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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="vectsp_2.html#NM3" title="VECTSP_2:NM.3">Skew-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="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">R</font><br/>  for <font color="Olive" title="b2">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b2">A</font> is  <a href="lmod_5.html#V1" title="LMOD_5:attr.1">linearly-independent</a>  holds <br/> ex <font color="Olive" title="b3">I</font> being    <a href="mod_3.html#M1" title="MOD_3:mode.1">Basis</a> of <font color="Olive" title="b1">V</font> st <font color="Olive" title="b2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">I</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">R</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">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">A</font> is  <a href="lmod_5.html#V1" title="LMOD_5:attr.1">linearly-independent</a>  holds <br/> ex <font color="Olive" title="b2">I</font> being    <a href="mod_3.html#M1" title="MOD_3:mode.1">Basis</a> of <font color="Maroon" title="c2">V</font> st <font color="Olive" title="b1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">I</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <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"> ( <font color="Maroon" title="c3">A</font> is  <a href="lmod_5.html#V1" title="LMOD_5:attr.1">linearly-independent</a>  implies  ex <font color="Olive" title="b1">I</font> being    <a href="mod_3.html#M1" title="MOD_3:mode.1">Basis</a> of <font color="Maroon" title="c2">V</font> st <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">I</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:29"/>
<font color="Maroon" title="c3">A</font> is  <a href="lmod_5.html#V1" title="LMOD_5:attr.1">linearly-independent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">I</font> being    <a href="mod_3.html#M1" title="MOD_3:mode.1">Basis</a> of <font color="Maroon" title="c2">V</font> st <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">I</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font><span class="kw"> such that </span><br/><a NAME="E3:29"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
<font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font>
 <span class="kw">and </span><br/><a NAME="E4:29"/><span class="lab"><font color="Green" title="E21">A2</font></span>: 
<font color="Maroon" title="c4">B</font> is  <a href="mod_3.html#V1" title="MOD_3:attr.1">base</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mod_3.html#T18" target="_self" title="MOD_3:th.18">Th26</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">B</font> = <font color="Maroon" title="c4">B</font> as    <a href="mod_3.html#M1" title="MOD_3:mode.1">Basis</a> of <font color="Maroon" title="c2">V</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:29"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="mod_3.html#D4" target="_self" title="MOD_3:def.4">Def5</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c5">B</font>
; <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="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">B</font></span><br/>

<span class="kw">thus </span><a NAME="E6:29"/>
<font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:29"><span class="lab"><font color="Green" title="E20">A1</font></span></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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