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<b>let </b><font color="Maroon" title="c1">N</font> be  <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">IL</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> ;<br/><b>let </b><font color="Maroon" title="c3">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V7" title="AMI_1:attr.7">definite</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c2">IL</font>,<font color="Maroon" title="c1">N</font>;<br/><b>let </b><font color="Maroon" title="c4">f1</font>, <font color="Maroon" title="c5">f2</font> be    <a href="ami_1.html#M6" title="AMI_1:mode.6">IL-Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<font color="Maroon" title="c3">S</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:26"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c4">f1</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>
 <b>and </b><br/><a NAME="E2:26"/><i><font color="Green" title="E12">A2</font></i>: 
for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds <br/> ( <font color="Olive" title="b1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">n</font> iff <font color="Maroon" title="c4">f1</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Olive" title="b1">m</font> <a href="amistd_1.html#R1" title="AMISTD_1:pred.1">&lt;=</a> <font color="Maroon" title="c4">f1</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Olive" title="b2">n</font> )
 <b>and </b><br/><a NAME="E3:26"/><i><font color="Green" title="E13">A3</font></i>: 
<font color="Maroon" title="c5">f2</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>
 <b>and </b><br/><a NAME="E4:26"/><i><font color="Green" title="E14">A4</font></i>: 
for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds <br/> ( <font color="Olive" title="b1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">n</font> iff <font color="Maroon" title="c5">f2</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Olive" title="b1">m</font> <a href="amistd_1.html#R1" title="AMISTD_1:pred.1">&lt;=</a> <font color="Maroon" title="c5">f2</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Olive" title="b2">n</font> )
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <b>means </b><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1;<br/>
<b>assume </b><a NAME="E5:26"/>
<font color="Maroon" title="c4">f1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">f2</font>
 ;<br/>

<a NAME="E6:26"/><b>then </b>
 ex <font color="Olive" title="b1">c</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">c</font>]
 
<b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>
<a NAME="E7:26"/><b>then </b><i><font color="Green" title="E15">A5</font></i>: 
 ex <font color="Olive" title="b1">c</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">c</font>]
 
;<br/>
<b>consider </b><font color="Maroon" title="c6">d</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E9:26"/><i><font color="Green" title="E16">A6</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">d</font>]
 <b>and </b><br/><a NAME="E10:26"/><i><font color="Green" title="E17">A7</font></i>: 
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>] holds <br/><font color="Maroon" title="c6">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font>
 <b>from </b><i><a class="ref" href="nat_1.html#S5" title="NAT_1:sch.5">NAT_1:sch 5</a>(<a class="txt" href="amistd_1.html#E7:26"><i><font color="Green" title="E15">A5</font></i></a>);<br/></i>
<b>reconsider </b><font color="Maroon" title="c7">d</font> = <font color="Maroon" title="c6">d</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E12:26"/>
( <font color="Maroon" title="c4">f1</font> is <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> &amp; <font color="Maroon" title="c5">f2</font> is <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> )
 
<b>by </b><i><a class="txt" href="amistd_1.html#E1:26"><i><font color="Green" title="E11">A1</font></i></a>, <a class="txt" href="amistd_1.html#E3:26"><i><font color="Green" title="E13">A3</font></i></a>, <a class="ref" href="funct_2.html#D4" title="FUNCT_2:def.4">FUNCT_2:def 4</a></i>;<br/>
<a NAME="E13:26"/><b>then </b><i><font color="Green" title="E18">A9</font></i>: 
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">IL</font> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c5">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">IL</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c8">d2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E15:26"/><i><font color="Green" title="E19">A10</font></i>: 
( <font color="Maroon" title="c8">d2</font> <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="c5">f2</font> &amp; <font color="Maroon" title="c4">f1</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">d2</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/>
<b>reconsider </b><font color="Maroon" title="c9">d2</font> = <font color="Maroon" title="c8">d2</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="txt" href="amistd_1.html#E15:26"><i><font color="Green" title="E19">A10</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">d1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E18:26"/><i><font color="Green" title="E20">A11</font></i>: 
( <font color="Maroon" title="c10">d1</font> <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="c4">f1</font> &amp; <font color="Maroon" title="c5">f2</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">d1</font> )
 <b>by </b><i><a class="txt" href="amistd_1.html#E13:26"><i><font color="Green" title="E18">A9</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">d1</font> = <font color="Maroon" title="c10">d1</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="txt" href="amistd_1.html#E18:26"><i><font color="Green" title="E20">A11</font></i></a></i>;<br/>
<a NAME="E20:26"/><i><font color="Green" title="E21">A12</font></i>: 
( <font color="Maroon" title="c4">f1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> &amp; <font color="Maroon" title="c5">f2</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> )
 
<b>by </b><i><a class="txt" href="amistd_1.html#E1:26"><i><font color="Green" title="E11">A1</font></i></a>, <a class="txt" href="amistd_1.html#E3:26"><i><font color="Green" title="E13">A3</font></i></a>, <a class="ref" href="funct_2.html#D4" title="FUNCT_2:def.4">FUNCT_2:def 4</a></i>;<br/>
<a NAME="E21:26"/><i><font color="Green" title="E22">A13</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:26_1"/>
( ( <font color="Maroon" title="c11">d1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">d</font> &amp; <font color="Maroon" title="c9">d2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">d</font> ) or ( <font color="Maroon" title="c7">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">d1</font> &amp; <font color="Maroon" title="c9">d2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">d</font> ) or ( <font color="Maroon" title="c11">d1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">d</font> &amp; <font color="Maroon" title="c7">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">d2</font> ) or ( <font color="Maroon" title="c7">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">d1</font> &amp; <font color="Maroon" title="c7">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">d2</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_1"><b>suppose </b></a><a NAME="E1:26_1_1"/><i><font color="Green" title="E23">A14</font></i>: 
( <font color="Maroon" title="c11">d1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">d</font> &amp; <font color="Maroon" title="c9">d2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">d</font> )
 ;<br/><div class="add"><a NAME="E2:26_1_1"/><b>then </b>
<font color="Maroon" title="c5">f2</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Maroon" title="c9">d2</font> <a href="amistd_1.html#R1" title="AMISTD_1:pred.1">&lt;=</a> <font color="Maroon" title="c5">f2</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Maroon" title="c7">d</font>
 <b>by </b><i><a class="txt" href="amistd_1.html#E4:26"><i><font color="Green" title="E14">A4</font></i></a></i>;<br/><a NAME="E3:26_1_1"/><b>then </b>
<font color="Maroon" title="c7">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">d1</font>
 <b>by </b><i><a class="txt" href="amistd_1.html#E2:26"><i><font color="Green" title="E12">A2</font></i></a>, <a class="txt" href="amistd_1.html#E15:26"><i><font color="Green" title="E19">A10</font></i></a>, <a class="txt" href="amistd_1.html#E18:26"><i><font color="Green" title="E20">A11</font></i></a></i>;<br/><b>hence </b><a NAME="E4:26_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="amistd_1.html#E9:26"><i><font color="Green" title="E16">A6</font></i></a>, <a class="txt" href="amistd_1.html#E18:26"><i><font color="Green" title="E20">A11</font></i></a>, <a class="txt" href="amistd_1.html#E1:26_1_1"><i><font color="Green" title="E23">A14</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_2"><b>suppose </b></a><a NAME="E1:26_1_2"/><i><font color="Green" title="E23">A15</font></i>: 
( <font color="Maroon" title="c7">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">d1</font> &amp; <font color="Maroon" title="c9">d2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">d</font> )
 ;<br/><div class="add"><a NAME="E2:26_1_2"/>
<font color="Maroon" title="c5">f2</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Maroon" title="c9">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f1</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Maroon" title="c9">d2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:26_1_2_1"/>
not <font color="Maroon" title="c5">f2</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Maroon" title="c9">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f1</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Maroon" title="c9">d2</font>
 ;<br/>

<a NAME="E2:26_1_2_1"/><b>then </b>
<font color="Maroon" title="c7">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">d2</font>
 
<b>by </b><i><a class="txt" href="amistd_1.html#E10:26"><i><font color="Green" title="E17">A7</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:26_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="amistd_1.html#E9:26"><i><font color="Green" title="E16">A6</font></i></a>, <a class="txt" href="amistd_1.html#E15:26"><i><font color="Green" title="E19">A10</font></i></a>, <a class="txt" href="amistd_1.html#E1:26_1_2"><i><font color="Green" title="E23">A15</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E3:26_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="amistd_1.html#E9:26"><i><font color="Green" title="E16">A6</font></i></a>, <a class="txt" href="amistd_1.html#E15:26"><i><font color="Green" title="E19">A10</font></i></a>, <a class="txt" href="amistd_1.html#E20:26"><i><font color="Green" title="E21">A12</font></i></a>, <a class="txt" href="amistd_1.html#E21:26"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_3"><b>suppose </b></a><a NAME="E1:26_1_3"/><i><font color="Green" title="E23">A16</font></i>: 
( <font color="Maroon" title="c11">d1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">d</font> &amp; <font color="Maroon" title="c7">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">d2</font> )
 ;<br/><div class="add"><a NAME="E2:26_1_3"/>
<font color="Maroon" title="c4">f1</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Maroon" title="c11">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Maroon" title="c11">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:26_1_3_1"/>
not <font color="Maroon" title="c4">f1</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Maroon" title="c11">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Maroon" title="c11">d1</font>
 ;<br/>

<a NAME="E2:26_1_3_1"/><b>then </b>
<font color="Maroon" title="c7">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">d1</font>
 
<b>by </b><i><a class="txt" href="amistd_1.html#E10:26"><i><font color="Green" title="E17">A7</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:26_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="amistd_1.html#E9:26"><i><font color="Green" title="E16">A6</font></i></a>, <a class="txt" href="amistd_1.html#E18:26"><i><font color="Green" title="E20">A11</font></i></a>, <a class="txt" href="amistd_1.html#E1:26_1_3"><i><font color="Green" title="E23">A16</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E3:26_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="amistd_1.html#E9:26"><i><font color="Green" title="E16">A6</font></i></a>, <a class="txt" href="amistd_1.html#E18:26"><i><font color="Green" title="E20">A11</font></i></a>, <a class="txt" href="amistd_1.html#E20:26"><i><font color="Green" title="E21">A12</font></i></a>, <a class="txt" href="amistd_1.html#E21:26"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_4"><b>suppose </b></a><a NAME="E1:26_1_4"/><i><font color="Green" title="E23">A17</font></i>: 
( <font color="Maroon" title="c7">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">d1</font> &amp; <font color="Maroon" title="c7">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">d2</font> )
 ;<br/><div class="add"><a NAME="E2:26_1_4"/><b>then </b>
<font color="Maroon" title="c5">f2</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Maroon" title="c7">d</font> <a href="amistd_1.html#R1" title="AMISTD_1:pred.1">&lt;=</a> <font color="Maroon" title="c5">f2</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Maroon" title="c9">d2</font>
 <b>by </b><i><a class="txt" href="amistd_1.html#E4:26"><i><font color="Green" title="E14">A4</font></i></a></i>;<br/><a NAME="E3:26_1_4"/><b>then </b>
<font color="Maroon" title="c11">d1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">d</font>
 <b>by </b><i><a class="txt" href="amistd_1.html#E2:26"><i><font color="Green" title="E12">A2</font></i></a>, <a class="txt" href="amistd_1.html#E15:26"><i><font color="Green" title="E19">A10</font></i></a>, <a class="txt" href="amistd_1.html#E18:26"><i><font color="Green" title="E20">A11</font></i></a></i>;<br/><b>hence </b><a NAME="E4:26_1_4"/>
contradiction
 <b>by </b><i><a class="txt" href="amistd_1.html#E9:26"><i><font color="Green" title="E16">A6</font></i></a>, <a class="txt" href="amistd_1.html#E18:26"><i><font color="Green" title="E20">A11</font></i></a>, <a class="txt" href="amistd_1.html#E1:26_1_4"><i><font color="Green" title="E23">A17</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
