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<span class="kw">set </span><font color="Maroon" title="c1">M</font> =  <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a> ;<br/>
<span class="kw">thus </span><a NAME="E1:35_1_1"/>
 <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a>  is  <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a> 
  <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="algstr_0.html#D17" target="_self" title="ALGSTR_0:def.17">ALGSTR_0:def 17</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a>  is  <a href="algstr_0.html#V12" title="ALGSTR_0:attr.12">left_complementable</a> </span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="algstr_0.html#D16" target="_self" title="ALGSTR_0:def.16">ALGSTR_0:def 16</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> is  <a href="algstr_0.html#V10" title="ALGSTR_0:attr.10">right_complementable</a> </span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c2">x</font>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="algstr_0.html#D11" target="_self" title="ALGSTR_0:def.11">ALGSTR_0:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a> </span><br/>

<span class="kw">thus </span><a NAME="E1:35_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="algstr_0.html#D15" target="_self" title="ALGSTR_0:def.15">ALGSTR_0:def 15</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> is  <a href="algstr_0.html#V9" title="ALGSTR_0:attr.9">left_complementable</a> </span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c2">x</font>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="algstr_0.html#D10" target="_self" title="ALGSTR_0:def.10">ALGSTR_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a> </span><br/>

<span class="kw">thus </span><a NAME="E2:35_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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