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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> = the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>assume </b><a NAME="E1:52"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="orders_2.html#V4">antisymmetric</a>
 ;<br/>

<a NAME="E2:52"/><b>then </b>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="relat_2.html#R4">is_antisymmetric_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="orders_2.html#D6">ORDERS_2:def 6</a></i>;<br/>
<a NAME="E3:52"/><b>then </b>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="relat_2.html#V4">antisymmetric</a>
 
<b>by </b><i><a class="ref" href="oposet_1.html#T11" target="_self">Th11</a></i>;<br/>
<b>hence </b><a NAME="E4:52"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="oposet_1.html#V7" target="_self">SubAntisymmetric</a>
 <b>by </b><i><a class="ref" href="oposet_1.html#D15" target="_self">Def15</a></i>;<br/>


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