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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#V8" title="VALUED_2:attr.8">ext-real-functions-valued</a> )</span><br/>

<b>assume </b><a NAME="E1:66_4_1"/><i><font color="Green" title="E32">A4</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#V8" title="VALUED_2:attr.8">ext-real-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#D2" target="_self" title="VALUED_2:def.2">VALUED_2:def 2</a>,<a class="ref" href="valued_2.html#D20" target="_self" title="VALUED_2:def.20">VALUED_2:def 20</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#V2" title="VALUED_0:attr.2">ext-real-valued</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> )</span><br/>

<b>thus </b><a NAME="E2:66_4_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#V2" title="VALUED_0:attr.2">ext-real-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_4_1"><i><font color="Green" title="E32">A4</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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