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<b>let </b><font color="Maroon">z1</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">L</font>, <font color="Maroon">z2</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">L</font>;<br/>

<b>assume </b><a NAME="E1:15_1_2"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">z1</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">i</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">i</font></span>)</span>
 ;<br/>

<b>assume </b><a NAME="E2:15_1_2"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">z2</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">i</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">i</font></span>)</span>
 ;<br/>

<i><font color="Green">E51</font></i>:  <a href="relat_1.html#K1">dom</a> <font color="Maroon">z1</font> = 
 <a href="numbers.html#K5">NAT</a> 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">z2</font>
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:15_1_2_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">z1</font>
 ;<br/><b>then reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>thus </b><font color="Maroon">z1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">x'</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">x'</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">z2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:15_1_2"/>
<font color="Maroon">z1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">z2</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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