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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>assume </b><a NAME="E1:109"/><i><font color="Green" title="E54">A1</font></i>: 
<span class="p1">(<span class="default"><a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a><br/>

<b>consider </b><font color="Maroon" title="c5">h</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1">(<span class="default"><a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c4">g</font></span>)</span>;<br/>
<a NAME="E3:109"/><i><font color="Green" title="E55">A2</font></i>: 
( <font color="Maroon" title="c5">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c3">f</font> &amp; <font color="Maroon" title="c5">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c4">g</font> )
 
<b>by </b><i><a class="txt" href="partfun1.html#E1:109"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">h</font> = <font color="Maroon" title="c5">h</font> as   <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> <b>by </b><i><a class="ref" href="partfun1.html#T168" target="_self" title="PARTFUN1:th.168">Th168</a></i>;<br/>
<a NAME="E5:109"/>
( <font color="Maroon" title="c6">h</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp; <font color="Maroon" title="c3">f</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c6">h</font> &amp; <font color="Maroon" title="c4">g</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c6">h</font> )
 
<b>by </b><i><a class="txt" href="partfun1.html#E3:109"><i><font color="Green" title="E55">A2</font></i></a>, <a class="ref" href="partfun1.html#T169" target="_self" title="PARTFUN1:th.169">Th169</a>, <a class="ref" href="partfun1.html#T171" target="_self" title="PARTFUN1:th.171">Th171</a></i>;<br/>
<b>hence </b><a NAME="E6:109"/>
<font color="Maroon" title="c3">f</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c4">g</font>
 <b>by </b><i><a class="ref" href="partfun1.html#T158" target="_self" title="PARTFUN1:th.158">Th158</a></i>;<br/>


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