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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="qc_lang1.html#NM5">free_QC-variable</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="qc_lang1.html#K1">QC-variables</a> ;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="cqc_lang.html#NM1">Substitution</a>;<br/>











<b>assume </b><a NAME="E1:13"/><i><font color="Green">E9</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K6" target="_self">.--&gt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K4" target="_self">Subst</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K6" target="_self">.--&gt;</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>thus </b><a NAME="E2:13"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:13_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:13_1"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></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">c<sub>3</sub></font> <a href="cqc_lang.html#K6" target="_self">.--&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K6" target="_self">.--&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" target="_self">Th5</a>, <a class="ref" href="cqc_lang.html#T6" target="_self">Th6</a></i>;<br/>
<b>hence </b><a NAME="E4:13_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="cqc_lang.html#E1:13"><i><font color="Green">E9</font></i></a>, <a class="txt" href="cqc_lang.html#E1:13_1"><i><font color="Green">E10</font></i></a>, <a class="ref" href="cqc_lang.html#D3" target="_self">Def3</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E3:13"/>
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E4:13"/><b>then </b>
not <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E5:13"/><b>then </b>
not <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></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">c<sub>3</sub></font> <a href="cqc_lang.html#K6" target="_self">.--&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" target="_self">Th5</a></i>;<br/>
<b>hence </b><a NAME="E6:13"/>
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="cqc_lang.html#E1:13"><i><font color="Green">E9</font></i></a>, <a class="ref" href="cqc_lang.html#D3" target="_self">Def3</a></i>;<br/>


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