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<div class="add">

<b>let </b><font color="Maroon" title="c1">c1</font>, <font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font>, <font color="Maroon" title="c4">x3</font>, <font color="Maroon" title="c5">x4</font>, <font color="Maroon" title="c6">y1</font>, <font color="Maroon" title="c7">y2</font>, <font color="Maroon" title="c8">y3</font>, <font color="Maroon" title="c9">y4</font>, <font color="Maroon" title="c10">c2</font>, <font color="Maroon" title="c11">c3</font>, <font color="Maroon" title="c12">c4</font>, <font color="Maroon" title="c13">c5</font>, <font color="Maroon" title="c14">n1</font>, <font color="Maroon" title="c15">n2</font>, <font color="Maroon" title="c16">n3</font>, <font color="Maroon" title="c17">n4</font>, <font color="Maroon" title="c18">n</font>, <font color="Maroon" title="c19">c5b</font> be    <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"> ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y1</font>,<font color="Maroon" title="c1">c1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">c2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c7">y2</font>,<font color="Maroon" title="c10">c2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">c3</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <font color="Maroon" title="c4">x3</font>,<font color="Maroon" title="c8">y3</font>,<font color="Maroon" title="c11">c3</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">c4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <font color="Maroon" title="c5">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c12">c4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">c5</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">n1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y1</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">n2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c7">y2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">n3</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c4">x3</font>,<font color="Maroon" title="c8">y3</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">n4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c5">x4</font>,<font color="Maroon" title="c9">y4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">n</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K18" title="GATE_1:func.18">AND5</a> <font color="Maroon" title="c1">c1</font>,<font color="Maroon" title="c14">n1</font>,<font color="Maroon" title="c15">n2</font>,<font color="Maroon" title="c16">n3</font>,<font color="Maroon" title="c17">n4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">c5b</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c13">c5</font>,<font color="Maroon" title="c18">n</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c13">c5</font>,<font color="Maroon" title="c18">n</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">c5b</font> ) implies (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">c5</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">c5b</font> ) )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:37"/><i><font color="Green" title="E39">A1</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y1</font>,<font color="Maroon" title="c1">c1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">c2</font> )
 <b>and </b><br/><a NAME="E2:37"/><i><font color="Green" title="E40">A2</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c7">y2</font>,<font color="Maroon" title="c10">c2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">c3</font> )
 <b>and </b><br/><a NAME="E3:37"/><i><font color="Green" title="E41">A3</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <font color="Maroon" title="c4">x3</font>,<font color="Maroon" title="c8">y3</font>,<font color="Maroon" title="c11">c3</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">c4</font> )
 <b>and </b><br/><a NAME="E4:37"/><i><font color="Green" title="E42">A4</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <font color="Maroon" title="c5">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c12">c4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">c5</font> )
 <b>and </b><br/><a NAME="E5:37"/><i><font color="Green" title="E43">A5</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">n1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y1</font> )
 <b>and </b><br/><a NAME="E6:37"/><i><font color="Green" title="E44">A6</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">n2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c7">y2</font> )
 <b>and </b><br/><a NAME="E7:37"/><i><font color="Green" title="E45">A7</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">n3</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c4">x3</font>,<font color="Maroon" title="c8">y3</font> )
 <b>and </b><br/><a NAME="E8:37"/><i><font color="Green" title="E46">A8</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">n4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c5">x4</font>,<font color="Maroon" title="c9">y4</font> )
 <b>and </b><br/><a NAME="E9:37"/><i><font color="Green" title="E47">A9</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">n</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K18" title="GATE_1:func.18">AND5</a> <font color="Maroon" title="c1">c1</font>,<font color="Maroon" title="c14">n1</font>,<font color="Maroon" title="c15">n2</font>,<font color="Maroon" title="c16">n3</font>,<font color="Maroon" title="c17">n4</font> )
 <b>and </b><br/><a NAME="E10:37"/><i><font color="Green" title="E48">A10</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">c5b</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c13">c5</font>,<font color="Maroon" title="c18">n</font> )
 <b>and </b><br/><a NAME="E11:37"/><i><font color="Green" title="E49">A11</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c13">c5</font>,<font color="Maroon" title="c18">n</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">c5b</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">c5</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">c5b</font> )</span><br/>

<b>thus </b><a NAME="E12:37"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">c5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">c5b</font> )
 <b>by </b><i><a class="txt" href="gate_1.html#E11:37"><i><font color="Green" title="E49">A11</font></i></a>, <a class="ref" href="gate_1.html#D3" target="_self" title="GATE_1:def.3">Def3</a>, <a class="ref" href="gate_1.html#T5" target="_self" title="GATE_1:th.5">Th5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">c5b</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">c5</font> )</span><br/>

<b>assume </b><a NAME="E13:37"/>
 <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">c5b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">c5</font></span><br/>

<a NAME="E14:37"/><b>then </b>
 <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c13">c5</font>,<font color="Maroon" title="c18">n</font>
 
<b>by </b><i><a class="txt" href="gate_1.html#E10:37"><i><font color="Green" title="E48">A10</font></i></a></i>;<br/>
<a NAME="E15:37"/><b>then </b><i><font color="Green" title="E50">A12</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">c5</font> or  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">n</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T7" target="_self" title="GATE_1:th.7">Th7</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:37_1"/>
 <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <font color="Maroon" title="c5">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c12">c4</font></span><br/><a NAME="E2:37_1"/><b>then </b>
 <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K18" title="GATE_1:func.18">AND5</a> <font color="Maroon" title="c1">c1</font>,<font color="Maroon" title="c14">n1</font>,<font color="Maroon" title="c15">n2</font>,<font color="Maroon" title="c16">n3</font>,<font color="Maroon" title="c17">n4</font>
 <b>by </b><i><a class="txt" href="gate_1.html#E9:37"><i><font color="Green" title="E47">A9</font></i></a></i>;<br/><a NAME="E3:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c1">c1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">n1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">n2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">n3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">n4</font> )
 <b>by </b><i><a class="ref" href="gate_1.html#D18" target="_self" title="GATE_1:def.18">Def18</a></i>;<br/><a NAME="E4:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c1">c1</font> &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c2">x1</font> or  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">y1</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">n2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">n3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">n4</font> )
 <b>by </b><i><a class="txt" href="gate_1.html#E5:37"><i><font color="Green" title="E43">A5</font></i></a>, <a class="ref" href="gate_1.html#T7" target="_self" title="GATE_1:th.7">Th7</a></i>;<br/><a NAME="E5:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y1</font>,<font color="Maroon" title="c1">c1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">n2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">n3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">n4</font> )
 <b>by </b><i><a class="ref" href="gate_1.html#D11" target="_self" title="GATE_1:def.11">Def11</a>, <a class="ref" href="gate_1.html#T5" target="_self" title="GATE_1:th.5">Th5</a></i>;<br/><a NAME="E6:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">c2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">n2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">n3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">n4</font> )
 <b>by </b><i><a class="txt" href="gate_1.html#E1:37"><i><font color="Green" title="E39">A1</font></i></a></i>;<br/><a NAME="E7:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">c2</font> &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">x2</font> or  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">y2</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">n3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">n4</font> )
 <b>by </b><i><a class="txt" href="gate_1.html#E6:37"><i><font color="Green" title="E44">A6</font></i></a>, <a class="ref" href="gate_1.html#T7" target="_self" title="GATE_1:th.7">Th7</a></i>;<br/><a NAME="E8:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c7">y2</font>,<font color="Maroon" title="c10">c2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">n3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">n4</font> )
 <b>by </b><i><a class="ref" href="gate_1.html#D11" target="_self" title="GATE_1:def.11">Def11</a>, <a class="ref" href="gate_1.html#T5" target="_self" title="GATE_1:th.5">Th5</a></i>;<br/><a NAME="E9:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">c3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">n3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">n4</font> )
 <b>by </b><i><a class="txt" href="gate_1.html#E2:37"><i><font color="Green" title="E40">A2</font></i></a></i>;<br/><a NAME="E10:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">c3</font> &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c4">x3</font> or  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">y3</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">n4</font> )
 <b>by </b><i><a class="txt" href="gate_1.html#E7:37"><i><font color="Green" title="E45">A7</font></i></a>, <a class="ref" href="gate_1.html#T7" target="_self" title="GATE_1:th.7">Th7</a></i>;<br/><a NAME="E11:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">c3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <font color="Maroon" title="c4">x3</font>,<font color="Maroon" title="c8">y3</font>,<font color="Maroon" title="c11">c3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">n4</font> )
 <b>by </b><i><a class="ref" href="gate_1.html#D11" target="_self" title="GATE_1:def.11">Def11</a>, <a class="ref" href="gate_1.html#T5" target="_self" title="GATE_1:th.5">Th5</a></i>;<br/><a NAME="E12:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">c4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">n4</font> )
 <b>by </b><i><a class="txt" href="gate_1.html#E3:37"><i><font color="Green" title="E41">A3</font></i></a></i>;<br/><a NAME="E13:37_1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">c4</font> &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">x4</font> or  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">y4</font> ) )
 <b>by </b><i><a class="txt" href="gate_1.html#E8:37"><i><font color="Green" title="E46">A8</font></i></a>, <a class="ref" href="gate_1.html#T7" target="_self" title="GATE_1:th.7">Th7</a></i>;<br/><b>hence </b><a NAME="E14:37_1"/>
 <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <font color="Maroon" title="c5">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c12">c4</font>
 <b>by </b><i><a class="ref" href="gate_1.html#D11" target="_self" title="GATE_1:def.11">Def11</a>, <a class="ref" href="gate_1.html#T5" target="_self" title="GATE_1:th.5">Th5</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="E17:37"/>
 <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">c5</font>
 <b>by </b><i><a class="txt" href="gate_1.html#E4:37"><i><font color="Green" title="E42">A4</font></i></a>, <a class="txt" href="gate_1.html#E15:37"><i><font color="Green" title="E50">A12</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/>


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