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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/>



<b>thus </b><a NAME="E1:6"/>
( <font color="Maroon">c<sub>2</sub></font> is   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">c<sub>1</sub></font> implies (  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a>  &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> ) ) )
 <b>by </b><i><a class="txt" href="tbsp_1.html#E5"><i><font color="Green">Lemma5</font></i></a></i>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:6"/><i><font color="Green">E6</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></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">E7</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E4:6"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  holds <br/><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="tbsp_1.html#E3:6"><i><font color="Green">E7</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:6"/>
<font color="Maroon">c<sub>2</sub></font> is   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="tbsp_1.html#E2:6"><i><font color="Green">E6</font></i></a>, <a class="txt" href="tbsp_1.html#E5"><i><font color="Green">Lemma5</font></i></a></i>;<br/>


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