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<div class="add">

<a NAME="E1:89_1_1"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="toler_1.html#K1">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T56" target="_self">Th56</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> =  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> #) as  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V1">strict</a> <a href="yellow_0.html#V4" target="_self">full</a>  <a href="yellow_0.html#M1" target="_self">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="yellow_0.html#T57" target="_self">Th57</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
;<br/>

<b>thus </b><a NAME="E3:89_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="yellow_0.html#V7" target="_self">infs-inheriting</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D18" target="_self">YELLOW_0:def 18</a><br/>

<b>thus </b><a NAME="E1:89_1_1_1"/>
(  <a href="yellow_0.html#R2" target="_self">ex_inf_of</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> implies  <a href="yellow_0.html#K2" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E4:89_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="yellow_0.html#V8" target="_self">sups-inheriting</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D19" target="_self">YELLOW_0:def 19</a><br/>

<b>thus </b><a NAME="E1:89_1_1_2"/>
(  <a href="yellow_0.html#R1" target="_self">ex_sup_of</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> implies  <a href="yellow_0.html#K1" target="_self">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E5:89_1_1"/>
( not <font color="Maroon">c<sub>2</sub></font> is <a href="struct_0.html#V3">empty</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="yellow_0.html#V4" target="_self">full</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="orders_2.html#V1">strict</a> )
 ;<br/>


</div>
