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<span class="kw">let </span><font color="Maroon" title="c1">P</font> be   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> ; <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">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">P</font>  st <font color="Maroon" title="c1">P</font> is  <a href="proofs_1.html#V10" title="PROOFS_1:attr.10">consistent</a>  &amp;  not <font color="Maroon" title="c1">P</font> is  <a href="proofs_1.html#V12" title="PROOFS_1:attr.12">paraconsistent</a>  &amp; <font color="Olive" title="b1">B</font> is  <a href="proofs_1.html#V11" title="PROOFS_1:attr.11">consistent</a>  holds <br/> ex <font color="Olive" title="b2">B1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">P</font> st <br/>( <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">B1</font> &amp; <font color="Olive" title="b2">B1</font> is  <a href="proofs_1.html#V17" title="PROOFS_1:attr.17">maximally-consistent</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">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="c1">P</font> is  <a href="proofs_1.html#V10" title="PROOFS_1:attr.10">consistent</a>  &amp;  not <font color="Maroon" title="c1">P</font> is  <a href="proofs_1.html#V12" title="PROOFS_1:attr.12">paraconsistent</a>  &amp; <font color="Maroon" title="c2">B</font> is  <a href="proofs_1.html#V11" title="PROOFS_1:attr.11">consistent</a>  implies  ex <font color="Olive" title="b1">B1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">P</font> st <br/>( <font color="Maroon" title="c2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">B1</font> &amp; <font color="Olive" title="b1">B1</font> is  <a href="proofs_1.html#V17" title="PROOFS_1:attr.17">maximally-consistent</a>  ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:95"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
( <font color="Maroon" title="c1">P</font> is  <a href="proofs_1.html#V10" title="PROOFS_1:attr.10">consistent</a>  &amp;  not <font color="Maroon" title="c1">P</font> is  <a href="proofs_1.html#V12" title="PROOFS_1:attr.12">paraconsistent</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"> (  not <font color="Maroon" title="c2">B</font> is  <a href="proofs_1.html#V11" title="PROOFS_1:attr.11">consistent</a>  or  ex <font color="Olive" title="b1">B1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">P</font> st <br/>( <font color="Maroon" title="c2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">B1</font> &amp; <font color="Olive" title="b1">B1</font> is  <a href="proofs_1.html#V17" title="PROOFS_1:attr.17">maximally-consistent</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E2:95"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
<font color="Maroon" title="c2">B</font> is  <a href="proofs_1.html#V11" title="PROOFS_1:attr.11">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">  ex <font color="Olive" title="b1">B1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">P</font> st <br/>( <font color="Maroon" title="c2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">B1</font> &amp; <font color="Olive" title="b1">B1</font> is  <a href="proofs_1.html#V17" title="PROOFS_1:attr.17">maximally-consistent</a>  )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c3">S</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">P</font><span class="kw"> such that </span><br/><a NAME="E4:95"/><span class="lab"><font color="Green" title="E39">A3</font></span>: 
<font color="Maroon" title="c3">S</font> is  <a href="proofs_1.html#NV14" title="PROOFS_1:NV.14">inconsistent</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:95"><span class="lab"><font color="Green" title="E37">A1</font></span></a></span>;<br/>
<a NAME="E5:95"/><span class="lab"><font color="Green" title="E40">A5</font></span>: 
 for <font color="Olive" title="b1">B1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">P</font> holds <br/> ( <font color="Olive" title="b1">B1</font> is  <a href="proofs_1.html#V11" title="PROOFS_1:attr.11">consistent</a>  iff <font color="Olive" title="b1">B1</font> is <font color="Maroon" title="c3">S</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="#E4:95"><span class="lab"><font color="Green" title="E39">A3</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">B1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">P</font><span class="kw"> such that </span><br/><a NAME="E7:95"/><span class="lab"><font color="Green" title="E41">A10</font></span>: 
<font color="Maroon" title="c2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B1</font>
 <span class="kw">and </span><br/><a NAME="E8:95"/><span class="lab"><font color="Green" title="E42">A11</font></span>: 
<font color="Maroon" title="c4">B1</font> is <font color="Maroon" title="c3">S</font> <a href="proofs_1.html#V14" title="PROOFS_1:attr.14">-maximally-omitting</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:95"><span class="lab"><font color="Green" title="E38">A2</font></span></a>, <a class="ref" href="proofs_1.html#T22" target="_self" onmouseover="rs('proofs_1/T22')" onmouseout="rh()">Th61</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">B1</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="c2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B1</font> &amp; <font color="Maroon" title="c4">B1</font> is  <a href="proofs_1.html#V17" title="PROOFS_1:attr.17">maximally-consistent</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E9:95"/>
<font color="Maroon" title="c2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:95"><span class="lab"><font color="Green" title="E41">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"> <font color="Maroon" title="c4">B1</font> is  <a href="proofs_1.html#V17" title="PROOFS_1:attr.17">maximally-consistent</a> </span><br/>

<span class="kw">thus </span><a NAME="E10:95"/>
<font color="Maroon" title="c4">B1</font> is  <a href="proofs_1.html#V17" title="PROOFS_1:attr.17">maximally-consistent</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:95"><span class="lab"><font color="Green" title="E40">A5</font></span></a>, <a class="txt" href="#E8:95"><span class="lab"><font color="Green" title="E42">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/>


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