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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">M</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/><b>let </b><font color="Maroon">W</font> be    <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">M</font>;<br/>





<b>thus </b><a NAME="E1:15"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">M</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_4.html#D2">VECTSP_4:def 2</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_4.html#D2">VECTSP_4:def 2</a><br/>

<b>thus </b><a NAME="E2:15"/>
( the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U2">Zero</a> of <span class="p1">(<span class="default"><a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">M</font></span>)</span> &amp; the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <a href="realset1.html#K1">K101</a>(the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">M</font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font>) &amp; the <a href="vectsp_1.html#U2">lmult</a> of <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> the <a href="vectsp_1.html#U2">lmult</a> of <span class="p1">(<span class="default"><a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">M</font></span>)</span> <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">W</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 <b>by </b><i><a class="ref" href="vectsp_4.html#D2">VECTSP_4:def 2</a></i>;<br/>


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