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<b>let </b><font color="Maroon">IT</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A</font>,<font color="Maroon">C</font>;<br/>

<a NAME="E1:130_2_2"/><i><font color="Green">E46</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="mcart_1.html#K16">pr2</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="mcart_1.html#D13">MCART_1:def 13</a></i>;<br/>
<a NAME="E2:130_2_2"/><b>then </b><i><font color="Green">E47</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="mcart_1.html#K16">pr2</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:130_2_2"/>
( <font color="Maroon">IT</font> <a href="hidden.html#R1">=</a>  <a href="mcart_1.html#K16">pr2</a> <font color="Maroon">f</font> implies for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font> holds  <font color="Maroon">IT</font> <a href="funct_2.html#K3" target="_self">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3" target="_self">.</a> <font color="Olive">x</font></span>)</span> <a href="mcart_1.html#K2">`2</a>  )
 <b>by </b><i>, <a class="ref" href="mcart_1.html#D13">MCART_1:def 13</a></i>;<br/>

<b>assume </b><a NAME="E4:130_2_2"/>
for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font> holds  <font color="Maroon">IT</font> <a href="funct_2.html#K3" target="_self">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3" target="_self">.</a> <font color="Olive">x</font></span>)</span> <a href="mcart_1.html#K2">`2</a> 
 ;<br/>

<a NAME="E5:130_2_2"/><b>then </b><i><font color="Green">E112</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> holds <br/><font color="Maroon">IT</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font></span>)</span> <a href="mcart_1.html#K2">`2</a> 
 
;<br/>
<a NAME="E6:130_2_2"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">IT</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E7:130_2_2"/>
<font color="Maroon">IT</font> <a href="hidden.html#R1">=</a>  <a href="mcart_1.html#K16">pr2</a> <font color="Maroon">f</font>
 <b>by </b><i>, <a class="ref" href="mcart_1.html#D13">MCART_1:def 13</a></i>;<br/>


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