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<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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">a</font>, <font color="Olive" title="b2">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b3">o</font>, <font color="Olive" title="b4">o'</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="arrow.html#K3" title="ARROW:func.3">LinOrders</a> <font color="Maroon" title="c1">A</font> holds <br/> ( <!--HUMANRECFAILED-->not <!--HUMANRECFAILED-->( ( <font color="Olive" title="b1">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b3">o</font>,<font color="Olive" title="b2">b</font> implies <font color="Olive" title="b1">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b4">o'</font>,<font color="Olive" title="b2">b</font> ) &amp; ( <font color="Olive" title="b1">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b4">o'</font>,<font color="Olive" title="b2">b</font> implies <font color="Olive" title="b1">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b3">o</font>,<font color="Olive" title="b2">b</font> ) &amp; ( <font color="Olive" title="b2">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b3">o</font>,<font color="Olive" title="b1">a</font> implies <font color="Olive" title="b2">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b4">o'</font>,<font color="Olive" title="b1">a</font> ) &amp; ( <font color="Olive" title="b2">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b4">o'</font>,<font color="Olive" title="b1">a</font> implies <font color="Olive" title="b2">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b3">o</font>,<font color="Olive" title="b1">a</font> ) &amp; not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b3">o</font>,<font color="Olive" title="b2">b</font> iff <font color="Olive" title="b1">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b4">o'</font>,<font color="Olive" title="b2">b</font> ) ) &amp; not <!--HUMANRECFAILED-->( ( <font color="Olive" title="b1">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b3">o</font>,<font color="Olive" title="b2">b</font> implies <font color="Olive" title="b1">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b4">o'</font>,<font color="Olive" title="b2">b</font> ) &amp; ( <font color="Olive" title="b1">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b4">o'</font>,<font color="Olive" title="b2">b</font> implies <font color="Olive" title="b1">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b3">o</font>,<font color="Olive" title="b2">b</font> ) &amp; not <!--HUMANRECFAILED-->( ( <font color="Olive" title="b1">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b3">o</font>,<font color="Olive" title="b2">b</font> implies <font color="Olive" title="b1">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b4">o'</font>,<font color="Olive" title="b2">b</font> ) &amp; ( <font color="Olive" title="b1">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b4">o'</font>,<font color="Olive" title="b2">b</font> implies <font color="Olive" title="b1">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b3">o</font>,<font color="Olive" title="b2">b</font> ) &amp; ( <font color="Olive" title="b2">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b3">o</font>,<font color="Olive" title="b1">a</font> implies <font color="Olive" title="b2">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b4">o'</font>,<font color="Olive" title="b1">a</font> ) &amp; ( <font color="Olive" title="b2">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b4">o'</font>,<font color="Olive" title="b1">a</font> implies <font color="Olive" title="b2">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b3">o</font>,<font color="Olive" title="b1">a</font> ) ) ) )</span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</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">o</font>, <font color="Olive" title="b2">o'</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="arrow.html#K3" title="ARROW:func.3">LinOrders</a> <font color="Maroon" title="c1">A</font> holds <br/> ( <!--HUMANRECFAILED-->not <!--HUMANRECFAILED-->( ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b2">o'</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b2">o'</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b2">o'</font>,<font color="Maroon" title="c2">a</font> ) &amp; ( <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b2">o'</font>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c2">a</font> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c3">b</font> iff <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b2">o'</font>,<font color="Maroon" title="c3">b</font> ) ) &amp; not <!--HUMANRECFAILED-->( ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b2">o'</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b2">o'</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c3">b</font> ) &amp; not <!--HUMANRECFAILED-->( ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b2">o'</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b2">o'</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b2">o'</font>,<font color="Maroon" title="c2">a</font> ) &amp; ( <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b2">o'</font>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c2">a</font> ) ) ) )</span><br/><b>let </b><font color="Maroon" title="c4">o</font>, <font color="Maroon" title="c5">o'</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="arrow.html#K3" title="ARROW:func.3">LinOrders</a> <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <!--HUMANRECFAILED-->not <!--HUMANRECFAILED-->( ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c2">a</font> ) &amp; ( <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">a</font> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> iff <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> ) ) &amp; not <!--HUMANRECFAILED-->( ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> ) &amp; not <!--HUMANRECFAILED-->( ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c2">a</font> ) &amp; ( <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">a</font> ) ) ) )</span><br/>







<b>thus </b><a NAME="E1:21"/>
not <!--HUMANRECFAILED-->( ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c2">a</font> ) &amp; ( <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">a</font> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> iff <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <!--HUMANRECFAILED-->( ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> ) &amp; not <!--HUMANRECFAILED-->( ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c2">a</font> ) &amp; ( <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">a</font> ) ) )</span><br/>

<b>assume </b><a NAME="E2:21"/><i><font color="Green" title="E16">A1</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> iff <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</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">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c2">a</font> ) &amp; ( <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">a</font> ) )</span><br/>

<b>hence </b><a NAME="E3:21"/>
( <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c3">b</font> iff <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c3">b</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">a</font> iff <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c2">a</font> )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">a</font> )</span>
<div class="add"><b>assume </b><a NAME="E1:21_1"/>
<font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c2">a</font></span><br/><a NAME="E2:21_1"/><b>then </b>
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c3">b</font> <a href="arrow.html#R1" title="ARROW:pred.1">&lt;=_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">a</font> )
 <b>by </b><i><a class="ref" href="arrow.html#T4" target="_self" title="ARROW:th.4">Th4</a></i>;<br/><b>hence </b><a NAME="E3:21_1"/>
<font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="txt" href="#E2:21"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="arrow.html#T6" target="_self" title="ARROW:th.6">Th6</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>assume </b><a NAME="E5:21"/>
<font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c2">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">a</font></span><br/>

<a NAME="E6:21"/><b>then </b>
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c3">b</font> <a href="arrow.html#R1" title="ARROW:pred.1">&lt;=_</a> <font color="Maroon" title="c5">o'</font>,<font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="ref" href="arrow.html#T4" target="_self" title="ARROW:th.4">Th4</a></i>;<br/>
<b>hence </b><a NAME="E7:21"/>
<font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="txt" href="#E2:21"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="arrow.html#T6" target="_self" title="ARROW:th.6">Th6</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>
