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<span class="kw">thus </span><a NAME="E1:78_1_1"/>
( <font color="Maroon" title="c2">Y</font> is   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-symbols</a> <font color="Maroon" title="c1">A</font></span>)</span> implies  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">Y</font> is   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-symbol</a> of <font color="Maroon" title="c1">A</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">Y</font> is  not   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-symbols</a> <font color="Maroon" title="c1">A</font></span>)</span> implies  <a href="qc_lang1.html#K26" title="QC_LANG1:func.26">0</a> <font color="Maroon" title="c1">A</font> is   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-symbol</a> of <font color="Maroon" title="c1">A</font> )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="78_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:78_1_1_1"/><span class="lab"><font color="Green" title="E50">A1</font></span>: 
<font color="Maroon" title="c2">Y</font> is   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-symbols</a> <font color="Maroon" title="c1">A</font></span>)</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">  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">Y</font> is   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-symbol</a> of <font color="Maroon" title="c1">A</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c3">a</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <span class="kw"> such that </span><br/><a NAME="E3:78_1_1_1"/><span class="lab"><font color="Green" title="E51">A2</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">Y</font>
 ;<br/>
<a NAME="E4:78_1_1_1"/><span class="lab"><font color="Green" title="E52">A3</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:78_1_1_1"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="txt" href="#E3:78_1_1_1"><span class="lab"><font color="Green" title="E51">A2</font></span></a></span>;<br/>
<a NAME="E5:78_1_1_1"/>
<font color="Maroon" title="c3">a</font> is   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-symbol</a> of <font color="Maroon" title="c1">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:78_1_1_1"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="txt" href="#E4:78_1_1_1"><span class="lab"><font color="Green" title="E52">A3</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:78_1_1_1"/>
 the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">Y</font> is   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-symbol</a> of <font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:78_1_1_1"><span class="lab"><font color="Green" title="E51">A2</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/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E2:78_1_1"/>
( <font color="Maroon" title="c2">Y</font> is  not   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-symbols</a> <font color="Maroon" title="c1">A</font></span>)</span> implies  <a href="qc_lang1.html#K26" title="QC_LANG1:func.26">0</a> <font color="Maroon" title="c1">A</font> is   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-symbol</a> of <font color="Maroon" title="c1">A</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"> verum</span><br/>


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