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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:59_1_1_1"/>
( <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>  or <font color="Maroon" title="c2">Y</font> <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>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_1_1_1_1"><b>suppose </b></a><a NAME="E1:59_1_1_1_1"/>
<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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g</font> is  <a href="funct_2.html#V1" title="FUNCT_2:attr.1">quasi_total</a> <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><br/><div class="add"><b>hence </b><a NAME="E2:59_1_1_1_1"/>
<font color="Maroon" title="c3">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g</font> is  <a href="funct_2.html#V1" title="FUNCT_2:attr.1">quasi_total</a> <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"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_1_1_1_2"><b>suppose </b></a><a NAME="E1:59_1_1_1_2"/><i><font color="Green" title="E19">S</font></i>: 
<font color="Maroon" title="c2">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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"> <font color="Maroon" title="c3">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g</font> is  <a href="funct_2.html#V1" title="FUNCT_2:attr.1">quasi_total</a> <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><br/><div class="add"><a NAME="E2:59_1_1_1_2"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Y</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T67" target="_self" title="FUNCT_2:th.67">Th67</a></i>;<br/><b>then </b> <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g</font></span>)</span> = 
<font color="Maroon" title="c4">g</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Maroon" title="c2">Y</font>
<b>by </b><i><a class="ref" href="relat_1.html#T182" title="RELAT_1:th.182">RELAT_1:182</a></i>
<br/>.= 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g</font>
<b>by </b><i><a class="ref" href="relset_1.html#T38" title="RELSET_1:th.38">RELSET_1:38</a></i>
<br/>.= 
<font color="Maroon" title="c1">X</font>
<b>by </b><i><a class="txt" href="#E1:59_1_1_1_2"><i><font color="Green" title="E19">S</font></i></a>, <a class="ref" href="funct_2.html#D1" target="_self" title="FUNCT_2:def.1">Def1</a></i>
;<br/><b>hence </b><a NAME="E4:59_1_1_1_2"/>
<font color="Maroon" title="c3">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">g</font> is  <a href="funct_2.html#V1" title="FUNCT_2:attr.1">quasi_total</a> <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="funct_2.html#D1" target="_self" title="FUNCT_2:def.1">Def1</a>, <a class="txt" href="#E1:59_1_1_1_2"><i><font color="Green" title="E19">S</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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