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<span class="kw">thus </span><a NAME="E1:52_1_1"/>
( <font color="Maroon" title="c3">a</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V5" title="PROOFS_1:attr.5">-provable</a>  implies  for <font color="Olive" title="b1">C</font> being   <a href="proofs_1.html#NM9" title="PROOFS_1:NM.9">Extension</a> of <font color="Maroon" title="c1">B</font><br/>  for <font color="Olive" title="b2">E</font> being   <a href="proofs_1.html#NM11" title="PROOFS_1:NM.11">Extension</a> of <font color="Maroon" title="c2">R</font> holds  <font color="Olive" title="b1">C</font>,<font color="Olive" title="b2">E</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c3">a</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="proofs_1.html#T15" target="_self" onmouseover="rs('proofs_1/T15')" onmouseout="rh()">Th54</a></span>; <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"> ( (  for <font color="Olive" title="b1">C</font> being   <a href="proofs_1.html#NM9" title="PROOFS_1:NM.9">Extension</a> of <font color="Maroon" title="c1">B</font><br/>  for <font color="Olive" title="b2">E</font> being   <a href="proofs_1.html#NM11" title="PROOFS_1:NM.11">Extension</a> of <font color="Maroon" title="c2">R</font> holds  <font color="Olive" title="b1">C</font>,<font color="Olive" title="b2">E</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c3">a</font> ) implies <font color="Maroon" title="c3">a</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V5" title="PROOFS_1:attr.5">-provable</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:52_1_1"/><span class="lab"><font color="Green" title="E25">A10</font></span>: 
 for <font color="Olive" title="b1">C</font> being   <a href="proofs_1.html#NM9" title="PROOFS_1:NM.9">Extension</a> of <font color="Maroon" title="c1">B</font><br/>  for <font color="Olive" title="b2">E</font> being   <a href="proofs_1.html#NM11" title="PROOFS_1:NM.11">Extension</a> of <font color="Maroon" title="c2">R</font> holds  <font color="Olive" title="b1">C</font>,<font color="Olive" title="b2">E</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c3">a</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"> <font color="Maroon" title="c3">a</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V5" title="PROOFS_1:attr.5">-provable</a> </span><br/>

<a NAME="E3:52_1_1"/>
( <font color="Maroon" title="c1">B</font> is <font color="Maroon" title="c1">B</font> <a href="proofs_1.html#V6" title="PROOFS_1:attr.6">-extending</a>  &amp; <font color="Maroon" title="c2">R</font> is <font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V7" title="PROOFS_1:attr.7">-extending</a>  )
 
;<br/>
<span class="kw">hence </span><a NAME="E4:52_1_1"/>
<font color="Maroon" title="c3">a</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V5" title="PROOFS_1:attr.5">-provable</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52_1_1"><span class="lab"><font color="Green" title="E25">A10</font></span></a></span>; <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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