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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">M</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font><br/> for <font color="Olive" title="b2">F</font> being  <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b2">F</font> is  <a href="tops_2.html#V2" title="TOPS_2:attr.2">closed</a>  holds <br/><font color="Olive" title="b2">F</font> <a href="tops_2.html#K1" title="TOPS_2:func.1">|</a> <font color="Olive" title="b1">M</font> is  <a href="tops_2.html#V2" title="TOPS_2:attr.2">closed</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">M</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font> being  <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b1">F</font> is  <a href="tops_2.html#V2" title="TOPS_2:attr.2">closed</a>  holds <br/><font color="Olive" title="b1">F</font> <a href="tops_2.html#K1" title="TOPS_2:func.1">|</a> <font color="Maroon" title="c2">M</font> is  <a href="tops_2.html#V2" title="TOPS_2:attr.2">closed</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">F</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</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="c3">F</font> is  <a href="tops_2.html#V2" title="TOPS_2:attr.2">closed</a>  implies <font color="Maroon" title="c3">F</font> <a href="tops_2.html#K1" title="TOPS_2:func.1">|</a> <font color="Maroon" title="c2">M</font> is  <a href="tops_2.html#V2" title="TOPS_2:attr.2">closed</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:50"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
<font color="Maroon" title="c3">F</font> is  <a href="tops_2.html#V2" title="TOPS_2:attr.2">closed</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="c3">F</font> <a href="tops_2.html#K1" title="TOPS_2:func.1">|</a> <font color="Maroon" title="c2">M</font> is  <a href="tops_2.html#V2" title="TOPS_2:attr.2">closed</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">Q</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c2">M</font></span>)</span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tops_2.html#D2" target="_self" title="TOPS_2:def.2">TOPS_2:def 2</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">Q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F</font> <a href="tops_2.html#K1" title="TOPS_2:func.1">|</a> <font color="Maroon" title="c2">M</font> implies <font color="Maroon" title="c4">Q</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:50"/>
<font color="Maroon" title="c4">Q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F</font> <a href="tops_2.html#K1" title="TOPS_2:func.1">|</a> <font color="Maroon" title="c2">M</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="c4">Q</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">R</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font><span class="kw"> such that </span><br/><a NAME="E4:50"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
<font color="Maroon" title="c5">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F</font>
 <span class="kw">and </span><br/><a NAME="E5:50"/><span class="lab"><font color="Green" title="E20">A3</font></span>: 
<font color="Maroon" title="c5">R</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tops_2.html#D3" target="_self" title="TOPS_2:def.3">Def3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">R</font> = <font color="Maroon" title="c5">R</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> ;<br/>
<a NAME="E7:50"/><span class="lab"><font color="Green" title="E21">A4</font></span>: 
<font color="Maroon" title="c4">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">R</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c2">M</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:50"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="pre_topc.html#D10" title="PRE_TOPC:def.10">PRE_TOPC:def 10</a></span>;<br/>
<a NAME="E8:50"/>
<font color="Maroon" title="c6">R</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E4:50"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="tops_2.html#D2" target="_self" title="TOPS_2:def.2">Def2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:50"/>
<font color="Maroon" title="c4">Q</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="pre_topc.html#T43" title="PRE_TOPC:th.43">PRE_TOPC:43</a></span>; <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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