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<b>let </b><font color="Maroon">N</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="metric_1.html#L1">MetrStruct</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>



<b>thus </b><a NAME="E1:6"/>
( <font color="Maroon">f</font> is   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">N</font> implies (  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a>  &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font> ) ) )
 <b>by </b><i/>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:6"/><i><font color="Green">E44</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a> 
 <b>and </b><br/><a NAME="E3:6"/><i><font color="Green">E45</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>
 ;<br/>

<a NAME="E4:6"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:6"/>
<font color="Maroon">f</font> is   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">N</font>
 <b>by </b><i>, </i>;<br/>


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