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<span class="kw">take </span>
 <a href="proofs_1.html#K11" title="PROOFS_1:func.11">Theorems</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">R</font>)
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="proofs_1.html#K11" title="PROOFS_1:func.11">Theorems</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">R</font>) is <font color="Maroon" title="c1">X</font> <a href="proofs_1.html#V6" title="PROOFS_1:attr.6">-extending</a>  &amp;  <a href="proofs_1.html#K11" title="PROOFS_1:func.11">Theorems</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">R</font>) is <font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V18" title="PROOFS_1:attr.18">-closed</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E1:103_2_1"/>
(  <a href="proofs_1.html#K11" title="PROOFS_1:func.11">Theorems</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">R</font>) is <font color="Maroon" title="c1">X</font> <a href="proofs_1.html#V6" title="PROOFS_1:attr.6">-extending</a>  &amp;  <a href="proofs_1.html#K11" title="PROOFS_1:func.11">Theorems</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">R</font>) is <font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V18" title="PROOFS_1:attr.18">-closed</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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