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<b>let </b><font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c11">b</font>, <font color="Maroon" title="c12">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">A</font>;<br/>

<a NAME="E1:11"/><i><font color="Green" title="E21">A1</font></i>: 
( <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 or <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 )
 
<b>by </b><i><a class="txt" href="realset2.html#E11"><i><font color="Green" title="E2">Lm2</font></i></a>, <a class="ref" href="card_1.html#T88" title="CARD_1:th.88">CARD_1:88</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E2:11"/><i><font color="Green" title="E22">A2</font></i>: 
( <font color="Maroon" title="c11">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 or <font color="Maroon" title="c11">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 )
 
<b>by </b><i><a class="txt" href="realset2.html#E11"><i><font color="Green" title="E2">Lm2</font></i></a>, <a class="ref" href="card_1.html#T88" title="CARD_1:th.88">CARD_1:88</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E3:11"/><i><font color="Green" title="E23">A3</font></i>: 
( <font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 or <font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 )
 
<b>by </b><i><a class="txt" href="realset2.html#E11"><i><font color="Green" title="E2">Lm2</font></i></a>, <a class="ref" href="card_1.html#T88" title="CARD_1:th.88">CARD_1:88</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:11_1"/>
( <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 or <font color="Maroon" title="c11">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 or <font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 or ( <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 &amp; <font color="Maroon" title="c11">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 &amp; <font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 ) )
 </span><b>by </b><i><a class="txt" href="realset2.html#E11"><i><font color="Green" title="E2">Lm2</font></i></a>, <a class="ref" href="card_1.html#T88" title="CARD_1:th.88">CARD_1:88</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_1"><b>suppose </b></a><a NAME="E1:11_1_1"/>
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2
 ;<br/><div class="add"><b>hence </b><a NAME="E2:11_1_1"/>
<a href="realset2.html#K1" title="REALSET2:func.1">add_2</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><a href="realset2.html#K1" title="REALSET2:func.1">add_2</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font></span>)</span>,<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="realset2.html#K1" title="REALSET2:func.1">add_2</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">a</font>,<span class="p1">(<span class="default"><a href="realset2.html#K1" title="REALSET2:func.1">add_2</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c11">b</font>,<font color="Maroon" title="c12">d</font></span>)</span>
 <b>by </b><i><a class="txt" href="realset2.html#E2:11"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="realset2.html#E3:11"><i><font color="Green" title="E23">A3</font></i></a>, <a class="txt" href="realset2.html#E17"><i><font color="Green" title="E6">Lm6</font></i></a>, <a class="txt" href="realset2.html#E18"><i><font color="Green" title="E7">Lm7</font></i></a>, <a class="txt" href="realset2.html#E19"><i><font color="Green" title="E8">Lm8</font></i></a>, <a class="txt" href="realset2.html#E20"><i><font color="Green" title="E9">Lm9</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_2"><b>suppose </b></a><a NAME="E1:11_1_2"/>
<font color="Maroon" title="c11">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2
 ;<br/><div class="add"><b>hence </b><a NAME="E2:11_1_2"/>
<a href="realset2.html#K1" title="REALSET2:func.1">add_2</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><a href="realset2.html#K1" title="REALSET2:func.1">add_2</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font></span>)</span>,<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="realset2.html#K1" title="REALSET2:func.1">add_2</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">a</font>,<span class="p1">(<span class="default"><a href="realset2.html#K1" title="REALSET2:func.1">add_2</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c11">b</font>,<font color="Maroon" title="c12">d</font></span>)</span>
 <b>by </b><i><a class="txt" href="realset2.html#E1:11"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="realset2.html#E3:11"><i><font color="Green" title="E23">A3</font></i></a>, <a class="txt" href="realset2.html#E17"><i><font color="Green" title="E6">Lm6</font></i></a>, <a class="txt" href="realset2.html#E18"><i><font color="Green" title="E7">Lm7</font></i></a>, <a class="txt" href="realset2.html#E19"><i><font color="Green" title="E8">Lm8</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_3"><b>suppose </b></a><a NAME="E1:11_1_3"/>
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2
 ;<br/><div class="add"><b>hence </b><a NAME="E2:11_1_3"/>
<a href="realset2.html#K1" title="REALSET2:func.1">add_2</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><a href="realset2.html#K1" title="REALSET2:func.1">add_2</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font></span>)</span>,<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="realset2.html#K1" title="REALSET2:func.1">add_2</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">a</font>,<span class="p1">(<span class="default"><a href="realset2.html#K1" title="REALSET2:func.1">add_2</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c11">b</font>,<font color="Maroon" title="c12">d</font></span>)</span>
 <b>by </b><i><a class="txt" href="realset2.html#E1:11"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="realset2.html#E2:11"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="realset2.html#E17"><i><font color="Green" title="E6">Lm6</font></i></a>, <a class="txt" href="realset2.html#E18"><i><font color="Green" title="E7">Lm7</font></i></a>, <a class="txt" href="realset2.html#E19"><i><font color="Green" title="E8">Lm8</font></i></a>, <a class="txt" href="realset2.html#E20"><i><font color="Green" title="E9">Lm9</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_4"><b>suppose </b></a><a NAME="E1:11_1_4"/>
( <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 &amp; <font color="Maroon" title="c11">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 &amp; <font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:11_1_4"/>
<a href="realset2.html#K1" title="REALSET2:func.1">add_2</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><a href="realset2.html#K1" title="REALSET2:func.1">add_2</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font></span>)</span>,<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="realset2.html#K1" title="REALSET2:func.1">add_2</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">a</font>,<span class="p1">(<span class="default"><a href="realset2.html#K1" title="REALSET2:func.1">add_2</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c11">b</font>,<font color="Maroon" title="c12">d</font></span>)</span>
 <b>by </b><i><a class="txt" href="realset2.html#E18"><i><font color="Green" title="E7">Lm7</font></i></a>, <a class="txt" href="realset2.html#E19"><i><font color="Green" title="E8">Lm8</font></i></a>, <a class="txt" href="realset2.html#E20"><i><font color="Green" title="E9">Lm9</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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