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<b>let </b><font color="Maroon">X</font> be   <a href="csspace.html#NM1">ComplexUnitarySpace</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">z</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>;<br/>







 <a href="csspace.html#K15" target="_self">dist</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">z</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">z</font></span>)</span> = 
<span class="p1"><a href="csspace.html#K13" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">z</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">y</font></span>)</span></span>)</span></span><a href="csspace.html#K13" target="_self">.||</a></span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T47">RLVECT_1:47</a></i>
<br/>.= 
<span class="p1"><a href="csspace.html#K13" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">y</font></span>)</span></span>)</span></span><a href="csspace.html#K13" target="_self">.||</a></span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T47">RLVECT_1:47</a></i>
;<br/>
<a NAME="E2:84"/><b>then </b>
 <a href="csspace.html#K15" target="_self">dist</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">z</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">z</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="csspace.html#K13" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">x</font></span>)</span></span>)</span></span><a href="csspace.html#K13" target="_self">.||</a></span> <a href="real_1.html#K3">+</a> <span class="p1"><a href="csspace.html#K13" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">y</font></span>)</span></span><a href="csspace.html#K13" target="_self">.||</a></span>
 
<b>by </b><i><a class="ref" href="csspace.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E3:84"/><b>then </b>
 <a href="csspace.html#K15" target="_self">dist</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">z</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">z</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="csspace.html#K13" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">x</font></span>)</span></span><a href="csspace.html#K13" target="_self">.||</a></span> <a href="real_1.html#K3">+</a> <span class="p1"><a href="csspace.html#K13" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">y</font></span>)</span></span><a href="csspace.html#K13" target="_self">.||</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:84"/><b>then </b>
 <a href="csspace.html#K15" target="_self">dist</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">z</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">z</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="csspace.html#K15" target="_self">dist</a> <font color="Maroon">z</font>,<font color="Maroon">x</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1"><a href="csspace.html#K13" target="_self">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">y</font></span>)</span></span><a href="csspace.html#K13" target="_self">.||</a></span>
 
;<br/>
<b>hence </b><a NAME="E5:84"/>
 <a href="csspace.html#K15" target="_self">dist</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">z</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">z</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="csspace.html#K15" target="_self">dist</a> <font color="Maroon">z</font>,<font color="Maroon">x</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="csspace.html#K15" target="_self">dist</a> <font color="Maroon">z</font>,<font color="Maroon">y</font></span>)</span>
 ;<br/>


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