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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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being  <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>  st ( <font color="Maroon" title="c2">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) &amp; <font color="Olive" title="b1">f</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Olive" title="b2">g</font> holds <br/> <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Olive" title="b1">f</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Olive" title="b2">g</font></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c2">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) &amp; <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> implies  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c3">f</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c4">g</font> )</span><br/>





<b>assume </b><a NAME="E1:83"/>
( ( <font color="Maroon" title="c2">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) &amp; <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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c3">f</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c4">g</font></span><br/>

<b>then consider </b><font color="Maroon" title="c5">h</font> being   <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> such that </b><br/><a NAME="E3:83"/><i><font color="Green" title="E41">A1</font></i>: 
( <font color="Maroon" title="c5">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="c5">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="c5">h</font> )
 <b>by </b><i><a class="ref" href="partfun1.html#T162" target="_self" title="PARTFUN1:th.162">Th162</a></i>;<br/>
<a NAME="E4:83"/>
( <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="#E3:83"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="partfun1.html#D7" target="_self" title="PARTFUN1:def.7">Def7</a></i>;<br/>
<b>hence </b><a NAME="E5:83"/>
<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> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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