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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:59_1_1_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pre_circ.html#K3">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/><b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:59_1_1_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pre_circ.html#K3">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E4:59_1_1_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pre_circ.html#K3">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="dickson.html#E1:59_1_1_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><a NAME="E5:59_1_1_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="dickson.html#E3:59_1_1_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><a NAME="E6:59_1_1_1"/><b>then </b><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pre_circ.html#K3">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/><a NAME="E7:59_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="dickson.html#E5:59_1_1_1"><i><font color="Green">E45</font></i></a></i>;<br/><a NAME="E8:59_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><a NAME="E9:59_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="funct_1.html#T12">FUNCT_1:12</a></i>;<br/><b>hence </b><a NAME="E10:59_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> is    <a href="orders_2.html#L1">RelStr</a> 
 <b>by </b><i><a class="txt" href="dickson.html#E4:59_1_1_1"><i><font color="Green">E44</font></i></a>, <a class="txt" href="dickson.html#E6:59_1_1_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="yellow_1.html#D3">YELLOW_1:def 3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:59_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="pre_circ.html#K3">|</a> <font color="Maroon">c<sub>3</sub></font> is <a href="yellow_1.html#V1">RelStr-yielding</a>
 <b>by </b><i><a class="ref" href="yellow_1.html#D3">YELLOW_1:def 3</a></i>;<br/>


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