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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="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</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/><font color="Olive" title="b1">f</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</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="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</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 <font color="Maroon" title="c3">f</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c4">g</font> )</span><br/>





<b>assume </b><a NAME="E1:96"/>
( <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>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <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> or <font color="Maroon" title="c3">f</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c4">g</font> )</span><br/>

<a NAME="E2:96"/><b>then </b>
( <font color="Maroon" title="c3">f</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp; <font color="Maroon" title="c4">g</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> )
 
<b>by </b><i><a class="ref" href="funct_2.html#T132" target="_self" title="FUNCT_2:th.132">Th132</a></i>;<br/>
<b>hence </b><a NAME="E3:96"/>
(  not <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> or <font color="Maroon" title="c3">f</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c4">g</font> )
 <b>by </b><i><a class="ref" href="partfun1.html#T148" title="PARTFUN1:th.148">PARTFUN1:148</a></i>; <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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