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<span class="kw">let </span><font color="Maroon" title="c1">C</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">C</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  holds <br/> (  <a href="rfunct_3.html#K19" title="RFUNCT_3:func.19">max+</a> <font color="Olive" title="b1">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  &amp;  <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <font color="Olive" title="b1">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">C</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="rfunct_3.html#K19" title="RFUNCT_3:func.19">max+</a> <font color="Maroon" title="c2">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  &amp;  <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <font color="Maroon" title="c2">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  )</span><br/>



<a NAME="E1:19"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E2:19"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A2</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_3.html#D11" title="RFUNCT_3:def.11">RFUNCT_3:def 11</a></span>;<br/>
<a NAME="E3:19"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K19" title="RFUNCT_3:func.19">max+</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="rfunct_3.html#D10" title="RFUNCT_3:def.10">RFUNCT_3:def 10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:19"/>
(  <a href="rfunct_3.html#K19" title="RFUNCT_3:func.19">max+</a> <font color="Maroon" title="c2">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  &amp;  <a href="rfunct_3.html#K20" title="RFUNCT_3:func.20">max-</a> <font color="Maroon" title="c2">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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