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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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b2">f</font> being   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">PartFunc</a> of <font color="Maroon" title="c1">C</font>,<font color="Olive" title="b1">V</font> holds <br/> ( <font color="Olive" title="b2">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  iff  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Olive" title="b2">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">V</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</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> being   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">PartFunc</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">V</font> holds <br/> ( <font color="Olive" title="b1">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  iff  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</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="c3">f</font> be   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">PartFunc</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">V</font>; <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> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  iff  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Maroon" title="c3">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  )</span><br/>





<span class="kw">thus </span><a NAME="E1:44"/>
( <font color="Maroon" title="c3">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  implies  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Maroon" title="c3">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Maroon" title="c3">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  implies <font color="Maroon" title="c3">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:44"/><span class="lab"><font color="Green" title="E15">A2</font></span>: 
 <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Maroon" title="c3">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</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> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> </span><br/>

<a NAME="E3:44"/>
 <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Maroon" title="c3">f</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="vfunct_1.html#K4" title="VFUNCT_1:func.4">(#)</a> <font color="Maroon" title="c3">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vfunct_1.html#T23" target="_self" title="VFUNCT_1:th.23">Th29</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:44"/>
<font color="Maroon" title="c3">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="#E2:44"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="ref" href="vfunct_1.html#T34" target="_self" title="VFUNCT_1:th.34">Th40</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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