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<b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="setfam_1.html#V1">with_non-empty_elements</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a> non <a href="ami_1.html#V2">void</a> <a href="ami_1.html#V5">IC-Ins-separated</a> <a href="ami_1.html#V8">definite</a> <a href="amistd_1.html#V4" target="_self">standard</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>





<b>assume </b><a NAME="E1:48"/><i><font color="Green">E25</font></i>: 
 <a href="amistd_1.html#K5" target="_self">il.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5" target="_self">il.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:48"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> is   <a href="nat_1.html#NM1">Nat</a> &amp; <font color="Maroon">c<sub>5</sub></font> is   <a href="nat_1.html#NM1">Nat</a> )
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E4:48"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> is <a href="funct_2.html#V3">bijective</a> &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>2</sub></font> iff <font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="amistd_1.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> ) ) &amp;  <a href="amistd_1.html#K5" target="_self">il.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="amistd_1.html#D12" target="_self">Def12</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E6:48"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> is <a href="funct_2.html#V3">bijective</a> &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>2</sub></font> iff <font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="amistd_1.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> ) ) &amp;  <a href="amistd_1.html#K5" target="_self">il.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="ref" href="amistd_1.html#D12" target="_self">Def12</a></i>;<br/>
<a NAME="E7:48"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="amistd_1.html#E4:48"><i><font color="Green">E27</font></i></a>, <a class="txt" href="amistd_1.html#E6:48"><i><font color="Green">E28</font></i></a>, <a class="ref" href="amistd_1.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E8:48"/>
( <font color="Maroon">c<sub>6</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a>  )
 
<b>by </b><i><a class="txt" href="amistd_1.html#E4:48"><i><font color="Green">E27</font></i></a>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="funct_2.html#D4">FUNCT_2:def 4</a></i>;<br/>
<b>hence </b><a NAME="E9:48"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="amistd_1.html#E1:48"><i><font color="Green">E25</font></i></a>, <a class="txt" href="amistd_1.html#E2:48"><i><font color="Green">E26</font></i></a>, <a class="txt" href="amistd_1.html#E4:48"><i><font color="Green">E27</font></i></a>, <a class="txt" href="amistd_1.html#E6:48"><i><font color="Green">E28</font></i></a>, <a class="txt" href="amistd_1.html#E7:48"><i><font color="Green">E29</font></i></a>, <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>


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