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<b>let </b><font color="Maroon" title="c1">AS</font> be   <a href="dirort.html#NM1" title="DIRORT:NM.1">Oriented_Orthogonality_Space</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">AS</font> is <a href="dirort.html#V4" title="DIRORT:attr.4">left_transitive</a> implies <font color="Maroon" title="c1">AS</font> is <a href="dirort.html#V3" title="DIRORT:attr.3">right_transitive</a> )</span><br/>

<a NAME="E1:28"/>
( ( for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">u1</font>, <font color="Olive" title="b3">u2</font>, <font color="Olive" title="b4">v</font>, <font color="Olive" title="b5">v1</font>, <font color="Olive" title="b6">v2</font>, <font color="Olive" title="b7">w</font>, <font color="Olive" title="b8">w1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>  st <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b4">v</font>,<font color="Olive" title="b5">v1</font> &amp; <font color="Olive" title="b4">v</font>,<font color="Olive" title="b5">v1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b7">w</font>,<font color="Olive" title="b8">w1</font> &amp; <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b3">u2</font>,<font color="Olive" title="b6">v2</font> &amp; not <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">u1</font> &amp; not <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">v1</font> holds <br/><font color="Olive" title="b3">u2</font>,<font color="Olive" title="b6">v2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b7">w</font>,<font color="Olive" title="b8">w1</font> ) implies for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">u1</font>, <font color="Olive" title="b3">u2</font>, <font color="Olive" title="b4">v</font>, <font color="Olive" title="b5">v1</font>, <font color="Olive" title="b6">v2</font>, <font color="Olive" title="b7">w</font>, <font color="Olive" title="b8">w1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>  st <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b4">v</font>,<font color="Olive" title="b5">v1</font> &amp; <font color="Olive" title="b4">v</font>,<font color="Olive" title="b5">v1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b7">w</font>,<font color="Olive" title="b8">w1</font> &amp; <font color="Olive" title="b3">u2</font>,<font color="Olive" title="b6">v2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b7">w</font>,<font color="Olive" title="b8">w1</font> &amp; not <font color="Olive" title="b7">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">w1</font> &amp; not <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">v1</font> holds <br/><font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b3">u2</font>,<font color="Olive" title="b6">v2</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:28_1"/><i><font color="Green" title="E16">A1</font></i>: 
for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">u1</font>, <font color="Olive" title="b3">u2</font>, <font color="Olive" title="b4">v</font>, <font color="Olive" title="b5">v1</font>, <font color="Olive" title="b6">v2</font>, <font color="Olive" title="b7">w</font>, <font color="Olive" title="b8">w1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>  st <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b4">v</font>,<font color="Olive" title="b5">v1</font> &amp; <font color="Olive" title="b4">v</font>,<font color="Olive" title="b5">v1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b7">w</font>,<font color="Olive" title="b8">w1</font> &amp; <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b3">u2</font>,<font color="Olive" title="b6">v2</font> &amp; not <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">u1</font> &amp; not <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">v1</font> holds <br/><font color="Olive" title="b3">u2</font>,<font color="Olive" title="b6">v2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b7">w</font>,<font color="Olive" title="b8">w1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">u1</font>, <font color="Olive" title="b3">u2</font>, <font color="Olive" title="b4">v</font>, <font color="Olive" title="b5">v1</font>, <font color="Olive" title="b6">v2</font>, <font color="Olive" title="b7">w</font>, <font color="Olive" title="b8">w1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>  st <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b4">v</font>,<font color="Olive" title="b5">v1</font> &amp; <font color="Olive" title="b4">v</font>,<font color="Olive" title="b5">v1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b7">w</font>,<font color="Olive" title="b8">w1</font> &amp; <font color="Olive" title="b3">u2</font>,<font color="Olive" title="b6">v2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b7">w</font>,<font color="Olive" title="b8">w1</font> &amp; not <font color="Olive" title="b7">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">w1</font> &amp; not <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">v1</font> holds <br/><font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Olive" title="b3">u2</font>,<font color="Olive" title="b6">v2</font></span><br/>

<b>let </b><font color="Maroon" title="c2">u</font>, <font color="Maroon" title="c3">u1</font>, <font color="Maroon" title="c4">u2</font>, <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c6">v1</font>, <font color="Maroon" title="c7">v2</font>, <font color="Maroon" title="c8">w</font>, <font color="Maroon" title="c9">w1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">v1</font> &amp; <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">v1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> &amp; <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> &amp; not <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> &amp; not <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> implies <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )</span><br/>















<b>assume </b><a NAME="E2:28_1"/><i><font color="Green" title="E17">A2</font></i>: 
( <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">v1</font> &amp; <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">v1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> &amp; <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )</span><br/>

<a NAME="E3:28_1"/><i><font color="Green" title="E18">A3</font></i>: 
( ( not <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> &amp; not <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> &amp; not <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> &amp; not <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> ) or <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_1"><b>now </b></a><div class="add"><a NAME="E1:28_1_1_1"/><i><font color="Green" title="E19">A4</font></i>: 
(  not <font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">u1</font> or ( not <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> &amp; not <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> &amp; not <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> &amp; not <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> ) or <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 <b>by </b><i><a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1_1_1_1"/>
<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> &amp; not <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> &amp; not <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> &amp; not <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> ) or <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )</span><br/><a NAME="E2:28_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c9">w1</font>,<font color="Maroon" title="c8">w</font>
 <b>by </b><i><a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>;<br/><a NAME="E3:28_1_1_1_1"/><b>then </b>
( <font color="Maroon" title="c4">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v2</font> or <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E2:28_1"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E4:28_1_1_1_1"/>
( ( not <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> &amp; not <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> &amp; not <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> &amp; not <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> ) or <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E3:28_1_1_1"/>
( ( not <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> &amp; not <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> &amp; not <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> &amp; not <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> ) or <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E1:28_1"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="dirort.html#E2:28_1"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="dirort.html#E1:28_1_1_1"><i><font color="Green" title="E19">A4</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:28_1_1"/>
( ( not <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> &amp; not <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> &amp; not <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> &amp; not <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> ) or <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<div><i><font color="Green" title="E19">A5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1_2"/>
( <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">v1</font> &amp; <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">v1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> &amp; <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )</span><br/><a NAME="E2:28_1_2"/><b>then </b>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E1:28_1"><i><font color="Green" title="E16">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E3:28_1_2"/>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E3:28_1"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E20">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1_3"/>
( <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">v1</font> &amp; <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">v1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> &amp; <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )</span><br/><a NAME="E2:28_1_3"/><b>then </b>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E1:28_1"><i><font color="Green" title="E16">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E3:28_1_3"/>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E3:28_1"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E21">A7</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1_4"/>
( <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">v1</font> &amp; <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">v1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c2">u</font> &amp; <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )</span><br/><a NAME="E2:28_1_4"/><b>then </b>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c2">u</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E1:28_1"><i><font color="Green" title="E16">A1</font></i></a></i>;<br/><a NAME="E3:28_1_4"/><b>then </b>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c2">u</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> or <font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c2">u</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> )
 <b>by </b><i><a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E4:28_1_4"/>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E3:28_1"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E22">A8</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_5"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1_5"/>
( <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">v1</font> &amp; <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">v1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c2">u</font> &amp; <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )</span><br/><a NAME="E2:28_1_5"/><b>then </b>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c2">u</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E1:28_1"><i><font color="Green" title="E16">A1</font></i></a></i>;<br/><a NAME="E3:28_1_5"/><b>then </b>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c2">u</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> or <font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c2">u</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> )
 <b>by </b><i><a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E4:28_1_5"/>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E3:28_1"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E23">A9</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_6"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1_6"/>
( <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c5">v</font> &amp; <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">v1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> &amp; <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )</span><br/><a NAME="E2:28_1_6"/><b>then </b>
( <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c5">v</font> &amp; <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c5">v</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c2">u</font> &amp; <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 <b>by </b><i><a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>;<br/><a NAME="E3:28_1_6"/><b>then </b>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c2">u</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E1:28_1"><i><font color="Green" title="E16">A1</font></i></a></i>;<br/><a NAME="E4:28_1_6"/><b>then </b>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> )
 <b>by </b><i><a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E5:28_1_6"/>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E3:28_1"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E24">A10</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_7"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1_7"/>
( <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c5">v</font> &amp; <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">v1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> &amp; <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )</span><br/><a NAME="E2:28_1_7"/><b>then </b>
( <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c5">v</font> &amp; <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c5">v</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c2">u</font> &amp; <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> )
 <b>by </b><i><a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>;<br/><a NAME="E3:28_1_7"/><b>then </b>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c2">u</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E1:28_1"><i><font color="Green" title="E16">A1</font></i></a></i>;<br/><a NAME="E4:28_1_7"/><b>then </b>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> )
 <b>by </b><i><a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E5:28_1_7"/>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E3:28_1"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E25">A11</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_8"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1_8"/>
( <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c5">v</font> &amp; <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">v1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c2">u</font> &amp; <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )</span><br/><a NAME="E2:28_1_8"/><b>then </b>
( <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c5">v</font> &amp; <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c5">v</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> &amp; <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 <b>by </b><i><a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>;<br/><a NAME="E3:28_1_8"/><b>then </b>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c6">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> or <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E1:28_1"><i><font color="Green" title="E16">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E4:28_1_8"/>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E3:28_1"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_9"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1_9"/>
( <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c5">v</font> &amp; <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">v1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c2">u</font> &amp; <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )</span><br/><a NAME="E2:28_1_9"/><b>then </b>
( <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c5">v</font> &amp; <font color="Maroon" title="c6">v1</font>,<font color="Maroon" title="c5">v</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> &amp; <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> )
 <b>by </b><i><a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>;<br/><a NAME="E3:28_1_9"/><b>then </b>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c4">u2</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E1:28_1"><i><font color="Green" title="E16">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E4:28_1_9"/>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E3:28_1"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:28_1"/>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v1</font> or <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">u1</font> <a href="dirort.html#NR1" title="DIRORT:NR.1">'//'</a> <font color="Maroon" title="c4">u2</font>,<font color="Maroon" title="c7">v2</font> )
 <b>by </b><i><a class="txt" href="dirort.html#E2:28_1"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="dirort.html#E4:28_1"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="dirort.html#E5:28_1"><i><font color="Green" title="E20">A6</font></i></a>, <a class="txt" href="dirort.html#E6:28_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="dirort.html#E7:28_1"><i><font color="Green" title="E22">A8</font></i></a>, <a class="txt" href="dirort.html#E8:28_1"><i><font color="Green" title="E23">A9</font></i></a>, <a class="txt" href="dirort.html#E9:28_1"><i><font color="Green" title="E24">A10</font></i></a>, <a class="txt" href="dirort.html#E10:28_1"><i><font color="Green" title="E25">A11</font></i></a>, <a class="ref" href="dirort.html#D1" target="_self" title="DIRORT:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:28"/>
( <font color="Maroon" title="c1">AS</font> is <a href="dirort.html#V4" title="DIRORT:attr.4">left_transitive</a> implies <font color="Maroon" title="c1">AS</font> is <a href="dirort.html#V3" title="DIRORT:attr.3">right_transitive</a> )
 <b>by </b><i><a class="ref" href="dirort.html#D5" target="_self" title="DIRORT:def.5">Def5</a>, <a class="ref" href="dirort.html#D6" target="_self" title="DIRORT:def.6">Def6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
