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<b>let </b><font color="Maroon">b</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">r1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> , <font color="Maroon">r2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>thus </b><a href="binop_2.html#K34">diffreal</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">r1</font>,<font color="Maroon">r2</font> = 
<font color="Maroon">r1</font> <a href="binop_2.html#K10">-</a> <font color="Maroon">r2</font>
<b>by </b><i><a class="ref" href="binop_2.html#D10">BINOP_2:def 10</a></i>
<br/>.= 
<font color="Maroon">r1</font> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><a href="binop_2.html#K7">-</a> <font color="Maroon">r2</font></span>)</span>

<br/>.= 
<a href="binop_2.html#K33">addreal</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">r1</font>,<span class="p1">(<span class="default"><a href="binop_2.html#K7">-</a> <font color="Maroon">r2</font></span>)</span>
<b>by </b><i><a class="ref" href="binop_2.html#D9">BINOP_2:def 9</a></i>
<br/>.= 
<a href="binop_2.html#K33">addreal</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">r1</font>,<span class="p1">(<span class="default"><a href="binop_2.html#K31">compreal</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">r2</font></span>)</span>
<b>by </b><i><a class="ref" href="binop_2.html#D7">BINOP_2:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="binop_2.html#K33">addreal</a>  <a href="finseqop.html#K8">*</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span>,<a href="binop_2.html#K31">compreal</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">r1</font>,<font color="Maroon">r2</font>
<b>by </b><i><a class="ref" href="finseqop.html#T87">FINSEQOP:87</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:3_1_1"/>
( <font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="binop_2.html#K34">diffreal</a>  iff <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <a href="binop_2.html#K33">addreal</a>  <a href="finseqop.html#K8">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span>,<a href="binop_2.html#K31">compreal</a>  )
 <b>by </b><i><a class="ref" href="binop_1.html#T2">BINOP_1:2</a></i>;<br/>


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