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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>;<br/><b>let </b><font color="Maroon" title="c5">h</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:91"/><i><font color="Green" title="E42">A1</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c5">h</font>
 <b>and </b><br/><a NAME="E2:91"/><i><font color="Green" title="E43">A2</font></i>: 
<font color="Maroon" title="c4">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">f</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c6">x</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="partfun1.html#D6" target="_self" title="PARTFUN1:def.6">PARTFUN1:def 6</a><br/>

<b>assume </b><a NAME="E3:91"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">h</font></span>)</span>
 ;<br/>

<a NAME="E4:91"/><b>then </b>
( <font color="Maroon" title="c6">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">g</font> &amp; <font color="Maroon" title="c6">x</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> <font color="Maroon" title="c5">h</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font> )
 
<b>by </b><i><a class="txt" href="partfun1.html#E2:91"><i><font color="Green" title="E43">A2</font></i></a>, <a class="ref" href="relat_1.html#T25" title="RELAT_1:th.25">RELAT_1:25</a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E5:91"/><b>then </b>
( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">h</font></span>)</span> &amp; <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> )
 
<b>by </b><i><a class="txt" href="partfun1.html#E2:91"><i><font color="Green" title="E43">A2</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:91"/>
<font color="Maroon" title="c4">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
 <b>by </b><i><a class="txt" href="partfun1.html#E1:91"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="partfun1.html#D6" target="_self" title="PARTFUN1:def.6">Def6</a></i>;<br/>


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