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<b>let </b><font color="Maroon" title="c1">o1</font>, <font color="Maroon" title="c2">o2</font> be   <a href="multop_1.html#NM1" title="MULTOP_1:NM.1">TriOp</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:6_1_2"/><i><font color="Green" title="E1">A1</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> holds  <font color="Maroon" title="c1">o1</font> <a href="multop_1.html#K2" title="MULTOP_1:func.2">.</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Olive" title="b3">c</font>
 <b>and </b><br/><a NAME="E2:6_1_2"/><i><font color="Green" title="E2">A2</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> holds  <font color="Maroon" title="c2">o2</font> <a href="multop_1.html#K2" title="MULTOP_1:func.2">.</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Olive" title="b3">c</font>
 ;<br/>

<a NAME="E3:6_1_2"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> holds  <font color="Maroon" title="c1">o1</font> <a href="multop_1.html#K2" title="MULTOP_1:func.2">.</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o2</font> <a href="multop_1.html#K2" title="MULTOP_1:func.2">.</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>

<b>thus </b><font color="Maroon" title="c1">o1</font> <a href="multop_1.html#K2" title="MULTOP_1:func.2">.</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c5">c</font>
<b>by </b><i><a class="txt" href="algstr_3.html#E1:6_1_2"><i><font color="Green" title="E1">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c2">o2</font> <a href="multop_1.html#K2" title="MULTOP_1:func.2">.</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>
<b>by </b><i><a class="txt" href="algstr_3.html#E2:6_1_2"><i><font color="Green" title="E2">A2</font></i></a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:6_1_2"/>
<font color="Maroon" title="c1">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o2</font>
 <b>by </b><i><a class="ref" href="multop_1.html#T4" title="MULTOP_1:th.4">MULTOP_1:4</a></i>;<br/>


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