" title="c4">d</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T63" title="FUNCT_4:th.63">FUNCT_4:63</a></span>
;<br/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>)</span>)</span> = 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="funct_4.html#T64" title="FUNCT_4:th.64">FUNCT_4:64</a></span>
<br/>.= 
 <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>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T62" title="FUNCT_4:th.62">FUNCT_4:62</a></span>
;<br/>
<a NAME="E8:12"/><span class="kw">then </span>
 <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>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>)</span>)</span></span>)</span> <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"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="relat_1.html#T27" title="RELAT_1:th.27">RELAT_1:27</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:12"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c1">a</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c3">c</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:12"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E4:12"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</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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