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<div><i><font color="Green">E25</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><a NAME="E1:38_1_1_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><a NAME="E2:38_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="waybel_3.html#K6">.</a> <font color="Maroon">c<sub>3</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#D5">FUNCT_1:def 5</a></i>;<br/><b>hence </b><a NAME="E3:38_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="waybel_3.html#K6">.</a> <font color="Maroon">c<sub>3</sub></font> is   <a href="orders_2.html#NM1">Poset</a>
 <b>by </b><i><a class="ref" href="yellow16.html#D5" target="_self">Def5</a></i>;<br/></div><b>end;</b></div>
<a NAME="E2:38_1_1"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>2</sub></font> <a href="waybel_3.html#K6">.</a> <font color="Olive">b<sub>1</sub></font> is <a href="orders_2.html#V3">transitive</a>
 
;<br/>
<b>hence </b><a NAME="E3:38_1_1"/>
 <a href="yellow_1.html#K5">product</a> <font color="Maroon">c<sub>2</sub></font> is <a href="orders_2.html#V3">transitive</a>
 <b>by </b><i><a class="ref" href="waybel_3.html#T29">WAYBEL_3:29</a></i>;<br/>

<a NAME="E4:38_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>2</sub></font> <a href="waybel_3.html#K6">.</a> <font color="Olive">b<sub>1</sub></font> is <a href="orders_2.html#V4">antisymmetric</a>
 
<b>by </b><i><a class="txt" href="yellow16.html#E1:38_1_1"><i><font color="Green">E25</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:38_1_1"/>
 <a href="yellow_1.html#K5">product</a> <font color="Maroon">c<sub>2</sub></font> is <a href="orders_2.html#V4">antisymmetric</a>
 <b>by </b><i><a class="ref" href="waybel_3.html#T30">WAYBEL_3:30</a></i>;<br/>


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