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<b>let </b><font color="Maroon" title="c5">IT</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">C</font>;<br/>

<a NAME="E1:129_2_2"/><i><font color="Green" title="E43">A14</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="mcart_1.html#K16" title="MCART_1:func.16">pr2</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="ref" href="mcart_1.html#D13" title="MCART_1:def.13">MCART_1:def 13</a></i>;<br/>
<a NAME="E2:129_2_2"/><b>then </b><i><font color="Green" title="E44">A15</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="mcart_1.html#K16" title="MCART_1:func.16">pr2</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" target="_self" title="FUNCT_2:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E3:129_2_2"/>
( <font color="Maroon" title="c5">IT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mcart_1.html#K16" title="MCART_1:func.16">pr2</a> <font color="Maroon" title="c4">f</font> implies for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c5">IT</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  )
 <b>by </b><i><a class="txt" href="funct_2.html#E1:129_2_2"><i><font color="Green" title="E43">A14</font></i></a>, <a class="ref" href="mcart_1.html#D13" title="MCART_1:def.13">MCART_1:def 13</a></i>;<br/>

<b>assume </b><a NAME="E4:129_2_2"/>
for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c5">IT</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
 ;<br/>

<a NAME="E5:129_2_2"/><b>then </b><i><font color="Green" title="E45">A16</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</font> holds <br/><font color="Maroon" title="c5">IT</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
 
;<br/>
<a NAME="E6:129_2_2"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">IT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="txt" href="funct_2.html#E1:129_2_2"><i><font color="Green" title="E43">A14</font></i></a>, <a class="txt" href="funct_2.html#E2:129_2_2"><i><font color="Green" title="E44">A15</font></i></a>, <a class="ref" href="funct_2.html#D1" target="_self" title="FUNCT_2:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E7:129_2_2"/>
<font color="Maroon" title="c5">IT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mcart_1.html#K16" title="MCART_1:func.16">pr2</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="txt" href="funct_2.html#E5:129_2_2"><i><font color="Green" title="E45">A16</font></i></a>, <a class="ref" href="mcart_1.html#D13" title="MCART_1:def.13">MCART_1:def 13</a></i>;<br/>


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