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<span class="kw">let </span><font color="Maroon" title="c1">q</font>, <font color="Maroon" title="c2">q1</font>, <font color="Maroon" title="c3">q2</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="Red">::  thesis: </font></span></a><span class="hide">  <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">q</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c2">q1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">q</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c3">q2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> <font color="Maroon" title="c2">q1</font>,<font color="Maroon" title="c3">q2</font></span><br/>





<a NAME="E1:25"/>
(  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">q</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c2">q1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">q1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c1">q</font> &amp;  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">q</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c3">q2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c1">q</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T48" title="EUCLID:th.48">EUCLID:48</a></span>;<br/>
<span class="kw">hence </span> <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">q</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c2">q1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">q</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c3">q2</font></span>)</span> = 
 <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c1">q</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">q2</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c1">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan1k.html#T24" target="_self" title="JORDAN1K:th.24">Th24</a></span>
<br/>.= 
 <a href="topreal6.html#K1" title="TOPREAL6:func.1">dist</a> <font color="Maroon" title="c2">q1</font>,<font color="Maroon" title="c3">q2</font>
<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 class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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