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<b>let </b><font color="Maroon" title="c17">F</font> be  non <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a> <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">Abelian</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> <a href="vectsp_1.html#V8" title="VECTSP_1:attr.8">distributive</a> <a href="realset2.html#V1" title="REALSET2:attr.1">Field-like</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c18">B</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c19">P</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c18">B</font>;<br/><b>let </b><font color="Maroon" title="c20">e</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c18">B</font>;<br/>







<b>set </b><font color="Maroon" title="c21">A</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c17">F</font>;<br/>
<b>set </b><font color="Maroon" title="c22">od</font> = the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c17">F</font>;<br/>
<b>set </b><font color="Maroon" title="c23">nd</font> =  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c17">F</font>;<br/>
<b>set </b><font color="Maroon" title="c24">nm</font> =  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c17">F</font>;<br/>
<a NAME="E1:32"/>
 ex <font color="Olive" title="b1">om</font> being   <a href="realset1.html#M3" title="REALSET1:mode.3">DnT</a> of  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c17">F</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c17">F</font> st <br/>( <font color="Olive" title="b1">om</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c17">F</font> &amp; ( for <font color="Olive" title="b2">B</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b3">P</font> being  <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Olive" title="b2">B</font><br/> for <font color="Olive" title="b4">e</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">B</font>  st <font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c17">F</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c17">F</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Olive" title="b4">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c17">F</font> &amp; <font color="Olive" title="b3">P</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b1">om</font> <a href="realset1.html#K4" title="REALSET1:func.4">!</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c17">F</font>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c17">F</font></span>)</span> holds <br/> <a href="rlvect_1.html#G1" title="RLVECT_1:aggr.1">LoopStr</a>(# <font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">P</font>,<font color="Olive" title="b4">e</font> #) is   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">AbGroup</a> ) )
 
<b>by </b><i><a class="ref" href="realset2.html#D11" target="_self" title="REALSET2:def.11">Def11</a></i>;<br/>
<b>hence </b><a NAME="E2:32"/>
( <font color="Maroon" title="c18">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c17">F</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c17">F</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c20">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="realset2.html#K5" title="REALSET2:func.5">nmf</a> <font color="Maroon" title="c17">F</font> &amp; <font color="Maroon" title="c19">P</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c17">F</font></span>)</span> <a href="realset1.html#K4" title="REALSET1:func.4">!</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c17">F</font>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c17">F</font></span>)</span> implies  <a href="rlvect_1.html#G1" title="RLVECT_1:aggr.1">LoopStr</a>(# <font color="Maroon" title="c18">B</font>,<font color="Maroon" title="c19">P</font>,<font color="Maroon" title="c20">e</font> #) is   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">AbGroup</a> )
 ;<br/>


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