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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   <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>   <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Olive" title="b1">VS</font> holds   <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">VS</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="Olive" title="b1">VS</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">H</font></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   <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>   <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">VS</font> holds   <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">VS</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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">H</font> be   <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>   <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">VS</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">  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">VS</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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">H</font></span><br/>





<a NAME="E1:8"/>
<font color="Maroon" title="c3">H</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="vectsp_8.html#K2" title="VECTSP_8:func.2">Subspaces</a> <font color="Maroon" title="c2">VS</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_5.html#D3" onmouseover="rs('vectsp_5/D3')" onmouseout="rh()">VECTSP_5:def 3</a></span>;<br/>
<a NAME="E2:8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A1</font></span>: 
<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_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_8.html#D4" target="_self" onmouseover="rs('vectsp_8/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<a NAME="E3:8"/>
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">VS</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_4.html#T11" onmouseover="rs('vectsp_4/T11')" onmouseout="rh()">VECTSP_4:11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:8"/>
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">VS</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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E5">A1</font></span></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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