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<span class="kw">let </span><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> (<font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> (<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c1">p</font></span>)</span>,<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c2">q</font></span>)</span>)</span><br/>



<span class="kw">thus </span> <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> (<font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font>) = 
 <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">q</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">q</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1k.html#T23" target="_self" title="JORDAN1K:th.23">Th23</a></span>
<br/>.= 
 <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c2">q</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T41" title="EUCLID:th.41">EUCLID:41</a></span>
<br/>.= 
 <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> (<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T42" title="EUCLID:th.42">EUCLID:42</a>, <a class="ref" href="euclid.html#T54" title="EUCLID:th.54">EUCLID:54</a></span>
<br/>.= 
 <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c1">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T42" title="EUCLID:th.42">EUCLID:42</a>, <a class="ref" href="euclid.html#T54" title="EUCLID:th.54">EUCLID:54</a></span>
<br/>.= 
 <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T41" title="EUCLID:th.41">EUCLID:41</a></span>
<br/>.= 
 <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> (<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c1">p</font></span>)</span>,<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c2">q</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1k.html#T21" target="_self" title="JORDAN1K:th.21">Th21</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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