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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<a NAME="E1:8"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/>
<b>hence </b><a NAME="E2:8"/>
( ( <font color="Maroon">c<sub>3</sub></font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 ) &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="binop_1.html#V2">associative</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="binop_1.html#V1">commutative</a> implies <font color="Maroon">c<sub>3</sub></font> <a href="finsop_1.html#K2" target="_self">"**"</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="setwiseo.html#K7">$$</a> <span class="p1">(<span class="default"><a href="finsop_1.html#K5" target="_self">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="finsop_1.html#K3" target="_self">--&gt;</a> <span class="p3">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="finsop_1.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="finsop_1.html#E5"><i><font color="Green">Lemma3</font></i></a>, <a class="txt" href="finsop_1.html#E6"><i><font color="Green">Lemma4</font></i></a></i>;<br/>


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