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<b>let </b><font color="Maroon" title="c2">i1</font>, <font color="Maroon" title="c3">i2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>given </b><font color="Maroon" title="c4">f</font> being  <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><a NAME="E2:51_1_2_1"/><i><font color="Green" title="E29">A10</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">F</font>
 ;<br/><b>assume </b><a NAME="E3:51_1_2_1"/>
for <font color="Olive" title="b1">f</font> being <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Maroon" title="c2">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Olive" title="b1">f</font>
 ;<br/><a NAME="E4:51_1_2_1"/><b>then </b>
<font color="Maroon" title="c2">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="txt" href="comput_1.html#E2:51_1_2_1"><i><font color="Green" title="E29">A10</font></i></a></i>;<br/><b>hence </b><a NAME="E5:51_1_2_1"/>
( ( for <font color="Olive" title="b1">f</font> being <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Maroon" title="c3">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Olive" title="b1">f</font> ) implies <font color="Maroon" title="c2">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i2</font> )
 <b>by </b><i><a class="txt" href="comput_1.html#E2:51_1_2_1"><i><font color="Green" title="E29">A10</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:51_1_2"/>
( ( for <font color="Olive" title="b1">f</font> being <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  holds not <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">F</font> ) &amp; <font color="Maroon" title="c2">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c3">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <font color="Maroon" title="c2">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i2</font> )
 ;<br/>


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