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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E1:30_1_1"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D6" target="_self" title="VECTSP_1:def.6">Def16</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="vectsp_1.html#D8" target="_self" title="VECTSP_1:def.8">VECTSP_1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">thus </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30_1_1"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="vectsp_1.html#D6" target="_self" title="VECTSP_1:def.6">Def16</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="vectsp_1.html#D4" target="_self" title="VECTSP_1:def.4">VECTSP_1:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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