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<b>let </b><font color="Maroon" title="c2">R</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">R</font> is <a href="valued_2.html#V9" title="VALUED_2:attr.9">real-functions-valued</a> implies <font color="Maroon" title="c2">R</font> is <a href="valued_2.html#V7" title="VALUED_2:attr.7">complex-functions-valued</a> )</span><br/>

<b>assume </b><a NAME="E1:66_5_1"/><i><font color="Green" title="E32">A5</font></i>: 
 <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c2">R</font> is <a href="valued_2.html#V3" title="VALUED_2:attr.3">real-functions-membered</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="valued_2.html#D21" target="_self" title="VALUED_2:def.21">VALUED_2:def 21</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">R</font> is <a href="valued_2.html#V7" title="VALUED_2:attr.7">complex-functions-valued</a></span><br/>

<b>let </b><font color="Maroon" title="c3">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="valued_2.html#D1" target="_self" title="VALUED_2:def.1">VALUED_2:def 1</a>,<a class="ref" href="valued_2.html#D19" target="_self" title="VALUED_2:def.19">VALUED_2:def 19</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">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c2">R</font> implies <font color="Maroon" title="c3">y</font> is  <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> )</span><br/>

<b>thus </b><a NAME="E2:66_5_1"/>
( <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c2">R</font> implies <font color="Maroon" title="c3">y</font> is  <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> )
 <b>by </b><i><a class="txt" href="#E1:66_5_1"><i><font color="Green" title="E32">A5</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/>


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