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<b>let </b><font color="Maroon" title="c3">it1</font>, <font color="Maroon" title="c4">it2</font> be  <a href="ami_1.html#V1" title="AMI_1:attr.1">strict</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c2">N</font>;<br/>

<b>assume </b><a NAME="E1:32_1_2"/><i><font color="Green" title="E15">A20</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; the <a href="ami_1.html#U1" title="AMI_1:sel.1">Instruction-Counter</a> of <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp; the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp; the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instruction-Codes</a> of <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> &amp; the <a href="ami_1.html#U4" title="AMI_1:sel.4">Instructions</a> of <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">0,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> &amp; the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p2"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">0,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> )
 ;<br/>

<b>given </b><font color="Maroon" title="c5">f1</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <font color="Maroon" title="c3">it1</font>, <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <font color="Maroon" title="c3">it1</font><b> such that </b><a NAME="E2:32_1_2"/><i><font color="Green" title="E16">A21</font></i>: 
( ( for <font color="Olive" title="b1">s</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <font color="Maroon" title="c3">it1</font> holds  <font color="Maroon" title="c5">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span></span>)</span></span>)</span> ) &amp; the <a href="ami_1.html#U6" title="AMI_1:sel.6">Execution</a> of <font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c5">f1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">0,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <font color="Maroon" title="c3">it1</font></span>)</span></span>)</span></span>)</span> )
 ;<br/>

<b>assume </b><a NAME="E3:32_1_2"/><i><font color="Green" title="E17">A22</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; the <a href="ami_1.html#U1" title="AMI_1:sel.1">Instruction-Counter</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp; the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp; the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instruction-Codes</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> &amp; the <a href="ami_1.html#U4" title="AMI_1:sel.4">Instructions</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">0,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> &amp; the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p2"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">0,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> )
 ;<br/>

<b>given </b><font color="Maroon" title="c6">f2</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <font color="Maroon" title="c4">it2</font>, <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <font color="Maroon" title="c4">it2</font><b> such that </b><a NAME="E4:32_1_2"/><i><font color="Green" title="E18">A23</font></i>: 
( ( for <font color="Olive" title="b1">s</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <font color="Maroon" title="c4">it2</font> holds  <font color="Maroon" title="c6">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span></span>)</span></span>)</span> ) &amp; the <a href="ami_1.html#U6" title="AMI_1:sel.6">Execution</a> of <font color="Maroon" title="c4">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c6">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">0,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <font color="Maroon" title="c4">it2</font></span>)</span></span>)</span></span>)</span> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">c</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U5" title="AMI_1:sel.5">Object-Kind</a> of <font color="Maroon" title="c3">it1</font>;<br/><b>thus </b><font color="Maroon" title="c5">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">c</font> = 
<font color="Maroon" title="c7">c</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">c</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_1.html#E2:32_1_2"><i><font color="Green" title="E16">A21</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c6">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">c</font>
<b>by </b><i><a class="txt" href="amistd_1.html#E1:32_1_2"><i><font color="Green" title="E15">A20</font></i></a>, <a class="txt" href="amistd_1.html#E3:32_1_2"><i><font color="Green" title="E17">A22</font></i></a>, <a class="txt" href="amistd_1.html#E4:32_1_2"><i><font color="Green" title="E18">A23</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:32_1_2"/>
<font color="Maroon" title="c3">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">it2</font>
 <b>by </b><i><a class="txt" href="amistd_1.html#E1:32_1_2"><i><font color="Green" title="E15">A20</font></i></a>, <a class="txt" href="amistd_1.html#E2:32_1_2"><i><font color="Green" title="E16">A21</font></i></a>, <a class="txt" href="amistd_1.html#E3:32_1_2"><i><font color="Green" title="E17">A22</font></i></a>, <a class="txt" href="amistd_1.html#E4:32_1_2"><i><font color="Green" title="E18">A23</font></i></a>, <a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


</div>
