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<span class="kw">let </span><font color="Maroon" title="c1">B</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">  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">R</font> being   <a href="proofs_1.html#NM2" title="PROOFS_1:NM.2">Rule</a><br/>  for <font color="Olive" title="b3">E</font> being   <a href="proofs_1.html#NM11" title="PROOFS_1:NM.11">Extension</a> of <font color="Olive" title="b2">R</font><br/>  for <font color="Olive" title="b4">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Maroon" title="c1">B</font>,<font color="Olive" title="b2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b4">a</font> holds <br/><font color="Olive" title="b1">C</font>,<font color="Olive" title="b3">E</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b4">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">C</font> be   <a href="proofs_1.html#NM9" title="PROOFS_1:NM.9">Extension</a> of <font color="Maroon" title="c1">B</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">  for <font color="Olive" title="b1">R</font> being   <a href="proofs_1.html#NM2" title="PROOFS_1:NM.2">Rule</a><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="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Maroon" title="c1">B</font>,<font color="Olive" title="b1">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b3">a</font> holds <br/><font color="Maroon" title="c2">C</font>,<font color="Olive" title="b2">E</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b3">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">R</font> be   <a href="proofs_1.html#NM2" title="PROOFS_1:NM.2">Rule</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">  for <font color="Olive" title="b1">E</font> being   <a href="proofs_1.html#NM11" title="PROOFS_1:NM.11">Extension</a> of <font color="Maroon" title="c3">R</font><br/>  for <font color="Olive" title="b2">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c3">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b2">a</font> holds <br/><font color="Maroon" title="c2">C</font>,<font color="Olive" title="b1">E</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b2">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">E</font> be   <a href="proofs_1.html#NM11" title="PROOFS_1:NM.11">Extension</a> of <font color="Maroon" title="c3">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">  for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c3">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b1">a</font> holds <br/><font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c4">E</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b1">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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"> ( <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c3">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c5">a</font> implies <font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c4">E</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c5">a</font> )</span><br/>









<a NAME="E1:51"/>
( <font color="Maroon" title="c2">C</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="c4">E</font> is <font color="Maroon" title="c3">R</font> <a href="proofs_1.html#V7" title="PROOFS_1:attr.7">-extending</a>  )
 
;<br/>
<span class="kw">hence </span><a NAME="E2:51"/>
( <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c3">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c5">a</font> implies <font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c4">E</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c5">a</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="proofs_1.html#T5" target="_self" onmouseover="rs('proofs_1/T5')" onmouseout="rh()">Th44</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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