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<b>let </b><font color="Maroon">GF</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V3">Abelian</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="group_1.html#V4">associative</a> <a href="vectsp_1.html#V7">distributive</a> <a href="vectsp_1.html#V8">left_unital</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">V</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V3">Abelian</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="vectsp_1.html#V12">VectSp-like</a>  <a href="vectsp_1.html#L4">VectSpStr</a> of <font color="Maroon">GF</font>;<br/>



<a NAME="E1:27"/><i><font color="Green">E26</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font> &amp; the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">V</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">V</font> )
 
;<br/>
<a NAME="E2:27"/>
( the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">V</font> <a href="hidden.html#R1">=</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">V</font> <a href="realset1.html#K1">||</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font> &amp; the <a href="vectsp_1.html#U2">lmult</a> of <font color="Maroon">V</font> <a href="hidden.html#R1">=</a> the <a href="vectsp_1.html#U2">lmult</a> of <font color="Maroon">V</font> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">GF</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funct_2.html#T40">FUNCT_2:40</a></i>;<br/>
<b>hence </b><a NAME="E3:27"/>
<font color="Maroon">V</font> is    <a href="vectsp_4.html#M1" target="_self">Subspace</a> of <font color="Maroon">V</font>
 <b>by </b><i>, </i>;<br/>


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