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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"> for <font color="Olive" title="b1">I1</font>, <font color="Olive" title="b2">I2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b1">I1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Olive" title="b2">I2</font> &amp; <font color="Olive" title="b2">I2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Olive" title="b2">I2</font> holds <br/><font color="Olive" title="b1">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Olive" title="b2">I2</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>let </b><font color="Maroon" title="c2">I1</font>, <font color="Maroon" title="c3">I2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">I1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c3">I2</font> &amp; <font color="Maroon" title="c3">I2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c3">I2</font> implies <font color="Maroon" title="c2">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c3">I2</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>assume </b><a NAME="E1:88"/>
( <font color="Maroon" title="c2">I1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c3">I2</font> &amp; <font color="Maroon" title="c3">I2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c3">I2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c3">I2</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/>

<a NAME="E2:88"/><b>then </b>
<font color="Maroon" title="c2">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c3">I2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">J1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Olive" title="b2">J2</font></span>)</span> where <font color="Olive" title="b1">J1</font>, <font color="Olive" title="b2">J2</font> is   <a href="aofa_000.html#NM2" title="AOFA_000:NM.2">Algorithm</a> of <font color="Maroon" title="c1">A</font> : ( <font color="Olive" title="b1">J1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">J1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Olive" title="b2">J2</font> &amp; <font color="Olive" title="b2">J2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">J1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Olive" title="b2">J2</font> ) </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E3:88"/>
<font color="Maroon" title="c2">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c3">I2</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#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</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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