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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>, <a href="numbers.html#K7" title="NUMBERS:func.7">ExtREAL</a> ;<br/>





<a NAME="E1:36"/><i><font color="Green" title="E23">A1</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> )
 
<b>by </b><i><a class="ref" href="mesfunc7.html#T19" target="_self" title="MESFUNC7:th.19">Th19</a></i>;<br/>
<a NAME="E2:36"/><b>then </b><i><font color="Green" title="E24">A2</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">g</font> )
 
<b>by </b><i><a class="ref" href="mesfunc1.html#D10" title="MESFUNC1:def.10">MESFUNC1:def 10</a></i>;<br/>
<a NAME="E3:36"/>
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_1.html#T68" title="FUNCT_1:th.68">FUNCT_1:68</a></i>;<br/>
<a NAME="E4:36"/><b>then </b><i><font color="Green" title="E25">A3</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> )
 
<b>by </b><i><a class="txt" href="mesfunc7.html#E2:36"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></i>;<br/>
<a NAME="E5:36"/><b>then </b><i><font color="Green" title="E26">A4</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p4"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p4"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> )
 
<b>by </b><i><a class="ref" href="mesfunc1.html#D10" title="MESFUNC1:def.10">MESFUNC1:def 10</a></i>;<br/>
<a NAME="E6:36"/><i><font color="Green" title="E27">A5</font></i>: 
( <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p4"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> &amp; <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p4"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> )
 
<b>by </b><i><a class="ref" href="mesfunc7.html#T18" target="_self" title="MESFUNC7:th.18">Th18</a></i>;<br/>
<b>then </b><i><font color="Green" title="E28">A6</font></i>:  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p4"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <span class="p2">(<span class="default"><span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p4"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p4"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p4"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="mesfunc7.html#T19" target="_self" title="MESFUNC7:th.19">Th19</a></i>
<br/>.= 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span>
<b>by </b><i><a class="txt" href="mesfunc7.html#E4:36"><i><font color="Green" title="E25">A3</font></i></a></i>
;<br/>
<a NAME="E8:36"/>
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">g</font></span>)</span>
 
<b>by </b><i><a class="txt" href="mesfunc7.html#E2:36"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="xboole_1.html#T27" title="XBOOLE_1:th.27">XBOOLE_1:27</a></i>;<br/>
<a NAME="E9:36"/><b>then </b><i><font color="Green" title="E29">A7</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="mesfunc7.html#T19" target="_self" title="MESFUNC7:th.19">Th19</a></i>;<br/>
<a NAME="E10:36"/><b>then </b><i><font color="Green" title="E30">A8</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font>;<br/><b>assume </b><a NAME="E1:36_2"/><i><font color="Green" title="E31">A9</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span>
 ;<br/><b>then </b><i><font color="Green" title="E32">A10</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font> = 
<span class="p1">(<span class="default"><span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font>
<b>by </b><i><a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font></span>)</span>
<b>by </b><i><a class="txt" href="mesfunc7.html#E9:36"><i><font color="Green" title="E29">A7</font></i></a>, <a class="txt" href="mesfunc7.html#E10:36"><i><font color="Green" title="E30">A8</font></i></a>, <a class="txt" href="mesfunc7.html#E1:36_2"><i><font color="Green" title="E31">A9</font></i></a>, <a class="ref" href="mesfunc1.html#D3" title="MESFUNC1:def.3">MESFUNC1:def 3</a></i>
<br/>.= 
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font></span>)</span>
<b>by </b><i><a class="txt" href="mesfunc7.html#E1:36"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="mesfunc7.html#E10:36"><i><font color="Green" title="E30">A8</font></i></a>, <a class="txt" href="mesfunc7.html#E1:36_2"><i><font color="Green" title="E31">A9</font></i></a>, <a class="ref" href="mesfunc1.html#D10" title="MESFUNC1:def.10">MESFUNC1:def 10</a></i>
;<br/><a NAME="E3:36_2"/><i><font color="Green" title="E33">A11</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span>
 <b>by </b><i><a class="txt" href="mesfunc7.html#E9:36"><i><font color="Green" title="E29">A7</font></i></a>, <a class="txt" href="mesfunc7.html#E1:36_2"><i><font color="Green" title="E31">A9</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p4"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <span class="p2">(<span class="default"><span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p4"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p4"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p4"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font></span>)</span>
<b>by </b><i><a class="txt" href="mesfunc7.html#E7:36"><i><font color="Green" title="E28">A6</font></i></a>, <a class="ref" href="mesfunc1.html#D3" title="MESFUNC1:def.3">MESFUNC1:def 3</a></i>
<br/>.= 
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p5"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p5"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font></span>)</span>
<b>by </b><i><a class="txt" href="mesfunc7.html#E5:36"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="mesfunc7.html#E6:36"><i><font color="Green" title="E27">A5</font></i></a>, <a class="txt" href="mesfunc7.html#E3:36_2"><i><font color="Green" title="E33">A11</font></i></a>, <a class="ref" href="mesfunc1.html#D10" title="MESFUNC1:def.10">MESFUNC1:def 10</a></i>
<br/>.= 
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p5"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p5"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
<b>by </b><i><a class="txt" href="mesfunc7.html#E5:36"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="mesfunc7.html#E3:36_2"><i><font color="Green" title="E33">A11</font></i></a>, <a class="ref" href="mesfunc1.html#D10" title="MESFUNC1:def.10">MESFUNC1:def 10</a></i>
<br/>.= 
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p4">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p5"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
<b>by </b><i><a class="txt" href="mesfunc7.html#E3:36_2"><i><font color="Green" title="E33">A11</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
<b>by </b><i><a class="txt" href="mesfunc7.html#E3:36_2"><i><font color="Green" title="E33">A11</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E5:36_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p4"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <span class="p2">(<span class="default"><span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p4"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c4">x</font>
 <b>by </b><i><a class="txt" href="mesfunc7.html#E1:36"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="mesfunc7.html#E10:36"><i><font color="Green" title="E30">A8</font></i></a>, <a class="txt" href="mesfunc7.html#E1:36_2"><i><font color="Green" title="E31">A9</font></i></a>, <a class="txt" href="mesfunc7.html#E2:36_2"><i><font color="Green" title="E32">A10</font></i></a>, <a class="ref" href="mesfunc1.html#D10" title="MESFUNC1:def.10">MESFUNC1:def 10</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:36"/>
<span class="p1">(<span class="default"><span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p3"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><font color="Maroon" title="c3">g</font></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2"><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="mesfunc1.html#K12" title="MESFUNC1:func.12">+</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="mesfunc7.html#K1" title="MESFUNC7:func.1">.|</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="mesfunc7.html#E7:36"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="mesfunc7.html#E10:36"><i><font color="Green" title="E30">A8</font></i></a>, <a class="ref" href="partfun1.html#T34" title="PARTFUN1:th.34">PARTFUN1:34</a></i>;<br/>


</div>
