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<span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> is  <a href="waybel23.html#V4" title="WAYBEL23:attr.4">sups-closed</a>  implies <font color="Maroon" title="c2">S</font> is  <a href="waybel23.html#V2" title="WAYBEL23:attr.2">join-closed</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:21_2_1"/>
<font color="Maroon" title="c2">S</font> is  <a href="waybel23.html#V4" title="WAYBEL23:attr.4">sups-closed</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">S</font> is  <a href="waybel23.html#V2" title="WAYBEL23:attr.2">join-closed</a> </span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">S1</font> =  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">S</font> as   <a href="yellow_0.html#V8" title="YELLOW_0:attr.8">sups-inheriting</a>   <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c1">L</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel23.html#D4" target="_self" title="WAYBEL23:def.4">Def4</a></span>;<br/>
<a NAME="E3:21_2_1"/>
<font color="Maroon" title="c3">S1</font> is  <a href="yellow_0.html#V6" title="YELLOW_0:attr.6">join-inheriting</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E4:21_2_1"/>
<font color="Maroon" title="c2">S</font> is  <a href="waybel23.html#V2" title="WAYBEL23:attr.2">join-closed</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel23.html#D2" target="_self" title="WAYBEL23:def.2">Def2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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