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<b>let </b><font color="Maroon">K</font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">V</font> be   <a href="vectsp_2.html#NM6">LeftMod</a> of <font color="Maroon">K</font>;<br/>



<b>assume </b><a NAME="E1:7"/>
<font color="Maroon">K</font> is <a href="realset2.html#V3">trivial</a>
 ;<br/>

<a NAME="E2:7"/><b>then </b><i><font color="Green">E43</font></i>: 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">K</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">K</font>
 
<b>by </b><i/>;<br/>
<div><i><font color="Green">E47</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">r</font> be   <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">K</font>;<br/><b>thus </b><font color="Maroon">r</font> = 
<font color="Maroon">r</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">K</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">K</font>
<b>by </b><i>, <a class="ref" href="vectsp_1.html#T36">VECTSP_1:36</a></i>
;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font>;<br/><b>thus </b><font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">K</font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#D26">VECTSP_1:def 26</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font>
<b>by </b><i>, <a class="ref" href="vectsp_1.html#T59">VECTSP_1:59</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:7"/>
( ( for <font color="Olive">r</font> being  <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">K</font> holds  <font color="Olive">r</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">K</font> ) &amp; ( for <font color="Olive">a</font> being  <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font> holds  <font color="Olive">a</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> ) )
 <b>by </b><i/>;<br/>


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