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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"> ( <font color="Maroon" title="c1">P</font> is  <a href="proofs_1.html#V12" title="PROOFS_1:attr.12">paraconsistent</a>  implies <font color="Maroon" title="c1">P</font> is  <a href="proofs_1.html#V10" title="PROOFS_1:attr.10">consistent</a>  )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c2">S</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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">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">assume </span><a NAME="E2:74_1_1"/>
<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"> <font color="Maroon" title="c1">P</font> is  <a href="proofs_1.html#V10" title="PROOFS_1:attr.10">consistent</a> </span><br/>

<a NAME="E3:74_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">S</font> is  <a href="proofs_1.html#V11" title="PROOFS_1:attr.11">consistent</a> 
 
;<br/>
<a NAME="E4:74_1_1"/><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="c2">S</font> is  <a href="proofs_1.html#V10" title="PROOFS_1:attr.10">consistent</a> 
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E6:74_1_1"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
( <font color="Maroon" title="c3">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K9" title="PROOFS_1:func.9">\/</a> <font color="Maroon" title="c2">S</font> &amp;  not <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K9" title="PROOFS_1:func.9">\/</a> <font color="Maroon" title="c2">S</font> <a href="proofs_1.html#R3" title="PROOFS_1:pred.3">|-</a> <font color="Maroon" title="c3">a</font> )
 ;<br/>
<a NAME="E7:74_1_1"/>
( <font color="Maroon" title="c3">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c1">P</font> &amp;  not <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#R3" title="PROOFS_1:pred.3">|-</a> <font color="Maroon" title="c3">a</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:74_1_1"><span class="lab"><font color="Green" title="E28">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:74_1_1"/>
<font color="Maroon" title="c1">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"> verum</span><br/>


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