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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">b1</font> be  <a href="seq_1.html#V1">real-yielding</a>  <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">X</font>, <font color="Maroon">b2</font> be  <a href="seq_1.html#V1">real-yielding</a>  <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">X</font>, <font color="Maroon">b3</font> be  <a href="seq_1.html#V1">real-yielding</a>  <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">X</font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:78_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b2</font></span>)</span> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b3</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b2</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><font color="Maroon">b3</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><font color="Maroon">b3</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default"><font color="Maroon">b3</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b3</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b3</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:78"/>
<span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b2</font></span>)</span> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b3</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b3</font></span>)</span>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


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