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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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  <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> holds <br/><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></span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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> implies <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> )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c5">h</font> =  the    <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/>
<span class="kw">assume </span><a NAME="E1:83"/><span class="lab"><font color="Green" title="E40">A1</font></span>: 
<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> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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></span><br/>

<a NAME="E2:83"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A2</font></span>: 
 the    <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> <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E3:83"/><span class="lab"><font color="Green" title="E42">A3</font></span>: 
 the    <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> <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:83"><span class="lab"><font color="Green" title="E40">A1</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">h</font> =  the    <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> 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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:83"><span class="lab"><font color="Green" title="E41">A2</font></span></a>, <a class="ref" href="partfun1.html#T69" target="_self" title="PARTFUN1:th.69">Th168</a></span>;<br/>
<a NAME="E5:83"/><span class="lab"><font color="Green" title="E43">A4</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:83"><span class="lab"><font color="Green" title="E42">A3</font></span></a>, <a class="ref" href="partfun1.html#T71" target="_self" title="PARTFUN1:th.71">Th171</a></span>;<br/>
<a NAME="E6:83"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:83"><span class="lab"><font color="Green" title="E41">A2</font></span></a>, <a class="ref" href="partfun1.html#T71" target="_self" title="PARTFUN1:th.71">Th171</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:83"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:83"><span class="lab"><font color="Green" title="E41">A2</font></span></a>, <a class="txt" href="#E5:83"><span class="lab"><font color="Green" title="E43">A4</font></span></a>, <a class="ref" href="partfun1.html#T67" target="_self" title="PARTFUN1:th.67">Th158</a>, <a class="ref" href="partfun1.html#T70" target="_self" title="PARTFUN1:th.70">Th169</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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