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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">PR</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="calcul_1.html#K4" target="_self">set_of_CQC-WFF-seq</a> ,<a href="cqc_the1.html#K2">Proof_Step_Kinds</a> </span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>



<b>assume </b><a NAME="E1:48"/><i><font color="Green">E52</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">PR</font> )
 ;<br/>

<a NAME="E2:48"/>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">PR</font>
 
<b>by </b><i>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E3:48"/><b>then </b>
<font color="Maroon">PR</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">PR</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E4:48"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">PR</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font></span>)</span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R2">in</a>  <a href="calcul_1.html#K4" target="_self">set_of_CQC-WFF-seq</a> 
 
<b>by </b><i><a class="ref" href="mcart_1.html#T10">MCART_1:10</a></i>;<br/>
<b>hence </b><a NAME="E5:48"/>
<span class="p1">(<span class="default"><font color="Maroon">PR</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font></span>)</span> <a href="mcart_1.html#K1">`1</a>  is    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> 
 <b>by </b><i/>;<br/>


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