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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">u1</font>, <font color="Olive" title="b4">v1</font>, <font color="Olive" title="b5">w</font>, <font color="Olive" title="b6">y</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> holds <br/> ( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b3">u1</font>,<font color="Olive" title="b4">v1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="geomtrap.html#K5" title="GEOMTRAP:func.5">DTrapezium</a> (<font color="Maroon" title="c1">V</font>,<font color="Olive" title="b5">w</font>,<font color="Olive" title="b6">y</font>) iff <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">u1</font>,<font color="Olive" title="b4">v1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Olive" title="b5">w</font>,<font color="Olive" title="b6">y</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">u</font>, <font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c4">u1</font>, <font color="Maroon" title="c5">v1</font>, <font color="Maroon" title="c6">w</font>, <font color="Maroon" title="c7">y</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="geomtrap.html#K5" title="GEOMTRAP:func.5">DTrapezium</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c7">y</font>) iff <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c7">y</font> )</span><br/>













<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:69_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="geomtrap.html#K5" title="GEOMTRAP:func.5">DTrapezium</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c7">y</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c7">y</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">u9</font>, <font color="Maroon" title="c9">v9</font>, <font color="Maroon" title="c10">u19</font>, <font color="Maroon" title="c11">v19</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E3:69_1"/><span class="lab"><font color="Green" title="E65">A1</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c8">u9</font>,<font color="Maroon" title="c9">v9</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <span class="kw">and </span><br/><a NAME="E4:69_1"/><span class="lab"><font color="Green" title="E66">A2</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c10">u19</font>,<font color="Maroon" title="c11">v19</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <span class="kw">and </span><br/><a NAME="E5:69_1"/><span class="lab"><font color="Green" title="E67">A3</font></span>: 
<font color="Maroon" title="c8">u9</font>,<font color="Maroon" title="c9">v9</font>,<font color="Maroon" title="c10">u19</font>,<font color="Maroon" title="c11">v19</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c7">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="geomtrap.html#D7" target="_self" title="GEOMTRAP:def.7">Def7</a></span>;<br/><a NAME="E6:69_1"/><span class="lab"><font color="Green" title="E68">A4</font></span>: 
<font color="Maroon" title="c4">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">u19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1"><span class="lab"><font color="Green" title="E66">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/><a NAME="E7:69_1"/>
( <font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">u9</font> &amp; <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">v9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1"><span class="lab"><font color="Green" title="E65">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/><span class="kw">hence </span><a NAME="E8:69_1"/>
<font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c7">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1"><span class="lab"><font color="Green" title="E66">A2</font></span></a>, <a class="txt" href="#E5:69_1"><span class="lab"><font color="Green" title="E67">A3</font></span></a>, <a class="txt" href="#E6:69_1"><span class="lab"><font color="Green" title="E68">A4</font></span></a>, <a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:69"/>
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="geomtrap.html#K5" title="GEOMTRAP:func.5">DTrapezium</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c7">y</font>) iff <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">u1</font>,<font color="Maroon" title="c5">v1</font> <a href="geomtrap.html#R2" title="GEOMTRAP:pred.2">are_DTr_wrt</a> <font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c7">y</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="geomtrap.html#D7" target="_self" title="GEOMTRAP:def.7">Def7</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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