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

<span class="kw">set </span><font color="Maroon" title="c3">A</font> =  the <a href="proofs_1.html#U1" title="PROOFS_1:sel.1">Axioms</a> of <font color="Maroon" title="c1">P</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">Obj</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">P</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">R</font> =  the <a href="proofs_1.html#U2" title="PROOFS_1:sel.2">Rules</a> of <font color="Maroon" title="c1">P</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">O</font> =  <a href="proofs_1.html#K10" title="PROOFS_1:func.10">Omit</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">F</font>);<br/>
<span class="kw">let </span><font color="Maroon" title="c7">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">P</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="proofs_1.html#D29" target="_self" onmouseover="rs('proofs_1/D29')" onmouseout="rh()">PROOFS_1:def 29</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="c7">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="proofs_1.html#K10" title="PROOFS_1:func.10">Omit</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">F</font>) iff  for <font color="Olive" title="b1">S</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">B</font> holds  <font color="Olive" title="b1">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="proofs_1.html#K10" title="PROOFS_1:func.10">Omit</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">F</font>) )</span><br/>

<span class="kw">thus </span><a NAME="E1:92_1_1"/>
( <font color="Maroon" title="c7">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="proofs_1.html#K10" title="PROOFS_1:func.10">Omit</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">F</font>) implies  for <font color="Olive" title="b1">S</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">B</font> holds  <font color="Olive" title="b1">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="proofs_1.html#K10" title="PROOFS_1:func.10">Omit</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">F</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">S</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">B</font> holds  <font color="Olive" title="b1">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="proofs_1.html#K10" title="PROOFS_1:func.10">Omit</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">F</font>) ) implies <font color="Maroon" title="c7">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="proofs_1.html#K10" title="PROOFS_1:func.10">Omit</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">F</font>) )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="92_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">set </span><font color="Maroon" title="c8">PB</font> = <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K9" title="PROOFS_1:func.9">\/</a> <font color="Maroon" title="c7">B</font>;<br/>
<span class="kw">assume </span><a NAME="E1:92_1_1_1"/>
<font color="Maroon" title="c7">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="proofs_1.html#K10" title="PROOFS_1:func.10">Omit</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">F</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">S</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">B</font> holds  <font color="Olive" title="b1">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="proofs_1.html#K10" title="PROOFS_1:func.10">Omit</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">F</font>)</span><br/>

<a NAME="E2:92_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A1</font></span>: 
<font color="Maroon" title="c7">B</font> is <font color="Maroon" title="c2">F</font> <a href="proofs_1.html#V13" title="PROOFS_1:attr.13">-omitting</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="proofs_1.html#D25" target="_self" onmouseover="rs('proofs_1/D25')" onmouseout="rh()">Def17</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c9">S</font> be   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">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="c9">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="proofs_1.html#K10" title="PROOFS_1:func.10">Omit</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">F</font>)</span><br/>

<a NAME="E3:92_1_1_1"/>
( <font color="Maroon" title="c9">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">B</font> &amp; <font color="Maroon" title="c7">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">P</font> )
 
;<br/>
<a NAME="E4:92_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">P</font>
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">T</font> = <font color="Maroon" title="c9">S</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">P</font> ;<br/>
<a NAME="E6:92_1_1_1"/>
<font color="Maroon" title="c10">T</font> is <font color="Maroon" title="c2">F</font> <a href="proofs_1.html#V13" title="PROOFS_1:attr.13">-omitting</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:92_1_1_1"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="proofs_1.html#T20" target="_self" onmouseover="rs('proofs_1/T20')" onmouseout="rh()">Th59</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:92_1_1_1"/>
<font color="Maroon" title="c9">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="proofs_1.html#K10" title="PROOFS_1:func.10">Omit</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">F</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"> verum</span><br/>


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

<span class="kw">assume </span><a NAME="E2:92_1_1"/><span class="lab"><font color="Green" title="E36">A10</font></span>: 
 for <font color="Olive" title="b1">S</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">B</font> holds  <font color="Olive" title="b1">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="proofs_1.html#K10" title="PROOFS_1:func.10">Omit</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">F</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="c7">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="proofs_1.html#K10" title="PROOFS_1:func.10">Omit</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">F</font>)</span><br/>

<span class="kw">assume </span><a NAME="E3:92_1_1"/>
 not <font color="Maroon" title="c7">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="proofs_1.html#K10" title="PROOFS_1:func.10">Omit</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">F</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"> contradiction</span><br/>

<a NAME="E4:92_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A11</font></span>: 
 not <font color="Maroon" title="c7">B</font> is <font color="Maroon" title="c2">F</font> <a href="proofs_1.html#V13" title="PROOFS_1:attr.13">-omitting</a> 
 
;<br/>
<a NAME="E5:92_1_1"/>
 for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> holds <br/> the <a href="proofs_1.html#U1" title="PROOFS_1:sel.1">Axioms</a> of <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K8" title="PROOFS_1:func.8">\/</a> <font color="Maroon" title="c7">B</font>, the <a href="proofs_1.html#U2" title="PROOFS_1:sel.2">Rules</a> of <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b1">a</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="92_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">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="c8">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> implies  the <a href="proofs_1.html#U1" title="PROOFS_1:sel.1">Axioms</a> of <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K8" title="PROOFS_1:func.8">\/</a> <font color="Maroon" title="c7">B</font>, the <a href="proofs_1.html#U2" title="PROOFS_1:sel.2">Rules</a> of <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c8">a</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:92_1_1_2"/>
<font color="Maroon" title="c8">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</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">  the <a href="proofs_1.html#U1" title="PROOFS_1:sel.1">Axioms</a> of <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K8" title="PROOFS_1:func.8">\/</a> <font color="Maroon" title="c7">B</font>, the <a href="proofs_1.html#U2" title="PROOFS_1:sel.2">Rules</a> of <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c8">a</font></span><br/>

<a NAME="E2:92_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K9" title="PROOFS_1:func.9">\/</a> <font color="Maroon" title="c7">B</font> <a href="proofs_1.html#R3" title="PROOFS_1:pred.3">|-</a> <font color="Maroon" title="c8">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:92_1_1"><span class="lab"><font color="Green" title="E37">A11</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:92_1_1_2"/>
 the <a href="proofs_1.html#U1" title="PROOFS_1:sel.1">Axioms</a> of <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K8" title="PROOFS_1:func.8">\/</a> <font color="Maroon" title="c7">B</font>, the <a href="proofs_1.html#U2" title="PROOFS_1:sel.2">Rules</a> of <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Maroon" title="c8">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"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">S1</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="E7:92_1_1"/><span class="lab"><font color="Green" title="E38">A12</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">S1</font>
 <span class="kw">and </span><br/><a NAME="E8:92_1_1"/><span class="lab"><font color="Green" title="E39">A13</font></span>: 
<font color="Maroon" title="c8">S1</font> is  the <a href="proofs_1.html#U1" title="PROOFS_1:sel.1">Axioms</a> of <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K8" title="PROOFS_1:func.8">\/</a> <font color="Maroon" title="c7">B</font>, the <a href="proofs_1.html#U2" title="PROOFS_1:sel.2">Rules</a> of <font color="Maroon" title="c1">P</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/>
<span class="kw">set </span><font color="Maroon" title="c9">S2</font> = <font color="Maroon" title="c7">B</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c8">S1</font>;<br/>
<a NAME="E9:92_1_1"/>
( <span class="p1">(<span class="default"> the <a href="proofs_1.html#U1" title="PROOFS_1:sel.1">Axioms</a> of <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K8" title="PROOFS_1:func.8">\/</a> <font color="Maroon" title="c7">B</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c8">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the <a href="proofs_1.html#U1" title="PROOFS_1:sel.1">Axioms</a> of <font color="Maroon" title="c1">P</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c8">S1</font></span>)</span> <a href="proofs_1.html#K8" title="PROOFS_1:func.8">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">B</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c8">S1</font></span>)</span> &amp;  the <a href="proofs_1.html#U1" title="PROOFS_1:sel.1">Axioms</a> of <font color="Maroon" title="c1">P</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c8">S1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="proofs_1.html#U1" title="PROOFS_1:sel.1">Axioms</a> of <font color="Maroon" title="c1">P</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T17" onmouseover="rs('xboole_1/T17')" onmouseout="rh()">XBOOLE_1:17</a>, <a class="ref" href="xboole_1.html#T23" onmouseover="rs('xboole_1/T23')" onmouseout="rh()">XBOOLE_1:23</a></span>;<br/>
<a NAME="E10:92_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">S1</font> is  the <a href="proofs_1.html#U1" title="PROOFS_1:sel.1">Axioms</a> of <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K8" title="PROOFS_1:func.8">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">B</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c8">S1</font></span>)</span>, the <a href="proofs_1.html#U2" title="PROOFS_1:sel.2">Rules</a> of <font color="Maroon" title="c1">P</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="#E8:92_1_1"><span class="lab"><font color="Green" title="E39">A13</font></span></a>, <a class="ref" href="proofs_1.html#T10" target="_self" onmouseover="rs('proofs_1/T10')" onmouseout="rh()">Th48</a>, <a class="ref" href="xboole_1.html#T9" onmouseover="rs('xboole_1/T9')" onmouseout="rh()">XBOOLE_1:9</a></span>;<br/>
<a NAME="E11:92_1_1"/><span class="kw">then </span>
 for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> holds <br/> the <a href="proofs_1.html#U1" title="PROOFS_1:sel.1">Axioms</a> of <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K8" title="PROOFS_1:func.8">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">B</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c8">S1</font></span>)</span>, the <a href="proofs_1.html#U2" title="PROOFS_1:sel.2">Rules</a> of <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b1">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:92_1_1"><span class="lab"><font color="Green" title="E38">A12</font></span></a></span>;<br/>
<a NAME="E12:92_1_1"/><span class="kw">then </span>
 for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> holds <br/><font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K9" title="PROOFS_1:func.9">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">B</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c8">S1</font></span>)</span> <a href="proofs_1.html#R3" title="PROOFS_1:pred.3">|-</a> <font color="Olive" title="b1">a</font>
 
;<br/>
<a NAME="E13:92_1_1"/><span class="kw">then </span>
 not <font color="Maroon" title="c7">B</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c8">S1</font> is <font color="Maroon" title="c2">F</font> <a href="proofs_1.html#V13" title="PROOFS_1:attr.13">-omitting</a> 
 
;<br/>
<a NAME="E14:92_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A15</font></span>: 
 not <font color="Maroon" title="c7">B</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c8">S1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="proofs_1.html#K10" title="PROOFS_1:func.10">Omit</a> (<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">F</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="proofs_1.html#D25" target="_self" onmouseover="rs('proofs_1/D25')" onmouseout="rh()">Def17</a></span>;<br/>
<a NAME="E15:92_1_1"/>
<font color="Maroon" title="c7">B</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c8">S1</font> is   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T17" onmouseover="rs('xboole_1/T17')" onmouseout="rh()">XBOOLE_1:17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E16:92_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:92_1_1"><span class="lab"><font color="Green" title="E36">A10</font></span></a>, <a class="txt" href="#E14:92_1_1"><span class="lab"><font color="Green" title="E40">A15</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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