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<b>let </b><font color="Maroon">p1</font> be   <a href="unialg_1.html#NM1">PFuncFinSequence</a> of <font color="Maroon">A</font>, <font color="Maroon">p2</font> be   <a href="unialg_1.html#NM1">PFuncFinSequence</a> of <font color="Maroon">A</font>;<br/>

<b>assume </b><a NAME="E1:15_1_2"/><i><font color="Green">E30</font></i>: 
(  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U0</font> &amp; ( for <font color="Olive">n</font> being   <a href="hidden.html#M1">set</a> <br/> for <font color="Olive">o</font> being  <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">U0</font>  st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p1</font> &amp; <font color="Olive">o</font> <a href="hidden.html#R1">=</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U0</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> holds <br/><font color="Maroon">p1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Olive">o</font> <a href="unialg_2.html#K2" target="_self">/.</a> <font color="Maroon">A</font> ) &amp;  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U0</font> &amp; ( for <font color="Olive">n</font> being   <a href="hidden.html#M1">set</a> <br/> for <font color="Olive">o</font> being  <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">U0</font>  st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p2</font> &amp; <font color="Olive">o</font> <a href="hidden.html#R1">=</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U0</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> holds <br/><font color="Maroon">p2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Olive">o</font> <a href="unialg_2.html#K2" target="_self">/.</a> <font color="Maroon">A</font> ) )
 ;<br/>

<a NAME="E2:15_1_2"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U0</font> holds <br/><font color="Maroon">p1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_2_1"><b>proof </b></a><div class="add">

<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>assume </b><a NAME="E1:15_1_2_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U0</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">k</font> = the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U0</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> as   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">U0</font> <b>by </b><i/>;<br/>
<a NAME="E3:15_1_2_1"/>
( <font color="Maroon">p1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="unialg_2.html#K2" target="_self">/.</a> <font color="Maroon">A</font> &amp; <font color="Maroon">p2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="unialg_2.html#K2" target="_self">/.</a> <font color="Maroon">A</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:15_1_2_1"/>
<font color="Maroon">p1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:15_1_2"/>
<font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T17">FINSEQ_1:17</a></i>;<br/>


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