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<b>thus </b><a NAME="E1:7_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a> implies for <font color="Olive">b<sub>1</sub></font> being non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>3</sub></font> <a href="waybel_0.html#R4">preserves_sup_of</a> <font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="waybel_0.html#D37">WAYBEL_0:def 37</a></i>;<br/>

<b>assume </b><a NAME="E2:7_1_1"/><i><font color="Green">E5</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>3</sub></font> <a href="waybel_0.html#R4">preserves_sup_of</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D37">WAYBEL_0:def 37</a><br/>

<b>thus </b><a NAME="E3:7_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> is <a href="xboole_0.html#V1">empty</a> or  not <font color="Maroon">c<sub>4</sub></font> is <a href="waybel_0.html#V1">directed</a> or <font color="Maroon">c<sub>3</sub></font> <a href="waybel_0.html#R4">preserves_sup_of</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="yellow14.html#E2:7_1_1"><i><font color="Green">E5</font></i></a></i>;<br/>


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