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<b>let </b><font color="Maroon" title="c1">GF</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">Abelian</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a> <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">distributive</a> <a href="vectsp_1.html#V8" title="VECTSP_1:attr.8">left_unital</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">M</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">Abelian</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> <a href="vectsp_1.html#V12" title="VECTSP_1:attr.12">VectSp-like</a>  <a href="vectsp_1.html#L4" title="VECTSP_1:struct.4">VectSpStr</a> of <font color="Maroon" title="c1">GF</font>;<br/><b>let </b><font color="Maroon" title="c3">W</font>, <font color="Maroon" title="c4">W'</font>, <font color="Maroon" title="c5">W1</font> be    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">M</font>;<br/>





<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E22">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W</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="c4">W'</font>
 ;<br/>

<div><i><font color="Green" title="E23">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>now </b></a><div class="add"><b>thus </b>the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c5">W1</font> <a href="vectsp_5.html#K2" title="VECTSP_5:func.2">/\</a> <font color="Maroon" title="c3">W</font></span>)</span> = 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">W1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">W'</font>
<b>by </b><i><a class="txt" href="vectsp_5.html#E1:21"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="vectsp_5.html#D2" target="_self" title="VECTSP_5:def.2">Def2</a></i>
<br/>.= 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c5">W1</font> <a href="vectsp_5.html#K2" title="VECTSP_5:func.2">/\</a> <font color="Maroon" title="c4">W'</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_5.html#D2" target="_self" title="VECTSP_5:def.2">Def2</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:21"/>
<font color="Maroon" title="c5">W1</font> <a href="vectsp_5.html#K2" title="VECTSP_5:func.2">/\</a> <font color="Maroon" title="c3">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">W1</font> <a href="vectsp_5.html#K2" title="VECTSP_5:func.2">/\</a> <font color="Maroon" title="c4">W'</font>
 <b>by </b><i><a class="ref" href="vectsp_4.html#T37" title="VECTSP_4:th.37">VECTSP_4:37</a></i>;<br/>

<b>thus </b><a NAME="E4:21"/>
<font color="Maroon" title="c3">W</font> <a href="vectsp_5.html#K2" title="VECTSP_5:func.2">/\</a> <font color="Maroon" title="c5">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">W'</font> <a href="vectsp_5.html#K2" title="VECTSP_5:func.2">/\</a> <font color="Maroon" title="c5">W1</font>
 <b>by </b><i><a class="txt" href="vectsp_5.html#E2:21"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="vectsp_4.html#T37" title="VECTSP_4:th.37">VECTSP_4:37</a></i>;<br/>


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