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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>] or <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>] or <font color="Maroon">P<sub>3</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>] );<br/>
<b>consider </b><font color="Maroon" title="c1">L</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E2:22_1"/><i><font color="Green" title="E8">A5</font></i>: 
for <font color="Olive" title="b1">z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">L</font> iff ( <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>()</span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">z</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1" title="XBOOLE_0:sch.1">XBOOLE_0:sch 1</a>();<br/></i>
<a NAME="E3:22_1"/><i><font color="Green" title="E9">A6</font></i>: 
<font color="Maroon" title="c1">L</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>()</span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:22_1_1"/>
<font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">L</font>
 ;<br/>

<b>hence </b><a NAME="E2:22_1_1"/>
<font color="Maroon" title="c2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>()</span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="scheme1.html#E2:22_1"><i><font color="Green" title="E8">A5</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/>( ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>] implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>) ) &amp; ( <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>] implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>5</sub></font>(<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>) ) &amp; ( <font color="Maroon">P<sub>3</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>] implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>6</sub></font>(<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>) ) );<br/>
<a NAME="E4:22_1"/><i><font color="Green" title="E10">A7</font></i>: 
for <font color="Olive" title="b1">x1</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">L</font> holds <br/> ex <font color="Olive" title="b2">z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">z</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">x1</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:22_1_2"/><i><font color="Green" title="E11">A8</font></i>: 
<font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">L</font>
 ;<br/>

<a NAME="E2:22_1_2"/><b>then </b>
<font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>()</span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="txt" href="scheme1.html#E2:22_1"><i><font color="Green" title="E8">A5</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">z'</font>, <font color="Maroon" title="c4">a'</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:22_1_2"/><i><font color="Green" title="E12">A9</font></i>: 
( <font color="Maroon" title="c3">z'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon" title="c4">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">z'</font>,<font color="Maroon" title="c4">a'</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_2_1_1"/>
( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c3">z'</font>,<font color="Maroon" title="c4">a'</font>] or <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c3">z'</font>,<font color="Maroon" title="c4">a'</font>] or <font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c3">z'</font>,<font color="Maroon" title="c4">a'</font>] )
 </span><b>by </b><i><a class="txt" href="scheme1.html#E2:22_1"><i><font color="Green" title="E8">A5</font></i></a>, <a class="txt" href="scheme1.html#E1:22_1_2"><i><font color="Green" title="E11">A8</font></i></a>, <a class="txt" href="scheme1.html#E4:22_1_2"><i><font color="Green" title="E12">A9</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:22_1_2_1_1_1"/><i><font color="Green" title="E13">A10</font></i>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c3">z'</font>,<font color="Maroon" title="c4">a'</font>]
 ;<br/><div class="add"><b>take </b><font color="Maroon" title="c5">z</font> = <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon" title="c3">z'</font>,<font color="Maroon" title="c4">a'</font>);<br/><b>let </b><font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c7">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E2:22_1_2_1_1_1"/>
<font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/><a NAME="E3:22_1_2_1_1_1"/><b>then </b>
( <font color="Maroon" title="c3">z'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> &amp; <font color="Maroon" title="c4">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">y</font> )
 <b>by </b><i><a class="txt" href="scheme1.html#E4:22_1_2"><i><font color="Green" title="E12">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><b>hence </b><a NAME="E4:22_1_2_1_1_1"/>
( ( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>] implies <font color="Maroon" title="c5">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>) ) &amp; ( <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>] implies <font color="Maroon" title="c5">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>5</sub></font>(<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>) ) &amp; ( <font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>] implies <font color="Maroon" title="c5">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>6</sub></font>(<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>) ) )
 <b>by </b><i><a class="txt" href="scheme1.html#E1:22"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="scheme1.html#E4:22_1_2"><i><font color="Green" title="E12">A9</font></i></a>, <a class="txt" href="scheme1.html#E1:22_1_2_1_1_1"><i><font color="Green" title="E13">A10</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:22_1_2_1_1_2"/><i><font color="Green" title="E13">A11</font></i>: 
<font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c3">z'</font>,<font color="Maroon" title="c4">a'</font>]
 ;<br/><div class="add"><b>take </b><font color="Maroon" title="c5">z</font> = <font color="Maroon">F<sub>5</sub></font>(<font color="Maroon" title="c3">z'</font>,<font color="Maroon" title="c4">a'</font>);<br/><b>let </b><font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c7">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E2:22_1_2_1_1_2"/>
<font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/><a NAME="E3:22_1_2_1_1_2"/><b>then </b>
( <font color="Maroon" title="c3">z'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> &amp; <font color="Maroon" title="c4">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">y</font> )
 <b>by </b><i><a class="txt" href="scheme1.html#E4:22_1_2"><i><font color="Green" title="E12">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><b>hence </b><a NAME="E4:22_1_2_1_1_2"/>
( ( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>] implies <font color="Maroon" title="c5">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>) ) &amp; ( <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>] implies <font color="Maroon" title="c5">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>5</sub></font>(<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>) ) &amp; ( <font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>] implies <font color="Maroon" title="c5">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>6</sub></font>(<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>) ) )
 <b>by </b><i><a class="txt" href="scheme1.html#E1:22"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="scheme1.html#E4:22_1_2"><i><font color="Green" title="E12">A9</font></i></a>, <a class="txt" href="scheme1.html#E1:22_1_2_1_1_2"><i><font color="Green" title="E13">A11</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_2_1_1_3"><b>suppose </b></a><a NAME="E1:22_1_2_1_1_3"/><i><font color="Green" title="E13">A12</font></i>: 
<font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c3">z'</font>,<font color="Maroon" title="c4">a'</font>]
 ;<br/><div class="add"><b>take </b><font color="Maroon" title="c5">z</font> = <font color="Maroon">F<sub>6</sub></font>(<font color="Maroon" title="c3">z'</font>,<font color="Maroon" title="c4">a'</font>);<br/><b>let </b><font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c7">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E2:22_1_2_1_1_3"/>
<font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/><a NAME="E3:22_1_2_1_1_3"/><b>then </b>
( <font color="Maroon" title="c3">z'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> &amp; <font color="Maroon" title="c4">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">y</font> )
 <b>by </b><i><a class="txt" href="scheme1.html#E4:22_1_2"><i><font color="Green" title="E12">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><b>hence </b><a NAME="E4:22_1_2_1_1_3"/>
( ( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>] implies <font color="Maroon" title="c5">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>) ) &amp; ( <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>] implies <font color="Maroon" title="c5">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>5</sub></font>(<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>) ) &amp; ( <font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>] implies <font color="Maroon" title="c5">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>6</sub></font>(<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>) ) )
 <b>by </b><i><a class="txt" href="scheme1.html#E1:22"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="scheme1.html#E4:22_1_2"><i><font color="Green" title="E12">A9</font></i></a>, <a class="txt" href="scheme1.html#E1:22_1_2_1_1_3"><i><font color="Green" title="E13">A12</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E6:22_1_2"/>
 ex <font color="Olive" title="b1">z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Maroon">S<sub>2</sub></font>[<font color="Maroon" title="c2">x1</font>,<font color="Olive" title="b1">z</font>]
 ;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c2">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E6:22_1"/><i><font color="Green" title="E11">A13</font></i>: 
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">L</font> &amp; ( for <font color="Olive" title="b1">z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">L</font> holds <br/><font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">z</font>,<font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">z</font>] ) )
 <b>from </b><i><a class="ref" href="classes1.html#S1" title="CLASSES1:sch.1">CLASSES1:sch 1</a>(<a class="txt" href="scheme1.html#E4:22_1"><i><font color="Green" title="E10">A7</font></i></a>);<br/></i>
<a NAME="E7:22_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon">F<sub>3</sub></font>()
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:22_1_3"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">f</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">x1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:22_1_3"/><i><font color="Green" title="E12">A14</font></i>: 
( <font color="Maroon" title="c4">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">f</font> &amp; <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x1</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E4:22_1_3"/>
<font color="Maroon" title="c4">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>()</span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="txt" href="scheme1.html#E2:22_1"><i><font color="Green" title="E8">A5</font></i></a>, <a class="txt" href="scheme1.html#E6:22_1"><i><font color="Green" title="E11">A13</font></i></a>, <a class="txt" href="scheme1.html#E3:22_1_3"><i><font color="Green" title="E12">A14</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:22_1_3"/><i><font color="Green" title="E13">A15</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Maroon" title="c4">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_3_1_1"/>
( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>] or <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>] or <font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>] )
 </span><b>by </b><i><a class="txt" href="scheme1.html#E2:22_1"><i><font color="Green" title="E8">A5</font></i></a>, <a class="txt" href="scheme1.html#E6:22_1"><i><font color="Green" title="E11">A13</font></i></a>, <a class="txt" href="scheme1.html#E3:22_1_3"><i><font color="Green" title="E12">A14</font></i></a>, <a class="txt" href="scheme1.html#E6:22_1_3"><i><font color="Green" title="E13">A15</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:22_1_3_1_1_1"/><i><font color="Green" title="E14">A16</font></i>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>]
 ;<br/><div class="add"><a NAME="E2:22_1_3_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>)
 <b>by </b><i><a class="txt" href="scheme1.html#E6:22_1"><i><font color="Green" title="E11">A13</font></i></a>, <a class="txt" href="scheme1.html#E3:22_1_3"><i><font color="Green" title="E12">A14</font></i></a>, <a class="txt" href="scheme1.html#E6:22_1_3"><i><font color="Green" title="E13">A15</font></i></a></i>;<br/><b>hence </b><a NAME="E3:22_1_3_1_1_1"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>3</sub></font>()
 <b>by </b><i><a class="txt" href="scheme1.html#E2:22"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="scheme1.html#E3:22_1_3"><i><font color="Green" title="E12">A14</font></i></a>, <a class="txt" href="scheme1.html#E6:22_1_3"><i><font color="Green" title="E13">A15</font></i></a>, <a class="txt" href="scheme1.html#E1:22_1_3_1_1_1"><i><font color="Green" title="E14">A16</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:22_1_3_1_1_2"/><i><font color="Green" title="E14">A17</font></i>: 
<font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>]
 ;<br/><div class="add"><a NAME="E2:22_1_3_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>5</sub></font>(<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>)
 <b>by </b><i><a class="txt" href="scheme1.html#E6:22_1"><i><font color="Green" title="E11">A13</font></i></a>, <a class="txt" href="scheme1.html#E3:22_1_3"><i><font color="Green" title="E12">A14</font></i></a>, <a class="txt" href="scheme1.html#E6:22_1_3"><i><font color="Green" title="E13">A15</font></i></a></i>;<br/><b>hence </b><a NAME="E3:22_1_3_1_1_2"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>3</sub></font>()
 <b>by </b><i><a class="txt" href="scheme1.html#E3:22"><i><font color="Green" title="E6">A3</font></i></a>, <a class="txt" href="scheme1.html#E3:22_1_3"><i><font color="Green" title="E12">A14</font></i></a>, <a class="txt" href="scheme1.html#E6:22_1_3"><i><font color="Green" title="E13">A15</font></i></a>, <a class="txt" href="scheme1.html#E1:22_1_3_1_1_2"><i><font color="Green" title="E14">A17</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_3_1_1_3"><b>suppose </b></a><a NAME="E1:22_1_3_1_1_3"/><i><font color="Green" title="E14">A18</font></i>: 
<font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>]
 ;<br/><div class="add"><a NAME="E2:22_1_3_1_1_3"/><b>then </b>
<font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>6</sub></font>(<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>)
 <b>by </b><i><a class="txt" href="scheme1.html#E6:22_1"><i><font color="Green" title="E11">A13</font></i></a>, <a class="txt" href="scheme1.html#E3:22_1_3"><i><font color="Green" title="E12">A14</font></i></a>, <a class="txt" href="scheme1.html#E6:22_1_3"><i><font color="Green" title="E13">A15</font></i></a></i>;<br/><b>hence </b><a NAME="E3:22_1_3_1_1_3"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>3</sub></font>()
 <b>by </b><i><a class="txt" href="scheme1.html#E4:22"><i><font color="Green" title="E7">A4</font></i></a>, <a class="txt" href="scheme1.html#E3:22_1_3"><i><font color="Green" title="E12">A14</font></i></a>, <a class="txt" href="scheme1.html#E6:22_1_3"><i><font color="Green" title="E13">A15</font></i></a>, <a class="txt" href="scheme1.html#E1:22_1_3_1_1_3"><i><font color="Green" title="E14">A18</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E8:22_1_3"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>3</sub></font>()
 ;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c3">f</font> = <font color="Maroon" title="c2">f</font> as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>()</span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon">F<sub>3</sub></font>() <b>by </b><i><a class="txt" href="scheme1.html#E3:22_1"><i><font color="Green" title="E9">A6</font></i></a>, <a class="txt" href="scheme1.html#E6:22_1"><i><font color="Green" title="E11">A13</font></i></a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">f</font>
;<br/>

<b>thus </b><a NAME="E9:22_1"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font> iff ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>2</sub></font>() &amp; ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>] or <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>] or <font color="Maroon">P<sub>3</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>] ) ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>



<b>thus </b><a NAME="E1:22_1_4"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font> implies ( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>2</sub></font>() &amp; ( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>] or <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>] or <font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>] ) ) )
 <b>by </b><i><a class="txt" href="scheme1.html#E2:22_1"><i><font color="Green" title="E8">A5</font></i></a>, <a class="txt" href="scheme1.html#E6:22_1"><i><font color="Green" title="E11">A13</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>

<b>assume </b><a NAME="E2:22_1_4"/><i><font color="Green" title="E12">A19</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>2</sub></font>() &amp; ( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>] or <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>] or <font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>] ) )
 ;<br/>

<a NAME="E3:22_1_4"/><b>then </b><i><font color="Green" title="E13">A20</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>()</span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">f'</font>, <font color="Maroon" title="c7">r'</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_4_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">f'</font>,<font color="Maroon" title="c7">r'</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/><a NAME="E2:22_1_4_1"/><b>then </b>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f'</font> &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">r'</font> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><b>hence </b><a NAME="E3:22_1_4_1"/>
( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c6">f'</font>,<font color="Maroon" title="c7">r'</font>] or <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c6">f'</font>,<font color="Maroon" title="c7">r'</font>] or <font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c6">f'</font>,<font color="Maroon" title="c7">r'</font>] )
 <b>by </b><i><a class="txt" href="scheme1.html#E2:22_1_4"><i><font color="Green" title="E12">A19</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:22_1_4"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font>
 <b>by </b><i><a class="txt" href="scheme1.html#E2:22_1"><i><font color="Green" title="E8">A5</font></i></a>, <a class="txt" href="scheme1.html#E6:22_1"><i><font color="Green" title="E11">A13</font></i></a>, <a class="txt" href="scheme1.html#E3:22_1_4"><i><font color="Green" title="E13">A20</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>



<b>assume </b><a NAME="E10:22_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font>
 ;<br/>

<b>hence </b><a NAME="E11:22_1"/>
( ( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>] implies <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>) ) &amp; ( <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>] implies <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>5</sub></font>(<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>) ) &amp; ( <font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>] implies <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>6</sub></font>(<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>) ) )
 <b>by </b><i><a class="txt" href="scheme1.html#E6:22_1"><i><font color="Green" title="E11">A13</font></i></a></i>;<br/>


</div>
