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<span class="kw">set </span><font color="Maroon" title="c2">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="c3">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">take </span><font color="Maroon" title="c4">E</font> =  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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="c4">E</font> is  <a href="proofs_1.html#V11" title="PROOFS_1:attr.11">consistent</a> </span><br/>

<a NAME="E1:70_1_1"/>
<font color="Maroon" title="c1">P</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="c5">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:70_1_1"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
( <font color="Maroon" title="c5">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="c5">a</font> )
 ;<br/>
<a NAME="E4:70_1_1"/>
( <font color="Maroon" title="c5">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="c4">E</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="c4">E</font> <a href="proofs_1.html#R3" title="PROOFS_1:pred.3">|-</a> <font color="Maroon" title="c5">a</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:70_1_1"><span class="lab"><font color="Green" title="E28">A1</font></span></a></span>;<br/>
<a NAME="E5:70_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="c4">E</font> is  <a href="proofs_1.html#V10" title="PROOFS_1:attr.10">consistent</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E6:70_1_1"/>
<font color="Maroon" title="c4">E</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"> verum</span><br/>


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