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<span class="kw">let </span><font color="Maroon" title="c1">ET</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fintopo2.html#V1" title="FINTOPO2:attr.1">strict</a>   <a href="fintopo2.html#L1" title="FINTOPO2:struct.1">FMT_Space_Str</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="c1">ET</font> is  <a href="fintopo7.html#V5" title="FINTOPO7:attr.5">U_FMT_filter_base</a>  implies  <a href="fintopo7.html#K3" title="FINTOPO7:func.3">gen_filter</a> <font color="Maroon" title="c1">ET</font> is  <a href="fintopo7.html#V2" title="FINTOPO7:attr.2">U_FMT_filter</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:23"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
<font color="Maroon" title="c1">ET</font> is  <a href="fintopo7.html#V5" title="FINTOPO7:attr.5">U_FMT_filter_base</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">  <a href="fintopo7.html#K3" title="FINTOPO7:func.3">gen_filter</a> <font color="Maroon" title="c1">ET</font> is  <a href="fintopo7.html#V2" title="FINTOPO7:attr.2">U_FMT_filter</a> </span><br/>

<a NAME="E2:23"/>
 for <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="fintopo7.html#K3" title="FINTOPO7:func.3">gen_filter</a> <font color="Maroon" title="c1">ET</font></span>)</span> holds   <a href="fintopo2.html#K6" title="FINTOPO2:func.6">U_FMT</a> <font color="Olive" title="b1">x</font> is    <a href="card_fil.html#M1" title="CARD_FIL:mode.1">Filter</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fintopo7.html#K3" title="FINTOPO7:func.3">gen_filter</a> <font color="Maroon" title="c1">ET</font></span>)</span>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="23_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="fintopo7.html#K3" title="FINTOPO7:func.3">gen_filter</a> <font color="Maroon" title="c1">ET</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">  <a href="fintopo2.html#K6" title="FINTOPO2:func.6">U_FMT</a> <font color="Maroon" title="c2">x</font> is    <a href="card_fil.html#M1" title="CARD_FIL:mode.1">Filter</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fintopo7.html#K3" title="FINTOPO7:func.3">gen_filter</a> <font color="Maroon" title="c1">ET</font></span>)</span></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c3">x0</font> = <font color="Maroon" title="c2">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">ET</font> ;<br/>
<a NAME="E2:23_1"/>
 <a href="fintopo2.html#K6" title="FINTOPO2:func.6">U_FMT</a> <font color="Maroon" title="c3">x0</font> is   <a href="cardfil2.html#NM2" title="CARDFIL2:NM.2">filter_base</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">ET</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E17">A1</font></span></a></span>;<br/>
<a NAME="E3:23_1"/><span class="kw">then </span>
<span class="p1"><a href="cardfil2.html#K3" title="CARDFIL2:func.3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><a href="fintopo2.html#K6" title="FINTOPO2:func.6">U_FMT</a> <font color="Maroon" title="c3">x0</font></span>)</span></span><a href="cardfil2.html#K3" title="CARDFIL2:func.3">.]</a></span> is    <a href="card_fil.html#M1" title="CARD_FIL:mode.1">Filter</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">ET</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cardfil2.html#T25" onmouseover="rs('cardfil2/T25')" onmouseout="rh()">CARDFIL2:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:23_1"/>
 <a href="fintopo2.html#K6" title="FINTOPO2:func.6">U_FMT</a> <font color="Maroon" title="c2">x</font> is    <a href="card_fil.html#M1" title="CARD_FIL:mode.1">Filter</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fintopo7.html#K3" title="FINTOPO7:func.3">gen_filter</a> <font color="Maroon" title="c1">ET</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fintopo7.html#D9" target="_self" onmouseover="rs('fintopo7/D9')" onmouseout="rh()">Def7</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">hence </span><a NAME="E3:23"/>
 <a href="fintopo7.html#K3" title="FINTOPO7:func.3">gen_filter</a> <font color="Maroon" title="c1">ET</font> is  <a href="fintopo7.html#V2" title="FINTOPO7:attr.2">U_FMT_filter</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/>


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