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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#V2" title="RLVECT_1:attr.2">Abelian</a>  <a href="algstr_0.html#L2" title="ALGSTR_0:struct.2">addLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">V</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">VectSpStr</a> of <font color="Maroon" title="c1">K</font>;<br/><b>let </b><font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g</font> be   <a href="hahnban1.html#NM1" title="HAHNBAN1:NM.1">Functional</a> of <font color="Maroon" title="c2">V</font>;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">V</font>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="hahnban1.html#K3" title="HAHNBAN1:func.3">+</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#D6" target="_self" title="HAHNBAN1:def.6">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="hahnban1.html#K3" title="HAHNBAN1:func.3">+</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="c5">x</font>
<b>by </b><i><a class="ref" href="hahnban1.html#D6" target="_self" title="HAHNBAN1:def.6">Def6</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:23"/>
<font color="Maroon" title="c3">f</font> <a href="hahnban1.html#K3" title="HAHNBAN1:func.3">+</a> <font color="Maroon" title="c4">g</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c4">g</font> <a href="hahnban1.html#K3" title="HAHNBAN1:func.3">+</a> <font color="Maroon" title="c3">f</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


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