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<b>let </b><font color="Maroon" title="c1">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">N</font> being <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/> for <font color="Olive" title="b2">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">IL</font>,<font color="Olive" title="b1">N</font></span>)</span><br/> for <font color="Olive" title="b3">i</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">IL</font>,<font color="Olive" title="b1">N</font></span>)</span> holds   <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b3">i</font>,<font color="Olive" title="b2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font></span><br/><b>let </b><font color="Maroon" title="c2">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">IL</font>,<font color="Maroon" title="c2">N</font></span>)</span><br/> for <font color="Olive" title="b2">i</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">IL</font>,<font color="Maroon" title="c2">N</font></span>)</span> holds   <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b2">i</font>,<font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font></span><br/>



<b>set </b><font color="Maroon" title="c3">T</font> =  <a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">IL</font>,<font color="Maroon" title="c2">N</font>;<br/>
<b>let </b><font color="Maroon" title="c4">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">IL</font>,<font color="Maroon" title="c2">N</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">i</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">IL</font>,<font color="Maroon" title="c2">N</font></span>)</span> holds   <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b1">i</font>,<font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font></span><br/><b>let </b><font color="Maroon" title="c5">i</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">IL</font>,<font color="Maroon" title="c2">N</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font></span><br/>



<b>set </b><font color="Maroon" title="c6">f</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">IL</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">IL</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c1">IL</font></span>)</span>;<br/>
<a NAME="E1:27"/><i><font color="Green" title="E12">A1</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&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> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">IL</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">IL</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c1">IL</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">IL</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p5"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">IL</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c1">IL</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>;<br/>
<a NAME="E2:27"/>
the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">IL</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="ami_1.html#D2" target="_self" title="AMI_1:def.2">Def2</a></i>;<br/>
<a NAME="E3:27"/><b>then </b><i><font color="Green" title="E13">A2</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:27"/><i><font color="Green" title="E14">A3</font></i>: 
 <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">IL</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">IL</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">IL</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c1">IL</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#D2" target="_self" title="AMI_1:def.2">Def2</a></i>;<br/>
<b>thus </b> <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c5">i</font>,<font color="Maroon" title="c4">s</font> = 
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">IL</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p0"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">IL</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c1">IL</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">s</font>
<b>by </b><i><a class="txt" href="ami_1.html#E1:27"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="ami_1.html#E3:27"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="ami_1.html#D2" target="_self" title="AMI_1:def.2">Def2</a></i>
<br/>.= 
<font color="Maroon" title="c4">s</font>
<b>by </b><i><a class="txt" href="ami_1.html#E4:27"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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