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<b>let </b><font color="Maroon" title="c1">I</font> be  non <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a> <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a> <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a> <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</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">u</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="quofield.html#K9" title="QUOFIELD:func.9">Quot.</a> <font color="Maroon" title="c1">I</font> holds <br/> ( <span class="p1">(<span class="default"><a href="quofield.html#K18" title="QUOFIELD:func.18">quotmult</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">u</font>,<span class="p1">(<span class="default"><a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">u</font> &amp; <span class="p1">(<span class="default"><a href="quofield.html#K18" title="QUOFIELD:func.18">quotmult</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font></span>)</span>,<font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">u</font> )</span><br/><b>let </b><font color="Maroon" title="c2">u</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="quofield.html#K9" title="QUOFIELD:func.9">Quot.</a> <font color="Maroon" title="c1">I</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="quofield.html#K18" title="QUOFIELD:func.18">quotmult</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">u</font>,<span class="p1">(<span class="default"><a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">u</font> &amp; <span class="p1">(<span class="default"><a href="quofield.html#K18" title="QUOFIELD:func.18">quotmult</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font></span>)</span>,<font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">u</font> )</span><br/>



<i><font color="Green" title="E40">A1</font></i>: <span class="p1">(<span class="default"><a href="quofield.html#K18" title="QUOFIELD:func.18">quotmult</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">u</font>,<span class="p1">(<span class="default"><a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font></span>)</span> = 
 <a href="quofield.html#K11" title="QUOFIELD:func.11">qmult</a> <font color="Maroon" title="c2">u</font>,<span class="p1">(<span class="default"><a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#D13" target="_self" title="QUOFIELD:def.13">Def13</a></i>
<br/>.= 
<font color="Maroon" title="c2">u</font>
<b>by </b><i><a class="ref" href="quofield.html#T16" target="_self" title="QUOFIELD:th.16">Th16</a></i>
;<br/>
<span class="p1">(<span class="default"><a href="quofield.html#K18" title="QUOFIELD:func.18">quotmult</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font></span>)</span>,<font color="Maroon" title="c2">u</font> = 
 <a href="quofield.html#K11" title="QUOFIELD:func.11">qmult</a> <span class="p1">(<span class="default"><a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font></span>)</span>,<font color="Maroon" title="c2">u</font>
<b>by </b><i><a class="ref" href="quofield.html#D13" target="_self" title="QUOFIELD:def.13">Def13</a></i>
<br/>.= 
<font color="Maroon" title="c2">u</font>
<b>by </b><i><a class="ref" href="quofield.html#T16" target="_self" title="QUOFIELD:th.16">Th16</a></i>
;<br/>
<b>hence </b><a NAME="E3:47"/>
( <span class="p1">(<span class="default"><a href="quofield.html#K18" title="QUOFIELD:func.18">quotmult</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">u</font>,<span class="p1">(<span class="default"><a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">u</font> &amp; <span class="p1">(<span class="default"><a href="quofield.html#K18" title="QUOFIELD:func.18">quotmult</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="quofield.html#K14" title="QUOFIELD:func.14">q1.</a> <font color="Maroon" title="c1">I</font></span>)</span>,<font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">u</font> )
 <b>by </b><i><a class="txt" href="#E1:47"><i><font color="Green" title="E40">A1</font></i></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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