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<b>set </b><font color="Maroon" title="c2">SL</font> =  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">L</font></span>)</span>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>$1 is  <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a> <a href="yellow_0.html#V7" title="YELLOW_0:attr.7">infs-inheriting</a>  <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c1">L</font>;<br/>
<a NAME="E1:38_1_1"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">L</font></span>)</span>]
 
;<br/>
<a NAME="E2:38_1_1"/>
 <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">L</font></span>)</span> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K4" title="WAYBEL10:func.4">Sub</a> <font color="Maroon" title="c1">L</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel10.html#D3" target="_self" title="WAYBEL10:def.3">Def3</a></i>;<br/>
<a NAME="E3:38_1_1"/><b>then </b><i><font color="Green" title="E19">A2</font></i>: 
 <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K4" title="WAYBEL10:func.4">Sub</a> <font color="Maroon" title="c1">L</font></span>)</span>
 
;<br/>
<b>consider </b><font color="Maroon" title="c3">S</font> being  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a> <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>  <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of  <a href="waybel10.html#K4" title="WAYBEL10:func.4">Sub</a> <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E5:38_1_1"/><i><font color="Green" title="E20">A3</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K4" title="WAYBEL10:func.4">Sub</a> <font color="Maroon" title="c1">L</font></span>)</span> holds <br/> ( <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">S</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>] )
 <b>from </b><i><a class="ref" href="waybel10.html#S1" target="_self" title="WAYBEL10:sch.1">WAYBEL10:sch 1</a>(<a class="txt" href="waybel10.html#E1:38_1_1"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="waybel10.html#E3:38_1_1"><i><font color="Green" title="E19">A2</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon" title="c3">S</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">R</font> being <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Olive" title="b1">R</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">S</font> iff ( <font color="Olive" title="b1">R</font> is <a href="yellow_0.html#V7" title="YELLOW_0:attr.7">closure</a> &amp; <font color="Olive" title="b1">R</font> is <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a> ) )</span><br/>

<b>let </b><font color="Maroon" title="c4">R</font> be  <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">R</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">S</font> iff ( <font color="Maroon" title="c4">R</font> is <a href="yellow_0.html#V7" title="YELLOW_0:attr.7">closure</a> &amp; <font color="Maroon" title="c4">R</font> is <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a> ) )</span><br/>

<a NAME="E6:38_1_1"/>
<font color="Maroon" title="c4">R</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K4" title="WAYBEL10:func.4">Sub</a> <font color="Maroon" title="c1">L</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel10.html#D3" target="_self" title="WAYBEL10:def.3">Def3</a></i>;<br/>
<b>hence </b><a NAME="E7:38_1_1"/>
( <font color="Maroon" title="c4">R</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">S</font> iff ( <font color="Maroon" title="c4">R</font> is <a href="yellow_0.html#V7" title="YELLOW_0:attr.7">closure</a> &amp; <font color="Maroon" title="c4">R</font> is <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a> ) )
 <b>by </b><i><a class="txt" href="waybel10.html#E5:38_1_1"><i><font color="Green" title="E20">A3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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