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



<b>thus </b><a NAME="E1:19"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  implies  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:19_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a> 
 ;<br/>

<a NAME="E2:19_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="setwiseo.html#D2" target="_self">Def2</a></i>;<br/>
<b>hence </b><a NAME="E3:19_1"/>
 <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="binop_1.html#D8">BINOP_1:def 8</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:19"/>
(  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font> implies <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="setwiseo.html#D2" target="_self">Def2</a></i>;<br/>


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