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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">R</font> being   <a href="proofs_1.html#NM2" title="PROOFS_1:NM.2">Rule</a><br/>  for <font color="Olive" title="b2">B1</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b2">B1</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> &amp; (  for <font color="Olive" title="b4">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">B1</font> holds <br/><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="b4">b</font> ) holds <br/><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></span><br/><span class="kw">let </span><font color="Maroon" title="c2">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">B1</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">B1</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b2">a</font> &amp; (  for <font color="Olive" title="b3">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">B1</font> holds <br/><font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b3">b</font> ) holds <br/><font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</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="c3">B1</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">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Maroon" title="c3">B1</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">a</font> &amp; (  for <font color="Olive" title="b2">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B1</font> holds <br/><font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b2">b</font> ) holds <br/><font color="Maroon" title="c1">B</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">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">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="c3">B1</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c4">a</font> &amp; (  for <font color="Olive" title="b1">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B1</font> holds <br/><font color="Maroon" title="c1">B</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">b</font> ) implies <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c4">a</font> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:50"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
<font color="Maroon" title="c3">B1</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c4">a</font>
 <span class="kw">and </span><br/><a NAME="E2:50"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
 for <font color="Olive" title="b1">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B1</font> holds <br/><font color="Maroon" title="c1">B</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">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"> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c4">a</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c5">S</font> being   <a href="proofs_1.html#NM3" title="PROOFS_1:NM.3">Formula-finset</a><span class="kw"> such that </span><br/><a NAME="E4:50"/><span class="lab"><font color="Green" title="E26">A3</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">S</font>
 <span class="kw">and </span><br/><a NAME="E5:50"/><span class="lab"><font color="Green" title="E27">A4</font></span>: 
<font color="Maroon" title="c5">S</font> is <font color="Maroon" title="c3">B1</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="proofs_1.html#T7" target="_self" onmouseover="rs('proofs_1/T7')" onmouseout="rh()">Th45</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">S1</font> = <font color="Maroon" title="c3">B1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c5">S</font>;<br/>
<a NAME="E6:50"/>
 for <font color="Olive" title="b1">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c5">S</font> holds <br/><font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" onmouseover="rs('xboole_0/D4')" onmouseout="rh()">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E7:50"/><span class="kw">then </span>
 for <font color="Olive" title="b1">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c5">S</font> holds <br/><font color="Maroon" title="c1">B</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">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E25">A2</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">S2</font> being   <a href="proofs_1.html#NM3" title="PROOFS_1:NM.3">Formula-finset</a><span class="kw"> such that </span><br/><a NAME="E9:50"/><span class="lab"><font color="Green" title="E28">A7</font></span>: 
<font color="Maroon" title="c3">B1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c5">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">S2</font>
 <span class="kw">and </span><br/><a NAME="E10:50"/><span class="lab"><font color="Green" title="E29">A8</font></span>: 
<font color="Maroon" title="c7">S2</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="proofs_1.html#T9" target="_self" onmouseover="rs('proofs_1/T9')" onmouseout="rh()">Th47</a></span>;<br/>
<a NAME="E11:50"/>
<font color="Maroon" title="c5">S</font> is <font color="Maroon" title="c7">S2</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:50"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="txt" href="#E9:50"><span class="lab"><font color="Green" title="E28">A7</font></span></a>, <a class="ref" href="proofs_1.html#T10" target="_self" onmouseover="rs('proofs_1/T10')" onmouseout="rh()">Th48</a></span>;<br/>
<a NAME="E12:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A10</font></span>: 
<font color="Maroon" title="c7">S2</font> <a href="proofs_1.html#K3" title="PROOFS_1:func.3">\/</a> <font color="Maroon" title="c5">S</font> is <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:50"><span class="lab"><font color="Green" title="E29">A8</font></span></a>, <a class="ref" href="proofs_1.html#T13" target="_self" onmouseover="rs('proofs_1/T13')" onmouseout="rh()">Th52</a></span>;<br/>
<a NAME="E13:50"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">S2</font> <a href="proofs_1.html#K3" title="PROOFS_1:func.3">\/</a> <font color="Maroon" title="c5">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:50"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <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="E14:50"/>
<font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c4">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:50"><span class="lab"><font color="Green" title="E30">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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