<?xml version="1.0"?>
<div class="add">

<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">R</font>, <font color="Olive" title="b2">R1</font>, <font color="Olive" title="b3">R2</font> being   <a href="proofs_1.html#NM2" title="PROOFS_1:NM.2">Rule</a> holds <br/> ( <font color="Olive" title="b2">R1</font> <a href="proofs_1.html#K5" title="PROOFS_1:func.5">\/</a> <font color="Olive" title="b3">R2</font> is <font color="Maroon" title="c1">B</font>,<font color="Olive" title="b1">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</a>  iff ( <font color="Olive" title="b2">R1</font> is <font color="Maroon" title="c1">B</font>,<font color="Olive" title="b1">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</a>  &amp; <font color="Olive" title="b3">R2</font> is <font color="Maroon" title="c1">B</font>,<font color="Olive" title="b1">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">R</font>, <font color="Maroon" title="c3">R1</font>, <font color="Maroon" title="c4">R2</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"> ( <font color="Maroon" title="c3">R1</font> <a href="proofs_1.html#K5" title="PROOFS_1:func.5">\/</a> <font color="Maroon" title="c4">R2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</a>  iff ( <font color="Maroon" title="c3">R1</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</a>  &amp; <font color="Maroon" title="c4">R2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</a>  ) )</span><br/>







<span class="kw">thus </span><a NAME="E1:54"/>
( <font color="Maroon" title="c3">R1</font> <a href="proofs_1.html#K5" title="PROOFS_1:func.5">\/</a> <font color="Maroon" title="c4">R2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</a>  implies ( <font color="Maroon" title="c3">R1</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</a>  &amp; <font color="Maroon" title="c4">R2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</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="c3">R1</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</a>  &amp; <font color="Maroon" title="c4">R2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</a>  implies <font color="Maroon" title="c3">R1</font> <a href="proofs_1.html#K5" title="PROOFS_1:func.5">\/</a> <font color="Maroon" title="c4">R2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</a>  )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="54_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:54_1"/><span class="lab"><font color="Green" title="E25">A1</font></span>: 
<font color="Maroon" title="c3">R1</font> <a href="proofs_1.html#K5" title="PROOFS_1:func.5">\/</a> <font color="Maroon" title="c4">R2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</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="c3">R1</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</a>  &amp; <font color="Maroon" title="c4">R2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E2:54_1"/>
<font color="Maroon" title="c3">R1</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</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="c4">R2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</a> </span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="54_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">S</font> be   <a href="proofs_1.html#NM3" title="PROOFS_1:NM.3">Formula-finset</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="proofs_1.html#D15" target="_self" onmouseover="rs('proofs_1/D15')" onmouseout="rh()">PROOFS_1:def 15</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">t</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Olive" title="b1">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> holds <br/><font color="Maroon" title="c1">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b1">t</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">t</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"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c6">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> implies <font color="Maroon" title="c1">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c6">t</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:54_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c6">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</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="c1">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c6">t</font></span><br/>

<a NAME="E2:54_1_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c6">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="proofs_1.html#K5" title="PROOFS_1:func.5">\/</a> <font color="Maroon" title="c4">R2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:54_1_1"/>
<font color="Maroon" title="c1">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c6">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_1"><span class="lab"><font color="Green" title="E25">A1</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/>


</div><span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c5">S</font> be   <a href="proofs_1.html#NM3" title="PROOFS_1:NM.3">Formula-finset</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="proofs_1.html#D15" target="_self" onmouseover="rs('proofs_1/D15')" onmouseout="rh()">PROOFS_1:def 15</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">t</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Olive" title="b1">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</font> holds <br/><font color="Maroon" title="c1">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b1">t</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">t</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"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c6">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</font> implies <font color="Maroon" title="c1">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c6">t</font> )</span><br/>



<span class="kw">assume </span><a NAME="E3:54_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c6">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</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="c1">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c6">t</font></span><br/>

<a NAME="E4:54_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c6">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="proofs_1.html#K5" title="PROOFS_1:func.5">\/</a> <font color="Maroon" title="c4">R2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:54_1"/>
<font color="Maroon" title="c1">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c6">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_1"><span class="lab"><font color="Green" title="E25">A1</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/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:54"/><span class="lab"><font color="Green" title="E25">A10</font></span>: 
<font color="Maroon" title="c3">R1</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</a> 
 <span class="kw">and </span><br/><a NAME="E3:54"/><span class="lab"><font color="Green" title="E26">A11</font></span>: 
<font color="Maroon" title="c4">R2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</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="c3">R1</font> <a href="proofs_1.html#K5" title="PROOFS_1:func.5">\/</a> <font color="Maroon" title="c4">R2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V8" title="PROOFS_1:attr.8">-derivable</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">S</font> be   <a href="proofs_1.html#NM3" title="PROOFS_1:NM.3">Formula-finset</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="proofs_1.html#D15" target="_self" onmouseover="rs('proofs_1/D15')" onmouseout="rh()">PROOFS_1:def 15</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">t</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Olive" title="b1">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="proofs_1.html#K5" title="PROOFS_1:func.5">\/</a> <font color="Maroon" title="c4">R2</font> holds <br/><font color="Maroon" title="c1">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b1">t</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">t</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"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c6">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="proofs_1.html#K5" title="PROOFS_1:func.5">\/</a> <font color="Maroon" title="c4">R2</font> implies <font color="Maroon" title="c1">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c6">t</font> )</span><br/>



<span class="kw">assume </span><a NAME="E4:54"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c6">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> <a href="proofs_1.html#K5" title="PROOFS_1:func.5">\/</a> <font color="Maroon" title="c4">R2</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="c1">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c6">t</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="54_2"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:54_2"/><span class="kw">then </span>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c6">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</font> or <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c6">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="54_2_1"><span class="kw">suppose </span></a><a NAME="E1:54_2_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c6">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R1</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="c1">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c6">t</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:54_2_1"/>
<font color="Maroon" title="c1">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c6">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54"><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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="54_2_2"><span class="kw">suppose </span></a><a NAME="E1:54_2_2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c6">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">R2</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="c1">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c6">t</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:54_2_2"/>
<font color="Maroon" title="c1">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c6">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:54"><span class="lab"><font color="Green" title="E26">A11</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
