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<a NAME="E1:28_1_1"/><i><font color="Green">E34</font></i>: 
 <a href="relat_1.html#K1">dom</a> <a href="scmfsa_1.html#K6" target="_self">SCM+FSA-OK</a>  <a href="hidden.html#R1">=</a>  <a href="numbers.html#K4">INT</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E2:28_1_1"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K4">INT</a> 
 
<b>by </b><i><a class="ref" href="card_3.html#T18">CARD_3:18</a></i>;<br/>
<b>then </b><i><font color="Green">E35</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">u</font></span>)</span></span>)</span> = 
<a href="numbers.html#K4">INT</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">u</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<a href="numbers.html#K4">INT</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">t</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <a href="scmfsa_1.html#K6" target="_self">SCM+FSA-OK</a> 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:28_1_1_2"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmfsa_1.html#K6" target="_self">SCM+FSA-OK</a> 
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:28_1_1_2_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> or <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">t</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:28_1_1_2_1_1_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 ;<br/><div class="add"><a NAME="E2:28_1_1_2_1_1_1"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">t</font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">u</font></span>)</span>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/><a NAME="E3:28_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">u</font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">u</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">t</font> = 
<span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">u</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">t</font>
<b>by </b><i><a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon">u</font>
<b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>
;<br/><a NAME="E5:28_1_1_2_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">u</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K4">INT</a> 
 <b>by </b><i><a class="ref" href="int_1.html#D2">INT_1:def 2</a></i>;<br/><b>hence </b><a NAME="E6:28_1_1_2_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">u</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_1.html#K6" target="_self">SCM+FSA-OK</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:28_1_1_2_1_1_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">t</font>
 ;<br/><div class="add"><a NAME="E2:28_1_1_2_1_1_2"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">t</font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">u</font></span>)</span>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/><a NAME="E3:28_1_1_2_1_1_2"/><b>then </b>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">u</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E4:28_1_1_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">u</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/><b>hence </b><a NAME="E5:28_1_1_2_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">u</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_1.html#K6" target="_self">SCM+FSA-OK</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="card_3.html#T18">CARD_3:18</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:28_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">u</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_1.html#K6" target="_self">SCM+FSA-OK</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:28_1_1"/>
<font color="Maroon">s</font> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">u</font></span>)</span> is   <a href="scmfsa_1.html#NM1">SCM+FSA-State</a>
 <b>by </b><i>, <a class="ref" href="card_3.html#T18">CARD_3:18</a></i>;<br/>


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