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<b>let </b><font color="Maroon" title="c1">S</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="c2">G</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</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="rlvect_1.html#L1" title="RLVECT_1:struct.1">LoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c3">w</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">G</font>;<br/>





<b>assume </b><a NAME="E1:10"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c3">w</font> <a href="midsp_2.html#R2" title="MIDSP_2:pred.2">is_atlas_of</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">G</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">b</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c5">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font>;<br/>



<b>consider </b><font color="Maroon" title="c6">a</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E3:10"/><i><font color="Green" title="E12">A2</font></i>: 
<font color="Maroon" title="c3">w</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="midsp_2.html#E1:10"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="midsp_2.html#D3" target="_self" title="MIDSP_2:def.3">Def3</a></i>;<br/>
<i><font color="Green" title="E13">A3</font></i>: <font color="Maroon" title="c3">w</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">b</font> = 
 <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c5">x</font></span>)</span>
<b>by </b><i><a class="txt" href="midsp_2.html#E1:10"><i><font color="Green" title="E11">A1</font></i></a>, <a class="txt" href="midsp_2.html#E3:10"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="midsp_2.html#T6" target="_self" title="MIDSP_2:th.6">Th6</a></i>
<br/>.= 
<font color="Maroon" title="c5">x</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T30" title="RLVECT_1:th.30">RLVECT_1:30</a></i>
;<br/>
<b>take </b>
<font color="Maroon" title="c6">a</font>
;<br/>

<b>thus </b><a NAME="E5:10"/>
<font color="Maroon" title="c3">w</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="midsp_2.html#E4:10"><i><font color="Green" title="E13">A3</font></i></a></i>;<br/>


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