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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">x1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">x2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">x3</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/>







<b>reconsider </b><font color="Maroon">x1'</font> = <font color="Maroon">x1</font>, <font color="Maroon">x2'</font> = <font color="Maroon">x2</font>, <font color="Maroon">x3'</font> = <font color="Maroon">x3</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">n</font> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K1">REAL</a>  <b>by </b><i><a class="ref" href="euclid.html#D1">EUCLID:def 1</a></i>;<br/>
<b>thus </b><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><font color="Maroon">x2</font> <a href="euclid.html#K7">+</a> <font color="Maroon">x3</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">x1'</font> <a href="rvsum_1.html#K4">+</a> <font color="Maroon">x2'</font></span>)</span> <a href="rvsum_1.html#K4">+</a> <font color="Maroon">x3'</font>
<b>by </b><i><a class="ref" href="rvsum_1.html#T32">RVSUM_1:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <font color="Maroon">x2</font></span>)</span> <a href="euclid.html#K7">+</a> <font color="Maroon">x3</font>

;<br/>


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