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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being <a href="seq_1.html#NV1" title="SEQ_1:NV.1">real-yielding</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds <br/> ( <span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Olive" title="b2">f2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Olive" title="b2">f2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Olive" title="b2">f2</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Olive" title="b2">f2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> )</span><br/><b>let </b><font color="Maroon" title="c2">f1</font>, <font color="Maroon" title="c3">f2</font> be  <a href="seq_1.html#NV1" title="SEQ_1:NV.1">real-yielding</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> )</span><br/>





<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="rfunct_1.html#K3" title="RFUNCT_1:func.3">^</a> </span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font>
<b>by </b><i><a class="ref" href="rfunct_1.html#T47" target="_self" title="RFUNCT_1:th.47">Th47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="rfunct_1.html#K3" title="RFUNCT_1:func.3">^</a> </span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T61" target="_self" title="RFUNCT_1:th.61">Th61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="rfunct_1.html#K3" title="RFUNCT_1:func.3">^</a> </span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T62" target="_self" title="RFUNCT_1:th.62">Th62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T47" target="_self" title="RFUNCT_1:th.47">Th47</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> )</span><br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="rfunct_1.html#K3" title="RFUNCT_1:func.3">^</a> </span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font>
<b>by </b><i><a class="ref" href="rfunct_1.html#T47" target="_self" title="RFUNCT_1:th.47">Th47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="rfunct_1.html#K3" title="RFUNCT_1:func.3">^</a> </span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T61" target="_self" title="RFUNCT_1:th.61">Th61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f2</font>
<b>by </b><i><a class="ref" href="rfunct_1.html#T47" target="_self" title="RFUNCT_1:th.47">Th47</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span></span><br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="rfunct_1.html#K3" title="RFUNCT_1:func.3">^</a> </span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font>
<b>by </b><i><a class="ref" href="rfunct_1.html#T47" target="_self" title="RFUNCT_1:th.47">Th47</a></i>
<br/>.= 
<font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="rfunct_1.html#K3" title="RFUNCT_1:func.3">^</a> </span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T61" target="_self" title="RFUNCT_1:th.61">Th61</a></i>
<br/>.= 
<font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="rfunct_1.html#K3" title="RFUNCT_1:func.3">^</a> </span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T62" target="_self" title="RFUNCT_1:th.62">Th62</a></i>
<br/>.= 
<font color="Maroon" title="c2">f1</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T47" target="_self" title="RFUNCT_1:th.47">Th47</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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