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<b>let </b><font color="Maroon" title="c1">f</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/><b>let </b><font color="Maroon" title="c2">A</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>



<b>assume </b><a NAME="E1:36"/><i><font color="Green" title="E23">A1</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">f</font></span>)</span>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:36"/>
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_3.html#K3" title="FUNCT_3:func.3">"</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c2">A</font>
 ;<br/>

<a NAME="E3:36"/><b>then </b><i><font color="Green" title="E24">A2</font></i>: 
( <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="funct_3.html#K3" title="FUNCT_3:func.3">"</a> <font color="Maroon" title="c1">f</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="funct_3.html#K3" title="FUNCT_3:func.3">"</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> )
 
<b>by </b><i><a class="ref" href="funct_1.html#D13" title="FUNCT_1:def.13">FUNCT_1:def 13</a></i>;<br/>
<a NAME="E4:36"/><b>then </b>
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_3.html#D2" target="_self" title="FUNCT_3:def.2">Def2</a></i>;<br/>
<a NAME="E5:36"/><b>then </b>
( <font color="Maroon" title="c3">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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="c1">f</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> )
 
<b>by </b><i><a class="txt" href="funct_3.html#E3:36"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="funct_3.html#D2" target="_self" title="FUNCT_3:def.2">Def2</a></i>;<br/>
<a NAME="E6:36"/><b>then </b>
( <font color="Maroon" title="c1">f</font> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c1">f</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c1">f</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">f</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="funct_3.html#E1:36"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="funct_1.html#T147" title="FUNCT_1:th.147">FUNCT_1:147</a></i>;<br/>
<a NAME="E7:36"/><b>then </b>
( <span class="p1">(<span class="default"><a href="funct_3.html#K1" title="FUNCT_3:func.1">.:</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c1">f</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c1">f</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="funct_3.html#K1" title="FUNCT_3:func.1">.:</a> <font color="Maroon" title="c1">f</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_3.html#D1" target="_self" title="FUNCT_3:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E8:36"/>
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_3.html#K1" title="FUNCT_3:func.1">.:</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a></i>;<br/>


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