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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</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">R</font> being   <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font><br/> for <font color="Olive" title="b2">S</font> being   <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font> holds <br/> (  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">*</a> <font color="Olive" title="b2">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">S</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b1">R</font></span>)</span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">*</a> <font color="Olive" title="b2">S</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b2">S</font> )</span><br/><b>let </b><font color="Maroon" title="c4">R</font> be    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>; <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">S</font> being   <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font> holds <br/> (  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">*</a> <font color="Olive" title="b1">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">S</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c4">R</font></span>)</span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">*</a> <font color="Olive" title="b1">S</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Olive" title="b1">S</font> )</span><br/><b>let </b><font color="Maroon" title="c5">S</font> be    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">*</a> <font color="Maroon" title="c5">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c4">R</font></span>)</span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">*</a> <font color="Maroon" title="c5">S</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c5">S</font> )</span><br/>









<b>thus </b><i><font color="Green" title="E30">A1</font></i>:  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">*</a> <font color="Maroon" title="c5">S</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">*</a> <font color="Maroon" title="c5">S</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c1">A</font>
<b>by </b><i><a class="ref" href="relset_2.html#T51" target="_self" title="RELSET_2:th.51">Th51</a></i>
<br/>.= 
<font color="Maroon" title="c5">S</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c1">A</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T159" title="RELAT_1:th.159">RELAT_1:159</a></i>
<br/>.= 
<font color="Maroon" title="c5">S</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c4">R</font></span>)</span>
<b>by </b><i><a class="ref" href="relset_2.html#T51" target="_self" title="RELSET_2:th.51">Th51</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">*</a> <font color="Maroon" title="c5">S</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c5">S</font></span><br/>

<a NAME="E2:62"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c4">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">R</font>
 
;<br/>
<a NAME="E3:62"/><b>then </b>
<font color="Maroon" title="c5">S</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c4">R</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">S</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T156" title="RELAT_1:th.156">RELAT_1:156</a></i>;<br/>
<b>hence </b><a NAME="E4:62"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="relset_2.html#K6" title="RELSET_2:func.6">*</a> <font color="Maroon" title="c5">S</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c5">S</font>
 <b>by </b><i><a class="txt" href="relset_2.html#E1:62"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="relset_2.html#T51" target="_self" title="RELSET_2:th.51">Th51</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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