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<b>let </b><font color="Maroon">i1</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">i2</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>given </b><font color="Maroon">f</font> being  <a href="comput_1.html#V4" target="_self">homogeneous</a> <a href="funct_1.html#NM1">Function</a><b> such that </b><a NAME="E1:53_1_2_1"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font>
 ;<br/><b>assume </b><a NAME="E2:53_1_2_1"/>
for <font color="Olive">f</font> being <a href="comput_1.html#V4" target="_self">homogeneous</a> <a href="funct_1.html#NM1">Function</a>  st <font color="Olive">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> holds <br/><font color="Maroon">i1</font> <a href="hidden.html#R1">=</a>  <a href="comput_1.html#K3" target="_self">arity</a> <font color="Olive">f</font>
 ;<br/><a NAME="E3:53_1_2_1"/><b>then </b>
<font color="Maroon">i1</font> <a href="hidden.html#R1">=</a>  <a href="comput_1.html#K3" target="_self">arity</a> <font color="Maroon">f</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:53_1_2_1"/>
( ( for <font color="Olive">f</font> being <a href="comput_1.html#V4" target="_self">homogeneous</a> <a href="funct_1.html#NM1">Function</a>  st <font color="Olive">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> holds <br/><font color="Maroon">i2</font> <a href="hidden.html#R1">=</a>  <a href="comput_1.html#K3" target="_self">arity</a> <font color="Olive">f</font> ) implies <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font> )
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:53_1_2"/>
( ( for <font color="Olive">f</font> being <a href="comput_1.html#V4" target="_self">homogeneous</a> <a href="funct_1.html#NM1">Function</a>  holds not <font color="Olive">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> ) &amp; <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> 0 implies <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font> )
 ;<br/>


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