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<span class="kw">let </span><font color="Maroon" title="c1">FT</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</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">  for <font color="Olive" title="b1">X</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fintopo6.html#M1" title="FINTOPO6:mode.1">SubSpace</a> of <font color="Maroon" title="c1">FT</font>  st <font color="Maroon" title="c1">FT</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">filled</a>  holds <br/><font color="Olive" title="b1">X</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">filled</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">X</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fintopo6.html#M1" title="FINTOPO6:mode.1">SubSpace</a> of <font color="Maroon" title="c1">FT</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="c1">FT</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">filled</a>  implies <font color="Maroon" title="c2">X</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">filled</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:15"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
<font color="Maroon" title="c1">FT</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">filled</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">X</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">filled</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">X</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="fin_topo.html#D4" onmouseover="rs('fin_topo/D4')" onmouseout="rh()">FIN_TOPO:def 4</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="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="fin_topo.html#K1" title="FIN_TOPO:func.1">U_FT</a> <font color="Maroon" title="c3">x</font></span><br/>

<a NAME="E2:15"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">FT</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo6.html#D2" target="_self" onmouseover="rs('fintopo6/D2')" onmouseout="rh()">Def2</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">x2</font> = <font color="Maroon" title="c3">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FT</font> ;<br/>
<a NAME="E4:15"/><span class="lab"><font color="Green" title="E11">A2</font></span>: 
 <a href="fin_topo.html#K1" title="FIN_TOPO:func.1">U_FT</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="fin_topo.html#K1" title="FIN_TOPO:func.1">U_FT</a> <font color="Maroon" title="c4">x2</font></span>)</span> <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> <font color="Maroon" title="c2">X</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo6.html#D2" target="_self" onmouseover="rs('fintopo6/D2')" onmouseout="rh()">Def2</a></span>;<br/>
<a NAME="E5:15"/>
<font color="Maroon" title="c4">x2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="fin_topo.html#K1" title="FIN_TOPO:func.1">U_FT</a> <font color="Maroon" title="c4">x2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E10">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:15"/>
<font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="fin_topo.html#K1" title="FIN_TOPO:func.1">U_FT</a> <font color="Maroon" title="c3">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:15"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="xboole_0.html#D4" onmouseover="rs('xboole_0/D4')" onmouseout="rh()">XBOOLE_0:def 4</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/>


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