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<b>let </b><font color="Maroon">y1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y2</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:30_1_2"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">y2</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y2</font> )
 ;<br/>

<a NAME="E2:30_1_2"/><b>then </b>
( <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y1</font> <a href="hidden.html#R2">in</a>  <a href="pua2mss1.html#K3" target="_self">rng</a> <font color="Maroon">P</font> &amp; <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y2</font> <a href="hidden.html#R2">in</a>  <a href="pua2mss1.html#K3" target="_self">rng</a> <font color="Maroon">P</font> &amp; <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y2</font> )
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E3:30_1_2"/><b>then </b>
<font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y2</font>
 
<b>by </b><i>, <a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E4:30_1_2"/>
<font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>


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