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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V4">associative</a> <a href="group_1.html#V7">commutative</a> <a href="vectsp_1.html#V8">left_unital</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/>



<a NAME="E1:102"/><i><font color="Green">E51</font></i>: 
(  <a href="binop_1.html#K3">the_unity_wrt</a> the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  )
 
<b>by </b><i><a class="ref" href="fvsum_1.html#T7" target="_self">Th7</a>, <a class="ref" href="fvsum_1.html#T11" target="_self">Th11</a></i>;<br/>
<b>thus </b> <a href="group_4.html#K3">Product</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="finsop_1.html#K2">$$</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>

<br/>.= 
 <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="fvsum_1.html#E1:102"><i><font color="Green">E51</font></i></a>, <a class="ref" href="setwop_2.html#T35">SETWOP_2:35</a></i>
;<br/>


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