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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">S</font> is  <a href="toprealc.html#V2" title="TOPREALC:attr.2">real-functions-membered</a>  implies <font color="Maroon" title="c1">S</font> is  <a href="toprealc.html#V1" title="TOPREALC:attr.1">complex-functions-membered</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:38_1_1"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> is  <a href="valued_2.html#V3" title="VALUED_2:attr.3">real-functions-membered</a> 
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="toprealc.html#D2" target="_self" title="TOPREALC:def.2">TOPREALC:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">S</font> is  <a href="toprealc.html#V1" title="TOPREALC:attr.1">complex-functions-membered</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="valued_2.html#D2" title="VALUED_2:def.2">VALUED_2:def 2</a>,<a class="ref" href="toprealc.html#D1" target="_self" title="TOPREALC:def.1">TOPREALC:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> or <font color="Maroon" title="c2">x</font> is    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E2:38_1_1"/>
(  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> or <font color="Maroon" title="c2">x</font> is    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></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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