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<span class="kw">set </span><font color="Maroon" title="c1">a</font> =  the    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c2">X</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"> the    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">B</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T2" onmouseover="rs('xboole_1/T2')" onmouseout="rh()">XBOOLE_1:2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">R</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="proofs_1.html#NM2" title="PROOFS_1:NM.2">Rule</a> ;<br/>
<a NAME="E4:66_1_1"/>
(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c4">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c2">X</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">rng</a> <font color="Maroon" title="c4">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">X</font> )
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">R</font> = <font color="Maroon" title="c4">R</font> as    <a href="proofs_1.html#M1" title="PROOFS_1:mode.1">Rule</a> of <font color="Maroon" title="c2">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="proofs_1.html#D2" target="_self" onmouseover="rs('proofs_1/D2')" onmouseout="rh()">Def2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">P</font> =  <a href="proofs_1.html#G1" title="PROOFS_1:aggr.1">ProofSystem</a>(# <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c5">R</font> #) as   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="proofs_1.html#L1" title="PROOFS_1:struct.1">ProofSystem</a>  ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c6">P</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="c6">P</font> is  <a href="proofs_1.html#V10" title="PROOFS_1:attr.10">consistent</a>  &amp; <font color="Maroon" title="c6">P</font> is  <a href="proofs_1.html#V9" title="PROOFS_1:attr.9">strict</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E7:66_1_1"/>
<font color="Maroon" title="c6">P</font> is  <a href="proofs_1.html#V10" title="PROOFS_1:attr.10">consistent</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="c6">P</font> is  <a href="proofs_1.html#V9" title="PROOFS_1:attr.9">strict</a> </span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="66_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">take </span>
 the    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> 
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="proofs_1.html#D19" target="_self" onmouseover="rs('proofs_1/D19')" onmouseout="rh()">PROOFS_1:def 19</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"> (  the    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">P</font> &amp;  not <font color="Maroon" title="c6">P</font> <a href="proofs_1.html#R3" title="PROOFS_1:pred.3">|-</a>  the    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E1:66_1_1_1"/>
 the    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">P</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</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">  not <font color="Maroon" title="c6">P</font> <a href="proofs_1.html#R3" title="PROOFS_1:pred.3">|-</a>  the    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> </span><br/>

<a NAME="E2:66_1_1_1"/>
(  not  the    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> &amp; (  for <font color="Olive" title="b1">S</font> being   <a href="proofs_1.html#NM3" title="PROOFS_1:NM.3">Formula-finset</a>  holds <br/>(  not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">S</font>, the    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> </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="c5">R</font> or  ex <font color="Olive" title="b2">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">S</font> &amp;  not <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c5">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b2">b</font> ) ) ) )
 
;<br/>
<span class="kw">hence </span><a NAME="E3:66_1_1_1"/>
 not <font color="Maroon" title="c6">P</font> <a href="proofs_1.html#R3" title="PROOFS_1:pred.3">|-</a>  the    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="proofs_1.html#T12" target="_self" onmouseover="rs('proofs_1/T12')" onmouseout="rh()">Th51</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">thus </span><a NAME="E8:66_1_1"/>
<font color="Maroon" title="c6">P</font> is  <a href="proofs_1.html#V9" title="PROOFS_1:attr.9">strict</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"> verum</span><br/>


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