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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">x</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Maroon" title="c1">n</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c3">y</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font>;<br/>





<b>assume </b><a NAME="E1:9"/><i><font color="Green" title="E8">A1</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font>
 ;<br/>

<b>thus </b><span class="p1"><a href="normsp_1.html#K1" title="NORMSP_1:func.1">||.</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="normsp_1.html#K1" title="NORMSP_1:func.1">.||</a></span> = 
the <a href="normsp_1.html#U1" title="NORMSP_1:sel.1">norm</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">x</font>
<b>by </b><i><a class="ref" href="normsp_1.html#D1" title="NORMSP_1:def.1">NORMSP_1:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="real_ns1.html#K3" title="REAL_NS1:func.3">Euclid_norm</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">y</font>
<b>by </b><i><a class="txt" href="real_ns1.html#E1:9"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="real_ns1.html#D4" target="_self" title="REAL_NS1:def.4">Def4</a></i>
<br/>.= 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><font color="Maroon" title="c3">y</font></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<b>by </b><i><a class="ref" href="real_ns1.html#D3" target="_self" title="REAL_NS1:def.3">Def3</a></i>
;<br/>


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