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<b>let </b><font color="Maroon" title="c2">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="algstr_0.html#L4" title="ALGSTR_0:struct.4">multLoopStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">L</font> is <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a> implies ( <font color="Maroon" title="c2">L</font> is <a href="vectsp_1.html#V6" title="VECTSP_1:attr.6">left_unital</a> &amp; <font color="Maroon" title="c2">L</font> is <a href="vectsp_1.html#V3" title="VECTSP_1:attr.3">right_unital</a> ) )</span><br/>

<b>assume </b><a NAME="E1:30_1_1"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c2">L</font> is <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">L</font> is <a href="vectsp_1.html#V6" title="VECTSP_1:attr.6">left_unital</a> &amp; <font color="Maroon" title="c2">L</font> is <a href="vectsp_1.html#V3" title="VECTSP_1:attr.3">right_unital</a> )</span><br/>

<b>hence </b><a NAME="E2:30_1_1"/>
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> holds  <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c2">L</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D16" target="_self" title="VECTSP_1:def.16">Def16</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_1.html#D19" target="_self" title="VECTSP_1:def.19">VECTSP_1:def 19</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">L</font> is <a href="vectsp_1.html#V3" title="VECTSP_1:attr.3">right_unital</a></span><br/>

<b>thus </b><a NAME="E3:30_1_1"/>
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> holds  <font color="Olive" title="b1">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c2">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font>
 <b>by </b><i><a class="txt" href="vectsp_1.html#E1:30_1_1"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="vectsp_1.html#D16" target="_self" title="VECTSP_1:def.16">Def16</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_1.html#D13" target="_self" title="VECTSP_1:def.13">VECTSP_1:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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