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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>set </b><font color="Maroon">X</font> =  <a href="numbers.html#K5">NAT</a> ;<br/>
<b>set </b><font color="Maroon">f</font> = <font color="Maroon">n</font> <a href="comput_1.html#K7" target="_self">succ</a> <font color="Maroon">i</font>;<br/>
<a NAME="E1:68"/><i><font color="Green">E48</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="comput_1.html#K7" target="_self">succ</a> <font color="Maroon">i</font></span>)</span> <a href="tarski.html#R1">c=</a> <a href="numbers.html#K5">NAT</a>  <a href="finseq_2.html#K3">*</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E2:68"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="comput_1.html#K7" target="_self">succ</a> <font color="Maroon">i</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="seqm_3.html#D8">SEQM_3:def 8</a></i>;<br/>
<a NAME="E3:68"/><b>then </b>
<font color="Maroon">n</font> <a href="comput_1.html#K7" target="_self">succ</a> <font color="Maroon">i</font> is   <a href="partfun1.html#NM1">PartFunc</a> of <a href="numbers.html#K5">NAT</a>  <a href="finseq_2.html#K3">*</a> , <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i>, <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/>
<a NAME="E4:68"/><b>then </b>
<font color="Maroon">n</font> <a href="comput_1.html#K7" target="_self">succ</a> <font color="Maroon">i</font> is    <a href="rfunct_3.html#M2">Element</a> of  <a href="rfunct_3.html#K4">PFuncs</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="finseq_2.html#K3">*</a> </span>)</span>,<a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="partfun1.html#T119">PARTFUN1:119</a></i>;<br/>
<a NAME="E5:68"/><b>then </b>
<font color="Maroon">n</font> <a href="comput_1.html#K7" target="_self">succ</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">g</font> where <font color="Olive">g</font> is    <a href="rfunct_3.html#M2">Element</a> of  <a href="rfunct_3.html#K4">PFuncs</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="finseq_2.html#K3">*</a> </span>)</span>,<a href="numbers.html#K5">NAT</a>  : <font color="Olive">g</font> is <a href="comput_1.html#V4" target="_self">homogeneous</a> </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E6:68"/>
<font color="Maroon">n</font> <a href="comput_1.html#K7" target="_self">succ</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a> 
 ;<br/>


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