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<b>let </b><font color="Maroon">it1</font> be  <a href="ami_1.html#V1">strict</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">N</font>, <font color="Maroon">it2</font> be  <a href="ami_1.html#V1">strict</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">N</font>;<br/>

<b>assume </b><a NAME="E1:32_1_2"/><i><font color="Green">E92</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">it1</font> <a href="hidden.html#R1">=</a> <a href="numbers.html#K5">NAT</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><a href="numbers.html#K5">NAT</a> </span><a href="domain_1.html#K6">}</a></span> &amp; the <a href="ami_1.html#U1">Instruction-Counter</a> of <font color="Maroon">it1</font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a>  &amp; the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">it1</font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a>  &amp; the <a href="ami_1.html#U3">Instruction-Codes</a> of <font color="Maroon">it1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">0,1</span><a href="domain_1.html#K7">}</a></span> &amp; the <a href="ami_1.html#U4">Instructions</a> of <font color="Maroon">it1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span>,<span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K7">}</a></span> &amp; the <a href="ami_1.html#U5">Object-Kind</a> of <font color="Maroon">it1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="pre_circ.html#K2">--&gt;</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default"><span class="p3"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span>,<span class="p3"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K7">}</a></span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span> )
 ;<br/>

<b>given </b><font color="Maroon">f1</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <font color="Maroon">it1</font>, <a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <font color="Maroon">it1</font><b> such that </b><a NAME="E2:32_1_2"/><i><font color="Green">E93</font></i>: 
( ( for <font color="Olive">s</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <font color="Maroon">it1</font> holds  <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <font color="Olive">s</font> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K1">succ</a> <span class="p3">(<span class="default"><font color="Olive">s</font> <a href="funct_1.html#K1">.</a> <a href="numbers.html#K5">NAT</a> </span>)</span></span>)</span></span>)</span> ) &amp; the <a href="ami_1.html#U6">Execution</a> of <font color="Maroon">it1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f1</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <font color="Maroon">it1</font></span>)</span></span>)</span></span>)</span> )
 ;<br/>

<b>assume </b><a NAME="E3:32_1_2"/><i><font color="Green">E94</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">it2</font> <a href="hidden.html#R1">=</a> <a href="numbers.html#K5">NAT</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><a href="numbers.html#K5">NAT</a> </span><a href="domain_1.html#K6">}</a></span> &amp; the <a href="ami_1.html#U1">Instruction-Counter</a> of <font color="Maroon">it2</font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a>  &amp; the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">it2</font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a>  &amp; the <a href="ami_1.html#U3">Instruction-Codes</a> of <font color="Maroon">it2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">0,1</span><a href="domain_1.html#K7">}</a></span> &amp; the <a href="ami_1.html#U4">Instructions</a> of <font color="Maroon">it2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span>,<span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K7">}</a></span> &amp; the <a href="ami_1.html#U5">Object-Kind</a> of <font color="Maroon">it2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="pre_circ.html#K2">--&gt;</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default"><span class="p3"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span>,<span class="p3"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K7">}</a></span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span> )
 ;<br/>

<b>given </b><font color="Maroon">f2</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <font color="Maroon">it2</font>, <a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <font color="Maroon">it2</font><b> such that </b><a NAME="E4:32_1_2"/><i><font color="Green">E105</font></i>: 
( ( for <font color="Olive">s</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <font color="Maroon">it2</font> holds  <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <font color="Olive">s</font> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K1">succ</a> <span class="p3">(<span class="default"><font color="Olive">s</font> <a href="funct_1.html#K1">.</a> <a href="numbers.html#K5">NAT</a> </span>)</span></span>)</span></span>)</span> ) &amp; the <a href="ami_1.html#U6">Execution</a> of <font color="Maroon">it2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f2</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <font color="Maroon">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">c</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <font color="Maroon">it1</font>;<br/><b>thus </b><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">c</font> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K1">succ</a> <span class="p3">(<span class="default"><font color="Maroon">c</font> <a href="funct_1.html#K1">.</a> <a href="numbers.html#K5">NAT</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font>
<b>by </b><i>, , </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:32_1_2"/>
<font color="Maroon">it1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">it2</font>
 <b>by </b><i>, , , , <a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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