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<b>let </b><font color="Maroon" title="c1">f</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:24_1"/>
<font color="Maroon" title="c1">f</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ;<br/><b>then reconsider </b><font color="Maroon" title="c2">g</font> = <font color="Maroon" title="c1">f</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/><a NAME="E3:24_1"/><i><font color="Green" title="E14">A1</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><a NAME="E4:24_1"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds <br/><font color="Maroon" title="c2">g</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">x</font> is <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>
 ;<br/><b>hence </b><a NAME="E5:24_1"/>
<font color="Maroon" title="c1">f</font> is   <a href="seqm_3.html#NM1" title="SEQM_3:NM.1">Seq_of_Nat</a>
 <b>by </b><i><a class="txt" href="real_3.html#E3:24_1"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="real_3.html#T10" target="_self" title="REAL_3:th.10">Th10</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:24"/>
<font color="Maroon" title="c1">f</font> is   <a href="seqm_3.html#NM1" title="SEQM_3:NM.1">Seq_of_Nat</a>
 ;<br/>

<a NAME="E3:24"/><b>then </b>
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="seqm_3.html#D8" title="SEQM_3:def.8">SEQM_3:def 8</a></i>;<br/>
<b>hence </b><a NAME="E4:24"/>
<font color="Maroon" title="c1">f</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="ref" href="funct_2.html#T4" title="FUNCT_2:th.4">FUNCT_2:4</a></i>;<br/>


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