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<span class="kw">let </span><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V</font> being   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">F</font><br/>  for <font color="Olive" title="b2">m</font>, <font color="Olive" title="b3">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b3">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b1">V</font> holds <br/> not  <a href="pencil_4.html#K7" title="PENCIL_4:func.7">GrassmannSpace</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">m</font>,<font color="Olive" title="b3">n</font>) is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">F</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c2">V</font> holds <br/> not  <a href="pencil_4.html#K7" title="PENCIL_4:func.7">GrassmannSpace</a> (<font color="Maroon" title="c2">V</font>,<font color="Olive" title="b1">m</font>,<font color="Olive" title="b2">n</font>) is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">m</font>, <font color="Maroon" title="c4">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c2">V</font> implies  not  <a href="pencil_4.html#K7" title="PENCIL_4:func.7">GrassmannSpace</a> (<font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font>) is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:29"/>
<font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c2">V</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not  <a href="pencil_4.html#K7" title="PENCIL_4:func.7">GrassmannSpace</a> (<font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font>) is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a> </span><br/>

<a NAME="E2:29"/><span class="kw">then </span>
 not  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="pencil_4.html#K7" title="PENCIL_4:func.7">GrassmannSpace</a> (<font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pencil_4.html#T22" target="_self" title="PENCIL_4:th.22">Th24</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:29"/>
 not  <a href="pencil_4.html#K7" title="PENCIL_4:func.7">GrassmannSpace</a> (<font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font>) is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pencil_1.html#D4" title="PENCIL_1:def.4">PENCIL_1:def 4</a></span>; <a class="txt" 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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