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<b>let </b><font color="Maroon" title="c1">A</font> be   <a href="aofa_000.html#NM1" title="AOFA_000:NM.1">preIfWhileAlgebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font> <a href="aofa_000.html#NR1" title="AOFA_000:NR.1">nin</a>  <a href="aofa_000.html#K18" title="AOFA_000:func.18">ElementaryInstructions</a> <font color="Maroon" title="c1">A</font></span><br/>

<b>set </b><font color="Maroon" title="c2">I</font> =  <a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font>;<br/>
<a NAME="E1:87"/>
 <a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</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="E2:87"/><b>then </b>
 <a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font> <a href="aofa_000.html#NR1" title="AOFA_000:NR.1">nin</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/>
<a NAME="E3:87"/><b>then </b>
 <a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font> <a href="aofa_000.html#NR1" title="AOFA_000:NR.1">nin</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> <span class="p3">(<span class="default"><a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 3,<span class="p4">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">A</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/>
<a NAME="E4:87"/><b>then </b>
 <a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font> <a href="aofa_000.html#NR1" title="AOFA_000:NR.1">nin</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p3">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> <span class="p4">(<span class="default"><a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 3,<span class="p5">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">A</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> <span class="p3">(<span class="default"><a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 4,<span class="p4">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">A</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/>
<b>hence </b><a NAME="E5:87"/>
 <a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font> <a href="aofa_000.html#NR1" title="AOFA_000:NR.1">nin</a>  <a href="aofa_000.html#K18" title="AOFA_000:func.18">ElementaryInstructions</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</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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