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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>, <font color="Maroon">c<sub>3</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>4</sub></font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<a NAME="E1:21"/>
(  <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 or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/>
<b>hence </b><a NAME="E2:21"/>
( ( <font color="Maroon">c<sub>4</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>4</sub></font> is <a href="binop_1.html#V2">associative</a> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="binop_1.html#V1">commutative</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>4</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>4</sub></font> <a href="finsop_1.html#K2" target="_self">"**"</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="finsop_1.html#E18"><i><font color="Green">Lemma15</font></i></a>, <a class="txt" href="finsop_1.html#E19"><i><font color="Green">Lemma16</font></i></a></i>;<br/>


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