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<b>consider </b><font color="Maroon">A</font> being  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">og</font> being   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">A</font>, <font color="Maroon">ng</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font><b> such that </b><br/><a NAME="E2:4_1_1"/><i><font color="Green">E17</font></i>: 
( ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font> holds  <font color="Maroon">og</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">og</font> <a href="binop_1.html#K2">.</a> <font color="Olive">a</font>,<font color="Olive">b</font></span>)</span>,<font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">og</font> <a href="binop_1.html#K2">.</a> <font color="Olive">a</font>,<span class="p1">(<span class="default"><font color="Maroon">og</font> <a href="binop_1.html#K2">.</a> <font color="Olive">b</font>,<font color="Olive">c</font></span>)</span> ) &amp; ( for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font> holds <br/> ( <font color="Maroon">og</font> <a href="binop_1.html#K2">.</a> <font color="Olive">a</font>,<font color="Maroon">ng</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Maroon">og</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">ng</font>,<font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> ) ) &amp; ( for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>  ex <font color="Olive">b</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font> st <br/>( <font color="Maroon">og</font> <a href="binop_1.html#K2">.</a> <font color="Olive">a</font>,<font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">ng</font> &amp; <font color="Maroon">og</font> <a href="binop_1.html#K2">.</a> <font color="Olive">b</font>,<font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">ng</font> ) ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font> holds  <font color="Maroon">og</font> <a href="binop_1.html#K2">.</a> <font color="Olive">a</font>,<font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">og</font> <a href="binop_1.html#K2">.</a> <font color="Olive">b</font>,<font color="Olive">a</font> ) )
 <b>by </b><i/>;<br/>
<a NAME="E3:4_1_1"/>
(  <a href="rlvect_1.html#G1">LoopStr</a>(# <font color="Maroon">A</font>,<font color="Maroon">og</font>,<font color="Maroon">ng</font> #) is <a href="rlvect_1.html#V3">Abelian</a> &amp;  <a href="rlvect_1.html#G1">LoopStr</a>(# <font color="Maroon">A</font>,<font color="Maroon">og</font>,<font color="Maroon">ng</font> #) is <a href="rlvect_1.html#V4">add-associative</a> &amp;  <a href="rlvect_1.html#G1">LoopStr</a>(# <font color="Maroon">A</font>,<font color="Maroon">og</font>,<font color="Maroon">ng</font> #) is <a href="realset2.html#V1" target="_self">zeroed</a> &amp;  <a href="rlvect_1.html#G1">LoopStr</a>(# <font color="Maroon">A</font>,<font color="Maroon">og</font>,<font color="Maroon">ng</font> #) is <a href="realset2.html#V2" target="_self">complementable</a> )
 
<b>by </b><i>, , , , </i>;<br/>
<b>hence </b><a NAME="E4:4_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being non <a href="struct_0.html#V3">empty</a>  <a href="rlvect_1.html#L1">LoopStr</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="rlvect_1.html#V1">strict</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="rlvect_1.html#V3">Abelian</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="rlvect_1.html#V4">add-associative</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="realset2.html#V1" target="_self">zeroed</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="realset2.html#V2" target="_self">complementable</a> )
 ;<br/>


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