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<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="vectsp_1.html#V2" title="VECTSP_1:attr.2">left-distributive</a> <a href="algstr_2.html#NM1" title="ALGSTR_2:NM.1">doubleLoop</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">b</font>, <font color="Olive" title="b2">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> holds  <span class="p1">(<span class="default"><a href="algstr_2.html#K1" title="ALGSTR_2:func.1">-</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_2.html#K1" title="ALGSTR_2:func.1">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">a</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="algstr_2.html#K1" title="ALGSTR_2:func.1">-</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_2.html#K1" title="ALGSTR_2:func.1">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">a</font></span>)</span></span><br/>





<span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_2.html#K1" title="ALGSTR_2:func.1">-</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">a</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p2">(<span class="default"><a href="algstr_2.html#K1" title="ALGSTR_2:func.1">-</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">a</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#D12" title="VECTSP_1:def.12">VECTSP_1:def 12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">a</font>
<b>by </b><i><a class="ref" href="algstr_2.html#D7" target="_self" title="ALGSTR_2:def.7">Def7</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">G</font>
<b>by </b><i><a class="ref" href="algstr_1.html#T34" title="ALGSTR_1:th.34">ALGSTR_1:34</a></i>
;<br/>
<b>hence </b><a NAME="E2:16"/>
<span class="p1">(<span class="default"><a href="algstr_2.html#K1" title="ALGSTR_2:func.1">-</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_2.html#K1" title="ALGSTR_2:func.1">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">a</font></span>)</span>
 <b>by </b><i><a class="ref" href="algstr_2.html#D7" target="_self" title="ALGSTR_2:def.7">Def7</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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