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<b>let </b><font color="Maroon">f</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>

<b>assume </b><a NAME="E1:13"/><i><font color="Green">E35</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2
 ;<br/>

<b>thus </b><a NAME="E2:13"/>
( <font color="Maroon">f</font> is <a href="jordan23.html#V2" target="_self">weakly-one-to-one</a> implies <font color="Maroon">f</font> is <a href="jordan23.html#V3" target="_self">poorly-one-to-one</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1"/>
<font color="Maroon">f</font> is <a href="jordan23.html#V2" target="_self">weakly-one-to-one</a>
 ;<br/>

<a NAME="E2:13_1"/><b>then </b>
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:13_1"/>
<font color="Maroon">f</font> is <a href="jordan23.html#V3" target="_self">poorly-one-to-one</a>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E3:13"/>
<font color="Maroon">f</font> is <a href="jordan23.html#V3" target="_self">poorly-one-to-one</a>
 ;<br/>

<a NAME="E4:13"/><b>then </b>
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:13"/>
<font color="Maroon">f</font> is <a href="jordan23.html#V2" target="_self">weakly-one-to-one</a>
 <b>by </b><i/>;<br/>


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