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<b>let </b><font color="Maroon" title="c1">K</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">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">well-unital</a> <a href="vectsp_1.html#V8" title="VECTSP_1:attr.8">distributive</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">V</font> be   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font>;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font>;<br/><b>let </b><font color="Maroon" title="c4">A</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c2">V</font>,<span class="p2">(<span class="default"><a href="vectsp10.html#K9" title="VECTSP10:func.9">Ker</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span>;<br/><b>let </b><font color="Maroon" title="c5">v</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>;<br/>









<b>assume </b><a NAME="E1:71"/><i><font color="Green" title="E38">A1</font></i>: 
<font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <span class="p1">(<span class="default"><a href="vectsp10.html#K9" title="VECTSP10:func.9">Ker</a> <font color="Maroon" title="c3">f</font></span>)</span>
 ;<br/>

<a NAME="E2:71"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K9" title="VECTSP10:func.9">Ker</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp10.html#K8" title="VECTSP10:func.8">ker</a> <font color="Maroon" title="c3">f</font>
 
<b>by </b><i><a class="ref" href="vectsp10.html#D11" target="_self" title="VECTSP10:def.11">Def11</a></i>;<br/>
<b>hence </b><a NAME="E3:71"/>
<span class="p1">(<span class="default"><a href="vectsp10.html#K11" title="VECTSP10:func.11">CQFunctional</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">v</font>
 <b>by </b><i><a class="txt" href="vectsp10.html#E1:71"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="vectsp10.html#D12" target="_self" title="VECTSP10:def.12">Def12</a></i>;<br/>


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