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<b>let </b><font color="Maroon">A1</font> be  non <a href="realset1.html#V1">trivial</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">A2</font> be  non <a href="realset1.html#V1">trivial</a>  <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:31_1_2"/><i><font color="Green">E18</font></i>: 
 ex <font color="Olive">od1</font> being  <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">A1</font> ex <font color="Olive">nd1</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A1</font> ex <font color="Olive">om1</font> being   <a href="realset1.html#M3">DnT</a> of <font color="Olive">nd1</font>,<font color="Maroon">A1</font> ex <font color="Olive">nm1</font> being   <a href="subset_1.html#M2">Element</a> of <font color="Maroon">A1</font> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Olive">nd1</font></span><a href="realset1.html#K5">}</a></span> st <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="realset2.html#K1" target="_self">field</a> <font color="Maroon">A1</font>,<font color="Olive">od1</font>,<font color="Olive">om1</font>,<font color="Olive">nd1</font>,<font color="Olive">nm1</font>
 <b>and </b><br/><a NAME="E2:31_1_2"/><i><font color="Green">E19</font></i>: 
 ex <font color="Olive">od2</font> being  <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">A2</font> ex <font color="Olive">nd2</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A2</font> ex <font color="Olive">om2</font> being   <a href="realset1.html#M3">DnT</a> of <font color="Olive">nd2</font>,<font color="Maroon">A2</font> ex <font color="Olive">nm2</font> being   <a href="subset_1.html#M2">Element</a> of <font color="Maroon">A2</font> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Olive">nd2</font></span><a href="realset1.html#K5">}</a></span> st <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="realset2.html#K1" target="_self">field</a> <font color="Maroon">A2</font>,<font color="Olive">od2</font>,<font color="Olive">om2</font>,<font color="Olive">nd2</font>,<font color="Olive">nm2</font>
 ;<br/>

<font color="Maroon">A1</font> = 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">A2</font>
<b>by </b><i><a class="txt" href="realset2.html#E13"><i><font color="Green">Lemma51</font></i></a>, </i>
;<br/>
<b>hence </b><a NAME="E4:31_1_2"/>
<font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A2</font>
 ;<br/>


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