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<span class="kw">reconsider </span><font color="Maroon" title="c4">F</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> as   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c3">P</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="setfam_1.html#T61" title="SETFAM_1:th.61">SETFAM_1:61</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">F</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c4">F</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Maroon" title="c4">F</font> is  <a href="pcs_0.html#V22" title="PCS_0:attr.22">pcs-self-coherent-membered</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E2:197_1_1"/>
not <font color="Maroon" title="c4">F</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">F</font> is  <a href="pcs_0.html#V22" title="PCS_0:attr.22">pcs-self-coherent-membered</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">S</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">P</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="pcs_0.html#D44" target="_self" title="PCS_0:def.44">PCS_0:def 44</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> implies <font color="Maroon" title="c5">S</font> is  <a href="pcs_0.html#V21" title="PCS_0:attr.21">pcs-self-coherent</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E3:197_1_1"/>
<font color="Maroon" title="c5">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">S</font> is  <a href="pcs_0.html#V21" title="PCS_0:attr.21">pcs-self-coherent</a> </span><br/>

<a NAME="E4:197_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:197_1_1"/>
<font color="Maroon" title="c5">S</font> is  <a href="pcs_0.html#V21" title="PCS_0:attr.21">pcs-self-coherent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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