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<span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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> over <font color="Maroon" title="c1">K</font> holds   <a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <span class="p1">(<span class="default"><a href="mod_4.html#K4" title="MOD_4:func.4">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">ZeroF</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/><span class="kw">let </span><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> over <font color="Maroon" title="c1">K</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <span class="p1">(<span class="default"><a href="mod_4.html#K4" title="MOD_4:func.4">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">ZeroF</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/>



<span class="kw">set </span><font color="Maroon" title="c3">V</font> =  <a href="mod_4.html#K4" title="MOD_4:func.4">opp</a> <font color="Maroon" title="c2">W</font>;<br/>
<a NAME="E1:36"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
 <a href="mod_4.html#K1" title="MOD_4:func.1">opp</a> <span class="p1">(<span class="default"><a href="mod_4.html#K1" title="MOD_4:func.1">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T53" onmouseover="rs('funct_4/T53')" onmouseout="rh()">FUNCT_4:53</a></span>;<br/>
<span class="lab"><font color="Green" title="E18">A2</font></span>:  <a href="mod_4.html#K3" title="MOD_4:func.3">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#K4" title="MOD_4:func.4">opp</a> <font color="Maroon" title="c2">W</font></span>)</span> = 
 <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>  the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">W</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mod_4.html#T10" target="_self" onmouseover="rs('mod_4/T10')" onmouseout="rh()">Th10</a></span>
<br/>.= 
 the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">W</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T53" onmouseover="rs('funct_4/T53')" onmouseout="rh()">FUNCT_4:53</a></span>
;<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 <span class="p1">(<span class="default"><a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <span class="p2">(<span class="default"><a href="mod_4.html#K4" title="MOD_4:func.4">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#K2" title="MOD_4:func.2">opp</a> <span class="p2">(<span class="default"><a href="mod_4.html#K4" title="MOD_4:func.4">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">ZeroF</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <span class="p2">(<span class="default"><a href="mod_4.html#K4" title="MOD_4:func.4">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#K4" title="MOD_4:func.4">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#K4" title="MOD_4:func.4">opp</a> <font color="Maroon" title="c2">W</font></span>)</span>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K4" title="MOD_4:func.4">opp</a> <font color="Maroon" title="c2">W</font></span>)</span> #)
<span class="kw">by</span> <span class="lab"><a class="ref" href="mod_4.html#T7" target="_self" onmouseover="rs('mod_4/T7')" onmouseout="rh()">Th7</a></span>
<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">ZeroF</a> of <font color="Maroon" title="c2">W</font> #)
<span class="kw">by</span> <span class="lab"><a class="ref" href="mod_4.html#T9" target="_self" onmouseover="rs('mod_4/T9')" onmouseout="rh()">Th9</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:36"/>
 <a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <span class="p1">(<span class="default"><a href="mod_4.html#K4" title="MOD_4:func.4">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">ZeroF</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="mod_4.html#T8" target="_self" onmouseover="rs('mod_4/T8')" onmouseout="rh()">Th8</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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