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<span class="kw">let </span><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</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">VS</font> being   <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>  <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Maroon" title="c1">F</font><br/>  for <font color="Olive" title="b2">H</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="vectsp_8.html#K2" title="VECTSP_8:func.2">Subspaces</a> <font color="Olive" title="b1">VS</font></span>)</span>  holds  not <span class="p1">(<span class="default"><a href="vectsp_8.html#K4" title="VECTSP_8:func.4">carr</a> <font color="Olive" title="b1">VS</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Olive" title="b2">H</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">VS</font> be   <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>  <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Maroon" title="c1">F</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">  for <font color="Olive" title="b1">H</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="vectsp_8.html#K2" title="VECTSP_8:func.2">Subspaces</a> <font color="Maroon" title="c2">VS</font></span>)</span>  holds  not <span class="p1">(<span class="default"><a href="vectsp_8.html#K4" title="VECTSP_8:func.4">carr</a> <font color="Maroon" title="c2">VS</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Olive" title="b1">H</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">H</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="vectsp_8.html#K2" title="VECTSP_8:func.2">Subspaces</a> <font color="Maroon" title="c2">VS</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">  not <span class="p1">(<span class="default"><a href="vectsp_8.html#K4" title="VECTSP_8:func.4">carr</a> <font color="Maroon" title="c2">VS</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c3">H</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/>





<span class="kw">consider </span><font color="Maroon" title="c4">x</font> being    <a href="vectsp_8.html#M2" title="VECTSP_8:mode.2">Element</a> of  <a href="vectsp_8.html#K2" title="VECTSP_8:func.2">Subspaces</a> <font color="Maroon" title="c2">VS</font><span class="kw"> such that </span><br/><a NAME="E2:7"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#T4" onmouseover="rs('subset_1/T4')" onmouseout="rh()">SUBSET_1:4</a></span>;<br/>
<a NAME="E3:7"/>
<span class="p1">(<span class="default"><a href="vectsp_8.html#K4" title="VECTSP_8:func.4">carr</a> <font color="Maroon" title="c2">VS</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="vectsp_8.html#K4" title="VECTSP_8:func.4">carr</a> <font color="Maroon" title="c2">VS</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c3">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="funct_2.html#T35" onmouseover="rs('funct_2/T35')" onmouseout="rh()">FUNCT_2:35</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:7"/>
 not <span class="p1">(<span class="default"><a href="vectsp_8.html#K4" title="VECTSP_8:func.4">carr</a> <font color="Maroon" title="c2">VS</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c3">H</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">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"> verum</span><br/>


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