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<span class="kw">let </span><font color="Maroon" title="c2">Am</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">TM</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">Am</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  implies <font color="Maroon" title="c2">Am</font> is  <a href="topgen_4.html#V6" title="TOPGEN_4:attr.6">G_delta</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:22_2_1"/><span class="lab"><font color="Green" title="E11">A24</font></span>: 
<font color="Maroon" title="c2">Am</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</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="c2">Am</font> is  <a href="topgen_4.html#V6" title="TOPGEN_4:attr.6">G_delta</a> </span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_2_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:22_2_1_1"/>
( <font color="Maroon" title="c1">TM</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  or  not <font color="Maroon" title="c1">TM</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:22_2_1_1_1"/><span class="lab"><font color="Green" title="E12">A25</font></span>: 
<font color="Maroon" title="c1">TM</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</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="c2">Am</font> is  <a href="topgen_4.html#V6" title="TOPGEN_4:attr.6">G_delta</a> </span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c3">E</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#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">TM</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="topgen_4.html#T18" onmouseover="rs('topgen_4/T18')" onmouseout="rh()">TOPGEN_4:18</a></span>;<br/><a NAME="E3:22_2_1_1_1"/>
<font color="Maroon" title="c2">Am</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K6" title="SETFAM_1:func.6">meet</a> <font color="Maroon" title="c3">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_2_1_1_1"><span class="lab"><font color="Green" title="E12">A25</font></span></a>, <a class="ref" href="setfam_1.html#T1" onmouseover="rs('setfam_1/T1')" onmouseout="rh()">SETFAM_1:1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:22_2_1_1_1"/>
<font color="Maroon" title="c2">Am</font> is  <a href="topgen_4.html#V6" title="TOPGEN_4:attr.6">G_delta</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topgen_4.html#D7" onmouseover="rs('topgen_4/D7')" onmouseout="rh()">TOPGEN_4:def 7</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:22_2_1_1_2"/>
 not <font color="Maroon" title="c1">TM</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</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="c2">Am</font> is  <a href="topgen_4.html#V6" title="TOPGEN_4:attr.6">G_delta</a> </span><br/><div class="add"><a NAME="E2:22_2_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">Am</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is  <a href="topgen_4.html#V6" title="TOPGEN_4:attr.6">G_delta</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_2_1"><span class="lab"><font color="Green" title="E11">A24</font></span></a>, <a class="ref" href="topgen_4.html#T37" onmouseover="rs('topgen_4/T37')" onmouseout="rh()">TOPGEN_4:37</a></span>;<br/><span class="kw">hence </span><a NAME="E3:22_2_1_1_2"/>
<font color="Maroon" title="c2">Am</font> is  <a href="topgen_4.html#V6" title="TOPGEN_4:attr.6">G_delta</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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