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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">f</font>, <font color="Olive" title="b2">g</font> being   <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font>  st  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> holds <br/> <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">*</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font></span><br/><b>let </b><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font> be    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> implies  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">*</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:60"/><i><font color="Green" title="E20">A1</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font>
 <b>and </b><br/><a NAME="E2:60"/><i><font color="Green" title="E21">A2</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">*</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font></span><br/>

<b>thus </b> <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">*</a> <font color="Maroon" title="c2">f</font></span>)</span> = 
<font color="Maroon" title="c2">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c1">X</font>
<b>by </b><i><a class="txt" href="#E2:60"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="relat_1.html#T160" title="RELAT_1:th.160">RELAT_1:160</a></i>
<br/>.= 
<font color="Maroon" title="c1">X</font>
<b>by </b><i><a class="txt" href="#E1:60"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="relset_1.html#T38" title="RELSET_1:th.38">RELSET_1:38</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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