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<b>let </b><font color="Maroon" title="c1">K</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">W</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="vectsp_2.html#L1" title="VECTSP_2:struct.1">RightModStr</a> of <font color="Maroon" title="c1">K</font> holds   <a href="mod_4.html#K3" title="MOD_4:func.3">opp</a> <span class="p1">(<span class="default"><a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Olive" title="b1">W</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">W</font>,the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Olive" title="b1">W</font>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">U2</a> of <font color="Olive" title="b1">W</font>,the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Olive" title="b1">W</font> #)</span><br/><b>let </b><font color="Maroon" title="c2">W</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="vectsp_2.html#L1" title="VECTSP_2:struct.1">RightModStr</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="mod_4.html#K3" title="MOD_4:func.3">opp</a> <span class="p1">(<span class="default"><a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Maroon" title="c2">W</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">W</font>,the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c2">W</font>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">U2</a> of <font color="Maroon" title="c2">W</font>,the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">W</font> #)</span><br/>



<b>set </b><font color="Maroon" title="c3">V</font> =  <a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Maroon" title="c2">W</font>;<br/>
<i><font color="Green" title="E18">A1</font></i>:  <a href="algstr_0.html#G2" title="ALGSTR_0:aggr.2">addLoopStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K3" title="MOD_4:func.3">opp</a> <span class="p2">(<span class="default"><a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Maroon" title="c2">W</font></span>)</span></span>)</span>,the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K3" title="MOD_4:func.3">opp</a> <span class="p2">(<span class="default"><a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Maroon" title="c2">W</font></span>)</span></span>)</span>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">U2</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K3" title="MOD_4:func.3">opp</a> <span class="p2">(<span class="default"><a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Maroon" title="c2">W</font></span>)</span></span>)</span> #) = 
 <a href="algstr_0.html#G2" title="ALGSTR_0:aggr.2">addLoopStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Maroon" title="c2">W</font></span>)</span>,the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Maroon" title="c2">W</font></span>)</span>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">U2</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Maroon" title="c2">W</font></span>)</span> #)
<b>by </b><i><a class="ref" href="mod_4.html#T9" target="_self" title="MOD_4:th.9">Th9</a></i>
<br/>.= 
 <a href="algstr_0.html#G2" title="ALGSTR_0:aggr.2">addLoopStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">W</font>,the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c2">W</font>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">U2</a> of <font color="Maroon" title="c2">W</font> #)
<b>by </b><i><a class="ref" href="mod_4.html#T12" target="_self" title="MOD_4:th.12">Th12</a></i>
;<br/>
<i><font color="Green" title="E19">A2</font></i>:  <a href="mod_4.html#K4" title="MOD_4:func.4">opp</a> the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">lmult</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Maroon" title="c2">W</font></span>)</span> = 
 <a href="mod_4.html#K4" title="MOD_4:func.4">opp</a> <span class="p1">(<span class="default"><a href="mod_4.html#K6" title="MOD_4:func.6">opp</a> the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">W</font></span>)</span>
<b>by </b><i><a class="ref" href="mod_4.html#T13" target="_self" title="MOD_4:th.13">Th13</a></i>
<br/>.= 
the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">W</font>
<b>by </b><i><a class="ref" href="funct_4.html#T54" title="FUNCT_4:th.54">FUNCT_4:54</a></i>
;<br/>
<a NAME="E3:40"/>
 <a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <span class="p1">(<span class="default"><a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <font color="Maroon" title="c1">K</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">K</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T54" title="FUNCT_4:th.54">FUNCT_4:54</a></i>;<br/>
<b>hence </b><a NAME="E4:40"/>
 <a href="mod_4.html#K3" title="MOD_4:func.3">opp</a> <span class="p1">(<span class="default"><a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Maroon" title="c2">W</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">W</font>,the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c2">W</font>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">U2</a> of <font color="Maroon" title="c2">W</font>,the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">W</font> #)
 <b>by </b><i><a class="txt" href="mod_4.html#E1:40"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="mod_4.html#E2:40"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="mod_4.html#T10" target="_self" title="MOD_4:th.10">Th10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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